**3. Discussion**

In this study we demonstrated that YP, a meroterpenoid isolated from the brown alga *C. usneoides* [26], is able to decrease inflammation, cell differentiation and extracellular matrix (ECM) degradation in different osteoarthritis in vitro/ex vivo OA model systems. By using a pipeline with increasing complexity, from 2D monolayer cultures of THP-1 macrophages, primary chondrocytes and synoviocytes, to ex vivo culture of human cartilage explants and a newly developed OA explant-based co-culture model, YP consistently promoted a protective effect under pro-inflammatory and mineralizing stimuli. These results bring new evidences on the health benefits of YP as a protective OA agent by attenuating cartilage degrading processes under known OA promoting stimuli, with consequent cartilage maintenance promoting effects, with potential therapeutic application.

In OA, cartilage loss and synovial membrane inflammation are two major factors responsible for disease progression and associated outcomes. Complex and interconnected molecular events of cartilage homeostasis disruption associated to inflammation known to fuel cartilage degradation, are recognized as crucial for disease development and important targets for therapeutic approaches [32]. Cartilage degradation is associated with chondrocytes differentiation leading to apoptosis and deposition of a mineralized extracellular matrix, which in turn contributes to loss of ECM integrity and inflammation [33]. In fact, although the pathways involved in the crosstalk between inflammation and cartilage degradation are still not completely clarified, mineralizing and inflammatory events occur in a close related manner during OA progression [30]. BCP and calcium pyrophosphate (CPP) crystals, consistently associate with the early stage of OA and have a pathogenic role in the development and rapid progression to end-stage OA [11,12]. BCPs have been found in the synovial fluid and membrane, and cartilage from OA patients [34], and associated with the activation of macrophages, synovial fibroblasts and articular cells, resulting in increased cell proliferation and production of pro-inflammatory cytokines and MMPs [35,36]. In concordance, our results show an inflammatory response to hydroxyapatite stimulation in all tested OA models, similar to those obtained with the classical inflammatory cytokine IL-1β, and to previously reported effects in OA cell models [30,37]. Of particular relevance, at cartilage level, treatment with hydroxyapatite induced overexpression of Col10 and Runx2, indicative of triggered chondrocyte differentiation towards hypertrophy and calcification. In addition, up-regulation of COX-2 and IL-6, widely known to be associated with joint inflammation, and MMP3, a major responsible for ECM degradation, clearly demonstrate the detrimental potential of calcification in OA. This is in line with recent data showing that BCP upregulate IL-6 in in vivo murine OA models, which in turn induced the expression of genes involved in calcification, promoting BCP formation and potentiating a vicious cycle [38]. Increased levels of BCP and IL-6 were also associated with cartilage degradation through the induction of matrix-degrading enzymes activity in chondrocytes [38]. In another study, calcium-phosphate complexes were shown to induce MMP3 and MMP13, which in turn, promoted the release of calcium and phosphate through degradation of the ECM calcified cartilage, in a positive loop [39]. Additionally, the effect of IL-1β on cartilage is known to reflect not only the catabolic effect of aggrecanases and MMPs upregulation, but also the downregulation of chondrogenic extracellular matrix synthesis [40,41]. In concordance, our results showed that IL-1β induced an overexpression of MMP3. Overall, our results clearly demonstrated the potentialities of the developed ex vivo explant-based co-culture OA model to study the interplay between cartilage degradation and inflammation, reflecting early molecular events leading to subsequent phenotypic cartilage alterations, of critical value in drug development for potential anti-osteoarthritic compounds such as YP.

YP has previously shown to have anti-inflammatory properties associated with the inhibition of TNF α in LPS-activated human macrophages [26]. In the present study, we demonstrated that YP was able to counteract inflammation, cell di fferentiation and ECM degradation, induced not only by IL-1β but also by hydroxyapatite, in all OA models, including primary articular cells, cartilage explants and ex vivo explant-based co-culture systems. These e ffects were demonstrated at multiple levels. Through downregulation of master players involved in pro-inflammatory reactions, such as NF-kB, COX-2 and IL-6, and the ECM catabolic marker MMP3, YP is directly contributing to preserve cartilage homeostasis, by avoiding ECM disruption and cartilage collapse. Similarly, the capacity to downregulate crucial genes involved in chondrocyte di fferentiation such as Col10 and Runx2, suggests YP as an inhibitor of chondrocytes hypertrophic di fferentiation. The resulting decrease of apoptosis and ECM mineralization, indirectly contributes to a consequent decrease of pro-inflammatory reactions, ultimately preserving cartilage homeostasis. Although our studies were not directed to evaluate the effect of YP as a structural cartilage-modifying drug, its capacity to inhibit early molecular events leading to joint deterioration, suggests YP as a potential disease modifying OA drug, worth to be further investigated.

Additionally, this YP protective role might represent a promising alternative to the anti-inflammatory drugs commercially available to manage symptomatology associated with OA and chronic autoimmune and inflammatory diseases, mostly based on NSAIDs target to inactivate COX enzymes (COX-1 and COX-2) [42], or biologics targeting crucial pro-inflammatory cytokines such as TNF α and IL-1β [43,44]. Although some e ffectiveness has been shown in slowing inflammatory reactions, the growing list of adverse side e ffects and the high percentage of patients presenting no response to these treatments, clearly demonstrate the urgent need for safer and more e ffective anti-inflammatory drugs. In this field, natural derived products, such as YP, have been considered as promising and valid alternatives. Some examples are the tetracyclic triterpenoid glycoside Ginsenoside Rb1 (G-Rb1) and curcumin, which have shown both in vitro and in vivo the capacity of targeting the production of several pro-inflammatory species and promoting the synthesis of anti-inflammatory mediators, with cartilage protective e ffects [45–48].

Considering the pivotal role of NF-kB as a major regulator of inflammation, many strategies have been developed to block NF-kB signaling in a variety of inflammatory disease settings [49]. Although in the context of OA these strategies are still in their infancy, the crucial role of NF-kB signaling mediating inflammatory responses, but also the hypertrophic conversion of articular cartilage chondrocytes, leading to ECM damage and cartilage destruction, is of paramount importance in the disease context [50,51]. Our results demonstrate that YP is able to downregulate NF-kB expression and decrease IkB α phosphorylation in chondrocytes, strongly suggesting that YP cartilage protective properties are associated, at least in part, with the inhibition of NF-kB nuclear translocation and consequent decreased activation of catabolic pathways, including expression of cytokines and chemokines, inflammatory mediators, matrix degrading enzymes, and regulators of chondrocytes di fferentiation. In agreement, YP treatments consistently decreased levels of COX-2 and IL-6, MMP3, Col10 and Runx2 in cartilage tissue, clearly demonstrating the potential of YP in ameliorating cartilage homeostasis and integrity, a good rationale for the exploitation of YP in the treatment of OA.

### **4. Materials and Methods**

### *4.1. Isolation of Amentadione (YP)*

The meroditerpenoid amentadione (YP) was isolated from the brown alga *Cystoseira usneoides* collected off the coast of Tarifa (Spain) as previously described [26]. Briefly, the frozen alga was extracted with methanol and after evaporation of the solution under reduced pressure, the aqueous residue was extracted with diethyl ether. The resulting extract was subjected to column chromatography (CC) on silica gel (70–230 mesh) (Merck KGaA, Darmstadt, Germany) eluting with a mixture of *n*-hexane/diethyl ether (50:50, *v*/*v*), then diethyl ether, mixtures of chloroform/methanol (90:10 and 80:20, *v*/*v*), and finally methanol. The fraction that eluted with chloroform/methanol (90:10, *v*/*v*) was further separated by CC on silica gel using as eluents mixtures of *n*-hexane/ethyl acetate (50:50 to 30:70, *v*/*v*), then ethyl acetate, and finally methanol. The compound YP was obtained by reversed phase HPLC separation of selected subfractions using as eluent methanol/water (70:30, *v*/*v*). HPLC separations were performed on a LaChrom-Hitachi apparatus (Merck), equipped with Kromasil 100-5C18 columns (250 × 10 mm, 5 μm or 250 × 4.6 mm, 5 μm) (Hichrom, Reading, UK), using an RI-71 differential refractometer or L-7400 UV detector (Merck). The pure compound YP was identified as amentadione [52] by NMR and HRMS analysis (Figure S1) and the negative optical rotation. NMR spectra were recorded on an Agilent 500 spectrometer (Agilent Technologies, Santa Clara, CA, USA), HRMS spectra were obtained on a Waters SYNAPT G2 spectrometer (Waters, Milford, MA, USA), and optical rotation was measured on a JASCO P-2000 polarimeter (JASCO, Tokyo, Japan).


**1. Introduction**

Global Navigation Satellite System Reflectometry (GNSS-R) data have the potential to regionalize methane (CH4) emissions from land surface images by detecting their inundation status. Methane is an important greenhouse gas (GHG); its global warming potential over a 100-year horizon is 28 times higher than that of carbon dioxide (CO2) [1]. In 2011, the CH4 concentration was 1803 ppb, 150% higher than the preindustrial level, and a predominantly biogenic post-2006 increase has also been reported [2]. Concurrently, atmospheric methane's *δ*13CCH4 value has trended towards lighter (13C-depleted) values, implying a significant shift in the balance between the sources and sinks of CH4 [3] and a greater contribution of biogenic CH4 emission sources rather than fuel combustion to this rapid CH4 concentration increase [2]. Several hypotheses have been postulated for the cause of this isotopic shift, and these hypotheses can be summarized as one or a combination of the following: (i) a change in the oxidative capacity of the atmosphere [4]; (ii) changes in the relative strengths of anthropogenic sources, such as land-use changes on tropical wetlands to agriculture or waste and fossil fuel emissions with an overall net effect

of increasing emissions (e.g., [5]); and (iii) an increase in natural sources such as wetlands, potentially as a feedback effect from regional climatic change (e.g., [3]). Large gaps still exist between top-down and bottom-up CH4 total global emissions calculations, with much of the uncertainty associated with the emissions of wetlands and other natural emissions categories [6,7], particularly in tropical wetlands [7–9].

Because CH4 is emitted from inundated soil, which is spatiotemporally heterogeneous and has a flux pattern characterized by non-Gaussian/nonlinear behaviors [7], the appropriate evaluation of the CH4 flux requires the monitoring of the inundation status with spatiotemporally high-resolution techniques [10]. GNSS-R data became a popular input source in microwave remote sensing techniques following the deployment of the Cyclone Global Navigation Satellite System (CyGNSS), an eight-microsatellite constellation data system [11]. Every single CyGNSS microsatellite has two left-hand circular polarization (LHCP) down-looking antennas pointing to the Earth's surface with an inclination angle of approximately 28 degrees on either side of the satellite ground track [12].

The data can be used to globally detect the land surface inundation status almost daily with high-spatial-resolution L-band microwave signals (with estimated spatial resolutions of approximately 500–7000 m [13]) compared to common passive L-band microwave radiometers. A few studies have reported that the use of CyGNSS-based inundation maps for land surface methane emission simulations improved the representation of the CH4 emission status compared to the results obtained using common wetland maps (e.g., simulating a greater amount of CH4 emissions by detecting inundation under clouds/vegetation with GNSS-R data [14]).

There are several studies on the detection of inundation over wetlands with GNSS-R data e.g., [15–19]. However, the results in most studies remain spatiotemporally sparse. In most cases, the spatiotemporal interpolation is conducted with monthly observation datasets, or spatially interpolated with optical observation sensors e.g., [15,19]. Due to the limitations of L-band fine-spatial-resolution microwave remote sensing data like GNSS-R, there are only a few studies conducting the cross-validation of GNSS-R and L-band SARs observations [15]. Furthermore, from the perspective of the application of this study, most of the time, this sort of fine-spatial-resolution, satellite-derived wetland/inundation observation is downsampled or spatially thinned (a.k.a., superobservations) before being used in advanced simulation modeling approaches accompanied with high computation costs (e.g., coarse-spatial-resolution ensemble simulations or the use of superobservations to deal with observation error covariance in data assimilation tasks) by degrading the spatial resolution or thinning the observations (e.g., [14,20]). Due to the local heterogeneity of the inundation status and the non-Gaussian/nonlinear characteristics of the spatiotemporal CH4 emission distribution at the local scale [7–9], the deterioration of the spatial resolution of data can introduce large discrepancies to the emission values obtained between the top-down approach and bottom-up approach [6–9,20]. Therefore, the regionalization of CH4 emissions based on high-spatial-resolution L-band microwave data as a bottom-up approach still remains important [7–9,17]. Since most studies have used GNSS-R data for regional-scale simulations at a relatively coarse spatial resolution compared to remote sensing observations (e.g., 0.01◦-resolution CyGNSS-based watermasks are downsampled to a 0.5◦ resolution to match the WetCHARTs simulation grid [14]), few studies have paid attention to the differences among each specular point's footprint size (i.e., the glistening area). To rasterize each piece of specular point-scale vector data without downsampling for use in local-scale simulations, one must consider the difference among each specular point's footprint size to use these signals in fine-spatial-resolution, local-scale simulations (e.g., 10–50 m resolution irrigation models [10]). This information would also be essential for determining the spatial localization scale to ensure efficient data assimilation by determining the spatial localization scale at each specular point and adequately addressing the spatial observation error covariance.

More fundamentally, the amount of data of a certain quality provided by the GNSS-R microsatellite constellation is still limited, and the observations are prone to being conducted sparsely in space; in addition, the incidence angle varies widely among specular points, which is known to cause biases in the microwave reflectivity observations (unlike other spatially continuous microwave remote sensing observations, such as those obtained from passive microwave radiometers or synthetic aperture radars). The local incidence angles of the Phased-Array L-band Synthetic Aperture Radar-2 (PALSAR-2) ScanSAR instruments vary from 25 to 50 degrees, while CyGNSS incidence angles vary from 0 to 70 degrees [13,17]). To prepare inundation maps based on GNSS-R data for future applications or to be assimilated into simulation models, the spatiotemporal interpolation step needs to be processed before the data can be used in applications. Therefore, an adaptive quality control method that considers the size of each specular point and depends on each specular point vector and incidence angle but does not require ad hoc parameter tuning or region-specific empirical parameterization with external data, such as the normalized differential vegetation index (NDVI) or digital elevation model (DEM) data, is essential for this robust interpolation preprocessing step. To realize this globally consistent rasterization at a fine spatial resolution, the authors have developed a precision index calibration scheme implemented while processing the raw specular vector data to rasterize data while considering the differences in incidence angles and specular points' sizes/shapes/velocities. To compensate for the spatially sparse distribution of GNSS-R specular data, the temporal Kalman smoother is applied by using the precision index as the reciprocal observation error number in each 15-day cycle over the Mekong Delta as a demonstration; this case study area consists of double-/triple-rice-cropping systems, aquacultural ponds, mangroves and peatlands. Cross-validation with the PALSAR-2 quadruple polarimetric data (3–6 m resolution) product is also conducted, and the results are validated with ground inundation observation datasets [7–9,17]. The goal of this study is to demonstrate the usefulness of this quality control method by applying it to fine-spatiotemporal-resolution analyses over the Mekong Delta [i.e., (I) comparing it with a common change detection algorithm with the daily temporal resolution, (II) applying it with a 500 m rasterization with a 15-day temporal resolution, (III) and surveying the consistency with 3–6 m spatial-resolution L-band SAR backscatter intensities].


**5. Conclusions**

82 Metal Forming – Process, Tools, Design

**Figure 44.** % thinning versus punch tip radius for region B

Figure 45 illustrates the effect of the radius of conical-cylindrical region on the thickness distribution. As it shows, changes in the radius only affects region D and it has no effect on other regions of the part. For more accurate study, the thickness reduction in region D was investigated and the results are shown in Figure 46. As it can be seen, by increasing the

radius of region D and the conical angle the thickness reduction will be decreased.

**Figure 45.** Thickness distribution curve versus radius of conical–cylindrical region

**Figure 46.** % thinning versus radius of conical-cylindrical region

In this chapter, a new sheet hydroforming is proposed and applied for forming of two industrial parts that currently are produced in industry by conventional deep drawing and stamping in several stages. With the new method, these two parts were produced in one stage and without any defects. In addition, it is shown that the forming pressure and load are very low compared with those of other hydroforming methods.

In addition, for case study II, the effects of tool parameters such as the radius of the punch tip, punch-cylindrical radius, friction between punch and sheet, friction coefficient between blank holder and sheet, sheet thickness and punch angle, on formability and thickness distribution of the conical parts were studied through using hydrodynamic deep drawing assisted by radial pressure. It was observed that with increasing the conical workpiece angle the thickness reduction will decrease in B area. Moreover, as the conical angle increases, bursting occurs at lower pressure in such a way that beyond one specific angle, the conical workpiece can be formed in the die chamber without applying any pressure. Also, with the cone angle increasing, the thickness distribution will be improved and the likelihood of bursting decreases.


2. Preliminaries

engineering and application value, and has been employed in Apollo entry guidance [6] and shuttle entry guidance [7]. Nevertheless, in reference trajectory reentry guidance, since HSV owns particular characteristics such as strong nonlinear, large flight envelope, complex entry environment, and precise terminal guidance accuracy requirement, it is difficult for HSV to track the nominal profile properly. Many scholars have done continuous research on it [8–12]. For following nominal profile problem in reentry reference trajectory guidance, namely trajectory tracking law, traditional PID control law of shuttle was given in [7]. Roenneke et al. [13] derived a linear control law tracking the drag reference in drag state space to achieve guidance command. In [14], a feedback linearization method for shuttle entry guidance trajectory tracking law to extend its application range was presented. In [15, 16], a feedback tracking law is designed by taking advantage of the linear structure of system dynamics in the energy space to achieve bounded tracking of the flat outputs. These foregoing approaches improved performances of trajectory tracking laws for aerial vehicles. However, they are not applied to HSV which owns particular characteristics. Dukeman [17] proposed a linear trajectory tracking law based on linear quadratic regulator (LQR) by constructing weighting matrices with Bryson principle [18], and the tracking law was very robust with respect to varying initial conditions and worked satisfactorily even for entries from widely different orbits than that of the reference profile. The capacity of the approach in [17] against other reentry process interferences such as aerodynamic parameter error, nevertheless, was relatively poor, and simulations demonstrated that performances for HSV tracking nominal profile under various disturbances depended directly on weighting matrices in LQR. In this study, one focuses on constructing

LQR weighting matrices to strengthen robustness of HSV trajectory tracking law.

under different disturbances.

134 Advances in Some Hypersonic Vehicles Technologies

The weighting matrices Q and R are the most important parameters in LQR optimization and determine the output performances of systems [19]. Trial-and-error method has been employed to construct these matrices, which is simple, but primarily depends on people's experience and intuitive adjustment. In trial-and-error method, elements of weighting matrices must be repeatedly experimented to get a proper value, and is not feasible for application in large scale system. In [18, 20], certain general guidelines were followed to construct weighting matrices simply and normally, but might not lead to satisfactory responses. Connecting closedloop poles to feedback gains for LQR were presented in [21–24] using pole-assignment approach, which resulted in more accurate responses. However, it was difficult to balance state and control variables and to account for control effectiveness using the approaches in [21–24]. A trade-off between penalties on the state and control inputs for optimization of the cost function was considered in [25], where specified closed-loop eigenvalues were obtained, but the computation normally needed more iterations. Genetic algorithm (GA) can be applied to find a global optimal solution [26–28], and the differential evolution algorithms inspired from GA are efficient evolution strategies for fast optimization technique [29–31]. However, the approaches in [26–31] have little improvement for HSV profile-following performances

In this study, a novel method to construct weighting matrices with time-varying parameters on the basis of Bryson principle is proposed. This idea employs current flight states to provide flexible and accurate feedback gains in HSV trajectory tracking law under various interferences

In this section, the concepts and basic results on reentry dynamics, LQR, Bryson principle, and their applications in hypersonic vehicle trajectory tracking law are introduced, which are the research foundation of the following sections.

#### 2.1. Reentry dynamics

For a lifting reentry vehicle, the common control variables are the bank angle σ, and the angle of attack α. The state variables include the radial distance from the Earth center to the vehicle r, the longitude θ, the latitude ϕ, the Earth-relative velocity v, the flight path angle γ, and the heading angle ψ. The three-degree-of-freedom point-mass dynamics for the vehicle over a sphere rotating Earth are expressed as [32]:

$$
\dot{r} = \upsilon \sin \upsilon,\tag{1}
$$

$$\dot{\theta} = \frac{v \cos \varphi \sin \psi}{r \cos \phi},\tag{2}$$

$$\dot{\phi} = \frac{v \cos \gamma \cos \psi}{r} \,\tag{3}$$

$$\psi = -D - g\sin\chi + \omega^2 r \cos\phi (\sin\chi\cos\phi - \cos\chi\sin\phi\cos\psi). \tag{4}$$

$$\gamma = \frac{1}{v} \left[ L\cos\sigma - g\cos\chi + \frac{v^2\cos\chi}{r} + 2\omega v\cos\phi\sin\psi + \omega^2 r\cos\phi \left(\cos\chi\cos\phi + \sin\chi\sin\phi\cos\psi\right) \right], \tag{5}$$

$$\dot{\psi} = \frac{1}{v} \left[ \frac{v^2 \cos \gamma \sin \psi \tan \phi}{r} - 2\omega v \{ \tan \gamma \cos \phi \cos \psi - \sin \phi \} \right. \\ \quad + \frac{\omega^2 r}{\cos \gamma} \sin \phi \cos \phi \sin \psi + \frac{L \sin \sigma}{\cos \gamma} \Big], \tag{6}$$

where ω is the Earth's self-rotation rate, and g is the gravitational acceleration. L and D are the aerodynamic lift and drag accelerations defined by

$$L = \frac{1}{2m}\rho v^2 \mathcal{C}\_L \mathcal{S}, \ D = \frac{1}{2m}\rho v^2 \mathcal{C}\_D \mathcal{S},\tag{7}$$

where m is the mass of the vehicle, S is the reference area, CL is the lift coefficient, and CD is the drag coefficient. ρ is the atmospheric density expressed as an exponential model [33].

$$
\rho = \rho\_0 e^{-\beta \hbar},
\tag{8}
$$

In order to obtain a proper quadratic performance index, elements of weighting matrices must

The basic principle of Bryson principle is to normalize the contributions, and then the states and the control terms may behave effectively within the definition of the quadratic cost function. The normalization is accomplished by using the anticipated maximum values of the

Q tðÞ¼ diag q1ð Þt ; …; qnð Þt � � , RtðÞ¼ diag½ � r1ð Þt ;…;rmð Þt : (14)

Hypersonic Vehicles Profile-Following Based on LQR Design Using Time-Varying Weighting Matrices

2 þ … þ rmð Þτ umð Þτ

http://dx.doi.org/10.5772/intechopen.70659

2 ¼ … ¼ rmumð Þ max

(16)

137

(18)

2 ¼ 1: (17)

2 þ r1ð Þτ u1ð Þτ

xið Þ max , i ¼ 1, 2, …, n, ujð Þ max , j ¼ 1, 2, …, m:

2 ¼ r1u1ð Þ max

2 , i ¼ 1, 2, …n ,

2 , j ¼ 1, 2, …m:

Then, the elements to construct the weighting matrices can be obtained as time-invariant param-

Through simple calculation, Bryson principle can generate better results in a short time, which minimizes the quadratic index value in a proper scope. Because of that, Bryson principle is

In reentry reference trajectory guidance, the chief challenge of following the nominal profile lies in generating a proper compensatory signal, and LQR can solve this problem effectively. After generating a feasible reference entry profile containing altitude z, velocity v, flight path angle γ as reference parameters, and bank angle σref as guidance reference signal, one can download this profile into the onboard computer. After the vehicle enters the atmosphere, the deviations between nominal profile and the actual real-time data can be obtained by

2 � �dτ: (15)

be chosen properly, and Bryson principle can solve this problem effectively.

Then, develop the quadratic index in the following expression.

2 þ … þ qnð Þτ xnð Þτ

Normalize all the contributions to 1 with the help of all the maximum values.

Determine each maximum value of all the states and control terms.

�

2 ¼ … ¼ qnxnð Þ max

8 >>><

>>>:

widely applied to the selection of weighting matrices in LQR.

2.3. Reentry reference trajectory guidance based on LQR

qi ¼ 1 xið Þ max

rj ¼ 1 ujð Þ max

q1ð Þτ x1ð Þτ

q1x1ð Þ max

J ¼ ðtf t

eters.

individual states and control quantities. The method can be explained as follows. First, define the weighting matrices Q(t) and R(t) as diagonal matrices, namely:

where ρ0 is the atmospheric density at sea level, h is the altitude of the vehicle, and β is a constant.

To guide the vehicle from the initial point to the terminal interface with multiple constraints, a reference trajectory is usually optimized offline, and a profile-following law is utilized to track the reference trajectory onboard. In the longitudinal profile-following, the linear quadratic regulator (LQR) law is a good choice [10].

#### 2.2. Linear quadratic regulator

This subsection introduces LQR and Bryson principle. For a linear system, the dynamics can be described by

$$\begin{cases} \dot{\mathbf{x}}(t) = A(t)\mathbf{x}(t) + B(t)\boldsymbol{\mu}(t),\\ \mathbf{y}(t) = \mathbf{C}(t)\mathbf{x}(t), \end{cases} \tag{9}$$

where A(t), B(t) and C(t) are system matrices, x(t)=[x1(t), x2(t), ……, xn(t)]T is the state, and u(t)=[u1(t), u2(t), ……, un(t)]T is the control input.

The quadratic performance index required to be minimized can be written as

$$J(t, t\_f) = \int\_{t}^{t\_f} \left[ \mathbf{x}^T(\tau) \mathbf{Q}(\tau) \mathbf{x}(\tau) + \mathbf{u}^T(\tau) \mathbf{R}(\tau) \mathbf{u}(\tau) \right] d\tau,\tag{10}$$

where the weighting matrix Q(t) is symmetrical positive semi-definite and weighting matrix R(t) is symmetrical positive definite. The specific procedure of LQR minimizing quadratic performance index is as follows.

The Riccati equation is given as

$$P(t)A(t) - P(t)B(t)R(t)^{-1}B(t)^TP(t) + Q(t) + A(t)^TP(t) = 0. \tag{11}$$

After getting the solution P(t) corresponding to each time instant t by solving Eq. (11), the feedback gain matrix can be obtained as

$$K(t) = R(t)^{-1} B^T(t) P(t). \tag{12}$$

Based on Eq. (12), the control input can be designed as

$$
\mu(t) = -K(t)\mathbf{x}(t). \tag{13}
$$

In order to obtain a proper quadratic performance index, elements of weighting matrices must be chosen properly, and Bryson principle can solve this problem effectively.

The basic principle of Bryson principle is to normalize the contributions, and then the states and the control terms may behave effectively within the definition of the quadratic cost function. The normalization is accomplished by using the anticipated maximum values of the individual states and control quantities. The method can be explained as follows.

First, define the weighting matrices Q(t) and R(t) as diagonal matrices, namely:

$$Q(t) = \text{diag}\left[q\_1(t), \dots, q\_n(t)\right] \quad , \quad R(t) = \text{diag}[r\_1(t), \dots, r\_m(t)]. \tag{14}$$

Then, develop the quadratic index in the following expression.

where m is the mass of the vehicle, S is the reference area, CL is the lift coefficient, and CD is the

�βh

, (8)

(9)

drag coefficient. ρ is the atmospheric density expressed as an exponential model [33].

constant.

described by

regulator (LQR) law is a good choice [10].

136 Advances in Some Hypersonic Vehicles Technologies

u(t)=[u1(t), u2(t), ……, un(t)]T is the control input.

J t; tf � � ¼

2.2. Linear quadratic regulator

performance index is as follows. The Riccati equation is given as

feedback gain matrix can be obtained as

ρ ¼ ρ0e

where ρ0 is the atmospheric density at sea level, h is the altitude of the vehicle, and β is a

To guide the vehicle from the initial point to the terminal interface with multiple constraints, a reference trajectory is usually optimized offline, and a profile-following law is utilized to track the reference trajectory onboard. In the longitudinal profile-following, the linear quadratic

This subsection introduces LQR and Bryson principle. For a linear system, the dynamics can be

x t \_ðÞ¼ A tð Þx tð Þþ B tð Þu tð Þ,

where A(t), B(t) and C(t) are system matrices, x(t)=[x1(t), x2(t), ……, xn(t)]T is the state, and

where the weighting matrix Q(t) is symmetrical positive semi-definite and weighting matrix R(t) is symmetrical positive definite. The specific procedure of LQR minimizing quadratic

After getting the solution P(t) corresponding to each time instant t by solving Eq. (11), the

K tðÞ¼ R tð Þ�1

xTð Þτ Qð Þτ xð Þþ τ uTð Þτ Rð Þτ uð Þτ � �dτ, (10)

B tð ÞTP tð Þþ Q tð Þþ A tð ÞTP tðÞ¼ 0: (11)

BTð Þt P tð Þ: (12)

u tðÞ¼�K tð Þx tð Þ: (13)

y tðÞ¼ C tð Þx tð Þ,

The quadratic performance index required to be minimized can be written as

�

ðtf t

P tð ÞA tð Þ� P tð ÞB tð ÞR tð Þ�1

Based on Eq. (12), the control input can be designed as

$$J = \int\_{t}^{t\_f} \left( q\_1(\tau) \mathbf{x}\_1(\tau)^2 + \dots + q\_n(\tau) \mathbf{x}\_n(\tau)^2 + r\_1(\tau) u\_1(\tau)^2 + \dots + r\_m(\tau) u\_m(\tau)^2 \right) d\tau. \tag{15}$$

Determine each maximum value of all the states and control terms.

$$\begin{cases} \mathbf{x}\_i(\text{max}) \; , \; i = 1, 2, \dots, n \\ \mathbf{u}\_j(\text{max}) \; , \; j = 1, 2, \dots, m. \end{cases} \tag{16}$$

Normalize all the contributions to 1 with the help of all the maximum values.

$$
\eta\_1 \mathbf{x}\_1 (\text{max})^2 = \dots = \eta\_n \mathbf{x}\_n (\text{max})^2 = r\_1 \mu\_1 (\text{max})^2 = \dots = r\_m \mu\_m (\text{max})^2 = 1. \tag{17}
$$

Then, the elements to construct the weighting matrices can be obtained as time-invariant parameters.

$$\begin{cases} q\_i = \frac{1}{\chi\_i \left(\max\right)^2} \quad , \quad i = 1, 2, \dots \text{n} \\\\ r\_j = \frac{1}{\mu\_j \left(\max\right)^2} \quad , \quad j = 1, 2, \dots \text{m} \end{cases} \tag{18}$$

Through simple calculation, Bryson principle can generate better results in a short time, which minimizes the quadratic index value in a proper scope. Because of that, Bryson principle is widely applied to the selection of weighting matrices in LQR.

#### 2.3. Reentry reference trajectory guidance based on LQR

In reentry reference trajectory guidance, the chief challenge of following the nominal profile lies in generating a proper compensatory signal, and LQR can solve this problem effectively. After generating a feasible reference entry profile containing altitude z, velocity v, flight path angle γ as reference parameters, and bank angle σref as guidance reference signal, one can download this profile into the onboard computer. After the vehicle enters the atmosphere, the deviations between nominal profile and the actual real-time data can be obtained by navigation facilities. The deviations contain altitude error zδ, velocity error vδ and flight path angle error γδ.

Denote the compensatory bank angle by σδ. In order to minimize the deviations and keep the aerial vehicle tracking nominal profile properly, the optimal feedback gain of guidance compensatory signal σδ can be calculated by LQR in the following algorithm.

Algorithm 1. The actual guidance signal in trajectory tracking law based on LQR can be determined in the following procedure.

Step 1. Based on perturbation theory, one establishes the linear equations of motion by taking the deviations as state parameters.

$$\begin{cases} \delta \mathbf{x}'(t) = A(t)\delta \mathbf{x}(t) + B(t)\delta u(t), \\ y(t) = \mathbf{C}(t)\delta \mathbf{x}(t). \end{cases} \tag{19}$$

It has been verified in [17, 34] that using Algorithm 1, the aerial vehicle performs well in

Hypersonic Vehicles Profile-Following Based on LQR Design Using Time-Varying Weighting Matrices

http://dx.doi.org/10.5772/intechopen.70659

In this section, the problem of HSV profile-following using trajectory tracking law based on

The traditional reference guidance is not suitable for hypersonic vehicles because of its particular characteristics, including strong nonlinear, large flight envelope and complex entry environment. In the process of entry flight, it is difficult to constrain the deviation between real profile and nominal profile into a proper scope. Furthermore, strict terminal accuracy requirement demands that hypersonic vehicles track nominal profile precisely, that is, deviations in

Consequently, in the reference profile-following of HSV based on LQR, new problems occur in the selection of weighting matrices. In the initial flight stage, it is assumed that the deviations

> zδ0 ¼ 3 km, vδ0 ¼ 200m=s:

Let zδ1 and vδ1 be the anticipated maximum deviations accuracy in the terminal stage,

zδ1 ¼ 0:5 km, vδ1 ¼ 20m=s:

Substituting zδ0, vδ0, zδ1 and vδ1 into Eq. (21), one can get the weighting matrix Q0 and Q1 as

3 7

5: (27)

2 6 4

3 7 5, Q1 ¼

From Eqs. (25) and (26), one sees that zδ0 and vδ0 are bigger than zδ1 and vδ1, respectively. The weighting matrix Q0, which is determined by zδ0 and vδ0, can effectively eliminate the large initial stage deviations between the real and nominal profiles. Nevertheless, the capacity of Q0 for resisting disturbance in the process of flight is not strong enough to satisfy the terminal accuracy requirement. On the contrary, the weighting matrix Q1 constructed by zδ1 and vδ1 can eliminate the disturbance in the process of flight effectively. However, facing the existence of large deviations in the initial entry flight, it is difficult to keep HSV tracking the nominal

Therefore, compared with Q0, the weighting matrix Q1 is not applicable to initial deviations, and has good robustness to deal with disturbance in the process of entry flight. The

(25)

139

(26)

of altitude and velocity are zδ0 and vδ0, respectively, which are chosen to be

�

�

2 6 4

profile properly, which will further influence the terminal accuracy.

Q0 ¼

tracking reference trajectory.

3. Problem statement

LQR in Section 2 is presented.

the terminal stage must be smaller.

expressed as

where δx(t)=[zδ(t), vδ(t), γδ(t)]T and δu(t) = σδ(t).

Step 2. Construct the quadratic performance index as follows:

$$J(t, t\_f) = \int\_{t}^{t\_f} \left[ \delta \mathbf{x}^T(\tau) Q \delta \mathbf{x}(\tau) + \delta u(\tau) R \delta u(\tau) \right] d\tau. \tag{20}$$

Step 3. The weighting matrices Q and R in Eq. (20) are determined by Bryson principle. Since altitude z and velocity v are main factors in profile-following, q3, which is the weighting element of path angle γ, can be ignored. Using Eq. (18), the other elements of weighting matrices can be obtained as

$$q\_1 = \frac{1}{z\_{\delta\_{\text{max}}}} \quad \text{ } \quad q\_2 = \frac{1}{\upsilon\_{\delta\_{\text{max}}}} \text{ } \text{ } \quad r\_1 = \frac{1}{\sigma\_{\delta\_{\text{max}}}} \text{ } \tag{21}$$

where zδmax and vδmax are anticipated maximum deviations between the actual profile and the nominal profile, and σδmax is the maximum allowable modification of guidance signal σ. Based on Eq. (21), one can get the weighting matrices:

$$\mathcal{Q} = \text{diag}\left[q\_1, q\_2\right] \; , \; \mathcal{R} = r\_1. \tag{22}$$

Step 4. In order to minimize the index J in Eq. (20), one calculates the Riccati Eqs. (11) and (12) to obtain the optimal feedback gain K(t). Then, the compensatory signal can be obtained as

$$
\delta u(t) = -K(t)\delta x(t). \tag{23}
$$

Step 5. The actual guidance signal σ(t) which consists of guidance reference signal u(t) and guidance compensatory signal δu(t) can be obtained. It can be shown that

$$
\sigma(t) = u(t) + \delta u(t) = \sigma\_{ref} - \mathbf{K}(t)\delta \mathbf{x}(t). \tag{24}
$$

It has been verified in [17, 34] that using Algorithm 1, the aerial vehicle performs well in tracking reference trajectory.


**4.2 Measure**

This is the first essential step in any cultural change initiative – finding out where you are starting from by taking the time to learn the core values of your valued employees. By determining what is important to people at levels within your organization, you can align your culture effectively. And Baumgartner says not to be surprised that values can differ by level, function and, if your company has multiple offices, by location as well.


**Author details**

Victor B. Oti Department of Microbiology, Nasarawa State University, Nigeria

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


**3. Results**

The interaction between rootstock and year was always not significant; therefore, for the sake of simplicity it was omitted from the tables and graphs. Similarly, the factor year was statistically significant only for first flower formation and is reported only in the correspondent table.


**4.1.1 Navigation and other water uses**

Following the economic decline in the former Yugoslavia in the 1980-ies, the armed conflict in the early 1990-ies has caused an additional decrease of transport and navigation on the Sava river, reducing the cargo traffic, which was around 10 million tons in 1982, and 5.7 million tons in 1990, to less than 1 million tons. A lack of investments into the waterway maintenance and infrastructure development resulted in unfavourable navigation conditions, characterized by a limited draft during long periods, a limited fairway width and a limited height for passages under some bridges, as well as insufficient marking. Navigability of the waterway, which used to be a class IV waterway in the past, was reduced to class III at many sections of the river. Given such an initial situation, ratification of the *FASRB* and establishment of the ISRBC provided a good basis for rehabilitation and development of navigation on the Sava river, which was further strengthened by simultaneous ratification of the *Protocol on Navigation Regime to the FASRB* (2004).

Since the beginning of the *FASRB* implementation, considerable efforts have been invested by the ISRBC and the Parties to provide conditions necessary for the Sava river to become an important, environment-friendly and navigation-safe lifeline for inland transport (ISRBC, 2009b; Komatina, 2011b). The undertaken activities have been focused on two major issues: (a) planning for rehabilitation and development of the Sava river waterway infrastructure, and (b) improvement of technical standards and safety of navigation, with the aim to prevent the environmental risks associated with navigation.

With regard to **rehabilitation and development of the waterway infrastructure**, the preliminary documentation has been developed, and future steps have been agreed upon by the Parties (ISRBC, 2011a, 2011b). Based on the assessment of transport demand (Fig. 12) and economic analyses, the upgrade of the whole waterway to class Va was shown to be feasible, the costs being 10% higher than the costs of rehabilitation of the whole waterway to class IV (ISRBC, 2008a). Nevertheless, in order to minimize negative environmental impacts of the project, the ISRBC has decided to develop the waterway to class Va only at 40% of the total length (section Belgrade – Brčko), while the rest part will be rehabilitated to class IV. For the same reason, no change of the present watercourse (i.e. no straightening of the river) has been planned, so that, in sharp bends, only one-way navigation is foreseen. Additionally, several other activities have been performed, including a full restoration of the waterway marking system after 20 years, removal of unexploded ordnances from the river banks, and the initial phase of establishment of the Sava RIS in accordance with the *EU RIS Directive*.

This part provides a brief summary of the achievements made, not only in the fields of navigation, other water uses, water protection and hazard management, but also with regard to "cross-cutting issues" (i.e. information management, hydrological and meteorological issues, cooperation, public participation and stakeholder involvement), which are dealt with in order to provide an overall support to the implementation process. Further information can be found elsewhere (Komatina and Zlatić-Jugović, 2010; Komatina, 2011a), or at the ISRBC web-site, www.savacommission.org, where majority of the

Following the economic decline in the former Yugoslavia in the 1980-ies, the armed conflict in the early 1990-ies has caused an additional decrease of transport and navigation on the Sava river, reducing the cargo traffic, which was around 10 million tons in 1982, and 5.7 million tons in 1990, to less than 1 million tons. A lack of investments into the waterway maintenance and infrastructure development resulted in unfavourable navigation conditions, characterized by a limited draft during long periods, a limited fairway width and a limited height for passages under some bridges, as well as insufficient marking. Navigability of the waterway, which used to be a class IV waterway in the past, was reduced to class III at many sections of the river. Given such an initial situation, ratification of the *FASRB* and establishment of the ISRBC provided a good basis for rehabilitation and development of navigation on the Sava river, which was further strengthened by

simultaneous ratification of the *Protocol on Navigation Regime to the FASRB* (2004).

Since the beginning of the *FASRB* implementation, considerable efforts have been invested by the ISRBC and the Parties to provide conditions necessary for the Sava river to become an important, environment-friendly and navigation-safe lifeline for inland transport (ISRBC, 2009b; Komatina, 2011b). The undertaken activities have been focused on two major issues: (a) planning for rehabilitation and development of the Sava river waterway infrastructure, and (b) improvement of technical standards and safety of navigation, with the aim to

With regard to **rehabilitation and development of the waterway infrastructure**, the preliminary documentation has been developed, and future steps have been agreed upon by the Parties (ISRBC, 2011a, 2011b). Based on the assessment of transport demand (Fig. 12) and economic analyses, the upgrade of the whole waterway to class Va was shown to be feasible, the costs being 10% higher than the costs of rehabilitation of the whole waterway to class IV (ISRBC, 2008a). Nevertheless, in order to minimize negative environmental impacts of the project, the ISRBC has decided to develop the waterway to class Va only at 40% of the total length (section Belgrade – Brčko), while the rest part will be rehabilitated to class IV. For the same reason, no change of the present watercourse (i.e. no straightening of the river) has been planned, so that, in sharp bends, only one-way navigation is foreseen. Additionally, several other activities have been performed, including a full restoration of the waterway marking system after 20 years, removal of unexploded ordnances from the river banks, and the initial phase of establishment of the Sava RIS in accordance with the

**4.1 Current status of the** *FASRB* **implementation**

documents, mentioned throughout the text, are available.

prevent the environmental risks associated with navigation.

*EU RIS Directive*.

**4.1.1 Navigation and other water uses**

Fig. 12. Estimated margins of traffic volume on the Sava river for year 2027 (ISRBC, 2008a)

The **administrative and legal framework** has been strengthened by development of a set of rules and other documents related to technical issues and safety of navigation, harmonized with the corresponding EU and UNECE regulations (ISRBC, 2009b, 2009c). The *Protocol on Prevention of Water Pollution caused by Navigation to the FASRB* (ISRBC, 2009a) has been developed and signed, and is currently undergoing ratification. The *Protocol on Sediment Management to the FASRB*, aiming to regulate, *inter alia*, the sand and gravel exploitation in accordance with the *Sava River Basin Management Plan* (*Sava RBM Plan*), has entered the process of final harmonization by the Parties.

In order to ensure **environmental sustainability**, the issue of navigation development is considered as an integral part of the *Sava RBM Plan*, which is being developed in accordance with the *EU WFD*. A considerable attention has been paid, as well, to the improvement of technical standards and safety of navigation, through implementation of concrete projects (restoration of the waterway marking system, development of the Sava RIS) and strengthening of the administrative and legal framework, including the protocols to the *FASRB*, fully in line with the corresponding EU and UNECE regulations. Finally, the waterway planning has been based on a clear intention to minimize negative environmental impacts of the rehabilitation works, and accompanied with an active involvement of the ISRBC in the relevant processes on Danube and European levels (International Commission for the Protection of the Danube River [ICPDR] et al., 2008; *Manual on Good Practices in Sustainable Waterway Planning*, 2010).

Partly as a consequence of the above mentioned achievements, there are already several indicators of development in traffic and opening of new cargo flows on the Sava river, such as opening of transport of oil products from (Bosanski) Brod, new developments in Serbian ports (Sremska Mitrovica, Šabac), as well as the first passenger cruise along the whole Sava river waterway after 150 years.

Integrated Water Resources Management as a

climate change assessment in the basin.

**4.1.3 Cross-cutting issues**

initial phase launched.

planned.

Basis for Sustainable Development – The Case of the Sava River Basin 35

ICPDR. The *Protocol on Emergency Situations to the FASRB*, aiming to enhance prevention, preparedness, response and mutual assistance of the Parties in case of emergency situations, has been drafted and entered the process of harmonization by the Parties. As an important future activity, development of a water contingency management plan for the basin is

In the field of **flood management**, the *Flood Action Plan* for the Sava river basin (ICPDR & ISRBC, 2009) has been prepared in accordance with the *Flood Action Programme for the Danube River Basin* of the ICPDR, providing the first programme of measures for each Party to achieve the defined targets for flood management in its part of the Sava basin until 2015. The *Protocol on Flood Protection to the FASRB* (ISRBC, 2010a), which aims to provide the legal basis for cooperation of the Parties in line with the *EU Flood Directive*, including the preparation of the *Flood Risk Management Plan* for the Sava river basin, has been developed and signed, and is currently under ratification. A number of preparatory activities toward the *Flood Risk Management Plan* have been performed so far, including an assessment of current flood management practices in the Parties, establishment of a database on the existing flood protection facilities, preparation of a GIS-based, indicative flood extent map for the whole Sava river (Fig. 13), development of a preliminary hydrological model of the Sava river basin and the hydraulic model of the Sava river, and launching an UNECEsupported project, aiming to assist linking the flood risk management planning and the

Fig. 13. Indicative map of important flood prone areas along the Sava river (ISRBC, 2009d)

In the field of **information management**, the *Sava GIS Strategy* (ISRBC, 2008b) has been developed, taking into account the *EU INSPIRE Directive* and the Water Information System for Europe. Subsequently, the implementing documents for the Sava GIS establishment have been prepared, the funding for the initial phase of the GIS establishment secured, and the

As for the **hydrological and meteorological issues**, advances in the exchange of hydrometeorological information and data within the basin have been made, including a revival of the *Hydrological Yearbook of the Sava River Basin* (ISRBC, 2010b) after more than 20 years.

In addition to navigation, efforts have also been made to develop **other economic activities** that can benefit from the use of river infrastructure. Being aware of great potentials for development of tourism in the basin in an environmentally friendly manner, the first *Nautical and Tourist Guide of the Sava River* has been developed in cooperation with regional chambers of commerce of the Parties (ISRBC, 2011c), while the preparation of a master plan for development of nautical tourism in the basin is planned to be undertaken as the next step. The preparation of another project, focusing on the contribution of small and medium enterprises to sustainable development of the Sava river basin, which has recently been initiated, targets not only river transport and tourism, but also other economic activities, including fish farming and shipbuilding.

### **4.1.2 Water protection and hazard management**

The key activity in the field of **river basin management** has been the preparation of the first *Sava RBM Plan* in accordance with the *EU WFD*, given the commitment of the Parties to respect the *WFD*, although some of them (i.e. the non-EU member states) are not legally bound to do so. An important step in this regard was the development of the *Sava River Basin Analysis Report* (ISRBC, 2009d), a comprehensive document dealing with both water quality and quantity issues, hydrology and hydromorphology of the basin, and providing the first overview and thematic GIS maps of the basin (ISRBC, 2009e). To ensure an integrated approach from the very beginning of the *RBM Plan* preparation process, the Sava River Basin Analysis also included consideration of the flood management and navigation development issues. Further preparation of the first *Sava RBM Plan*, supported by the European Commission, is in progress. Following the drafting of the *Plan* in fall 2011, and the subsequent public consultation process, the *Sava RBM Plan* is expected to be finalized and adopted by the Parties in 2012.

As regional climate modelling suggests an overall reduction of around 15% to 30% in mean annual runoff in the Sava river basin by the middle of this century, which could be challenging for all investments made in the basin, the development of a *Climate Adaptation Plan for the Sava River Basin* has been undertaken by the World Bank. The main aim of this effort is to fill the knowledge gap on the climate change impact on the water sector in the basin and to show how to increase the climate resilience of critical water management infrastructure investments and of integrated water resource management in the region, by elaborating alternatives for adaptive management actions in water management sub-sectors, including navigation, hydropower, agricultural water use, flood protection and environmental protection.

In addition to these activities, the *Protocol on Sediment Management to the FASRB*, stipulating the preparation of a sediment management plan for the basin in accordance with the *Sava RBM Plan*, has been prepared and is undergoing final harmonization by the Parties, while the *Protocol on transboundary impact to the FASRB* is under development on the ISRBC level.

For the purpose of an efficient **accident prevention and control** in the Sava river basin, participation in testing of the existing Accident Emergency Warning System of the ICPDR is continuously being done, and efforts are being made to improve the work of the Principal International Alert Centres in the Parties to the *FASRB*, including the organization of training courses for the operational staff of the Alert Centres, in cooperation with the

In addition to navigation, efforts have also been made to develop **other economic activities** that can benefit from the use of river infrastructure. Being aware of great potentials for development of tourism in the basin in an environmentally friendly manner, the first *Nautical and Tourist Guide of the Sava River* has been developed in cooperation with regional chambers of commerce of the Parties (ISRBC, 2011c), while the preparation of a master plan for development of nautical tourism in the basin is planned to be undertaken as the next step. The preparation of another project, focusing on the contribution of small and medium enterprises to sustainable development of the Sava river basin, which has recently been initiated, targets not only river transport and tourism, but also other economic activities,

The key activity in the field of **river basin management** has been the preparation of the first *Sava RBM Plan* in accordance with the *EU WFD*, given the commitment of the Parties to respect the *WFD*, although some of them (i.e. the non-EU member states) are not legally bound to do so. An important step in this regard was the development of the *Sava River Basin Analysis Report* (ISRBC, 2009d), a comprehensive document dealing with both water quality and quantity issues, hydrology and hydromorphology of the basin, and providing the first overview and thematic GIS maps of the basin (ISRBC, 2009e). To ensure an integrated approach from the very beginning of the *RBM Plan* preparation process, the Sava River Basin Analysis also included consideration of the flood management and navigation development issues. Further preparation of the first *Sava RBM Plan*, supported by the European Commission, is in progress. Following the drafting of the *Plan* in fall 2011, and the subsequent public consultation process, the *Sava RBM Plan* is expected to be finalized and

As regional climate modelling suggests an overall reduction of around 15% to 30% in mean annual runoff in the Sava river basin by the middle of this century, which could be challenging for all investments made in the basin, the development of a *Climate Adaptation Plan for the Sava River Basin* has been undertaken by the World Bank. The main aim of this effort is to fill the knowledge gap on the climate change impact on the water sector in the basin and to show how to increase the climate resilience of critical water management infrastructure investments and of integrated water resource management in the region, by elaborating alternatives for adaptive management actions in water management sub-sectors, including navigation, hydropower, agricultural water use, flood protection and

In addition to these activities, the *Protocol on Sediment Management to the FASRB*, stipulating the preparation of a sediment management plan for the basin in accordance with the *Sava RBM Plan*, has been prepared and is undergoing final harmonization by the Parties, while the *Protocol on transboundary impact to the FASRB* is under development on the ISRBC level. For the purpose of an efficient **accident prevention and control** in the Sava river basin, participation in testing of the existing Accident Emergency Warning System of the ICPDR is continuously being done, and efforts are being made to improve the work of the Principal International Alert Centres in the Parties to the *FASRB*, including the organization of training courses for the operational staff of the Alert Centres, in cooperation with the

including fish farming and shipbuilding.

adopted by the Parties in 2012.

environmental protection.

**4.1.2 Water protection and hazard management**

ICPDR. The *Protocol on Emergency Situations to the FASRB*, aiming to enhance prevention, preparedness, response and mutual assistance of the Parties in case of emergency situations, has been drafted and entered the process of harmonization by the Parties. As an important future activity, development of a water contingency management plan for the basin is planned.

In the field of **flood management**, the *Flood Action Plan* for the Sava river basin (ICPDR & ISRBC, 2009) has been prepared in accordance with the *Flood Action Programme for the Danube River Basin* of the ICPDR, providing the first programme of measures for each Party to achieve the defined targets for flood management in its part of the Sava basin until 2015.

The *Protocol on Flood Protection to the FASRB* (ISRBC, 2010a), which aims to provide the legal basis for cooperation of the Parties in line with the *EU Flood Directive*, including the preparation of the *Flood Risk Management Plan* for the Sava river basin, has been developed and signed, and is currently under ratification. A number of preparatory activities toward the *Flood Risk Management Plan* have been performed so far, including an assessment of current flood management practices in the Parties, establishment of a database on the existing flood protection facilities, preparation of a GIS-based, indicative flood extent map for the whole Sava river (Fig. 13), development of a preliminary hydrological model of the Sava river basin and the hydraulic model of the Sava river, and launching an UNECEsupported project, aiming to assist linking the flood risk management planning and the climate change assessment in the basin.

Fig. 13. Indicative map of important flood prone areas along the Sava river (ISRBC, 2009d)