*2.2. Cosmetic Samples*

Cosmetics and personal care products from national and international brands were obtained from local sources. They included sunscreens intended for adults and for children, hair-care products, moisturizing face creams, antiwrinkle creams, make-up, lip protectors, make-up, lipsticks, among others. The samples were kept in their original containers and protected from light at room temperature.

## *2.3.* μ*-MSPD Procedure*

Cosmetic samples (0.1 g) were exactly weighed into a glass vial. Then, the sample was gently blended with 0.4 g of the drying agent anhydrous Na2SO4, and 0.4 g of the corresponding dispersing agent (Florisil or sand), into the vial, using a glass rod, until a homogeneous mixture was obtained (*ca*. 5 min). The mixture was then transferred into a glass Pasteur pipette (approximately 150 mm), with a small amount of glass wool at the bottom, containing 0.1 g of Florisil (to obtain a further degree of fractionation and an in-situ clean-up step). Finally, a small amount of glass wool was placed on top to compress the mixture. Elution with the corresponding solvent (ethyl acetate, ACN, MeOH or the mixture MeOH/acetone (1:1, v/v)) depending on the experiment was made by gravity flow, collecting the extract into a 1 mL or 2 mL volumetric flask. The obtained extracts were diluted 1:10 (v/v) and 1:100 (v/v) in ACN (or even more when necessary), and analyzed by GC–MS/MS. Fortified samples were spiked with 10 μL of the corresponding spiking solution to get the desired final concentration of the target compounds, and submitted to the same process described above. Figure 1 illustrates the described μ-MSPD procedure under the optimal conditions.

**Figure 1.** Schematic representation of the micro-matrix solid-phase dispersion (μ-MSPD) procedure under the optimal conditions.

## *2.4. GC–MS*/*MS Analysis*

The GC–MS/MS analysis was carried out employing a Thermo Scientific Trace 1310 gas chromatograph coupled to a triple quadrupole mass spectrometer (TSQ 8000) with IL 1310 autosampler from Thermo Scientific (San Jose, CA, USA). Separation was performed on a Zebron ZB-Semivolatiles (30 m × 0.25 mm i.d., 0.25 μm film thickness) obtained from Phenomenex (Torrance, CA, USA). Helium (purity 99.999%) was employed as carrier gas at a constant column flow of 1.0 mL min−1. The GC oven temperature was programmed from 60 ◦C (held 1 min) to 100 ◦C at 8 ◦C min−1, to 150 ◦C at 20 ◦C min−1, to 200 ◦C at 25 ◦C min−1 (held 5 min), to 220 ◦C at 8 ◦C min−1, and to 290 ◦C at 30 ◦C min−1 (held 3 min). Pulsed splitless mode (200 kPa, held 1 min) was used for injection and the injector temperature was set at 260 ◦C. The injection volume was 1 μL and the total run time was 23.5 min.

The mass spectrometer (MSD) was operated in the electron impact (EI) ionization positive mode (+70 eV). The temperatures of the transfer line and the ion source were set at 290 ◦C and 350 ◦C, respectively. Selected reaction monitoring (SRM) acquisition mode was implemented monitoring three transitions per compound (see Table 1 for UV filters, and Table S1 for the other compounds). The system was operated by Xcalibur 2.2 and Trace FinderTM 3.2 software.

## *2.5. Statistical Analysis*

Basic and descriptive statistical analysis were performed using Statgraphics Centurion XVII (Manugistics, Rockville, MD, USA) as software package.

### **3. Results and Discussion**

### *3.1. Chromatographic Analysis*

The chromatographic GC–MS/MS method for the determination of the target UV filters was previously proposed by the authors [16–18], and it was extended to other compounds including 25 fragrance allergens, 13 preservatives, 15 plasticizers, and 11 synthetic musks, making a total of 78 compounds. The chromatographic conditions have been previously described in Section 2.4. SRM acquisition mode was employed monitoring two or three transitions per compound (see Table 1 and Table S1).

#### *3.2. Optimization of the* μ*-MSPD Procedure*

The influence of the main parameters potentially affecting the μ-MSPD procedure must be evaluated to obtain an efficient extraction. Several factors, such as the amount of sample, desiccant and dispersing agents were maintained constant, based on previous studies [3,12–14]. The amount of sample was 0.1 g, which was mixed with 0.4 g of Na2SO4 to remove the moisture of the samples, which could negatively affect the extraction. Regarding the dispersing agent, its amount was fixed at 0.4 g. The studied parameters were the extraction solvent (factor A), the dispersing agent (factor B), and the extraction volume (factor C), and the different levels are summarized in Table 2. The choice of an appropriate solvent is essential in the development of extraction methods. For an efficient extraction, the solvent must solubilize the target compounds while leaving the sample matrix as intact as possible. Four solvents were investigated: ACN, ethyl acetate (EtAc), methanol (MeOH), and the mixture MeOH/acetone (1:1, v/v). The dispersing agent can be also a very important factor affecting the extraction. In addition, it can contribute to obtain cleaner extracts, preventing lipids and other co-extractable matrix materials from coming out to the extract. Based on our previous works [6,12,14,15], this factor was considered at two levels: Florisil and sand. The solvent volume was also studied at two levels: 1 mL and 2 mL. Larger solvent volumes were not evaluated since the purpose of this study was the development of a green miniaturized extraction protocol. Lower solvent volumes were also not considered since they are not suitable for practical purposes, making necessary the use of inserts to perform further chromatographic analysis.

**Table 2.** Experimental factors and levels included in the experimental design.

The influence of the three variables was studied using a multifactor strategy. The study consisted of a multifactor 4\*22 design, involving 16 randomized experiments and allowing three degrees of freedom to estimate the experimental error. The design has resolution V, which means that it is capable of evaluating all main effects and all two-factor interactions. Numerical analysis of data resulting from the experimental design was made employing the software package Statgraphics Centurion XVII (Manugistics, CA, USA). The experiments were performed using composite sample prepared as a mixture of four real samples including a sunscreen, a facial cream, a body lotion, and a lip protector. Since the composite sample contained six of the target compounds from the different families of the UV filters studied, it was decided to work with the sample as it, without compounds addition, to really evaluate the capability of the miniaturized procedure to break analyte-matrix interactions, providing efficient extractions. Besides, other compounds such as 11 fragrance allergens, seven preservatives, three plasticizers, and two synthetic musks, were detected in the composite sample. The analysis of variance, ANOVA, describes the impact of the studied factors on the obtained responses. Results for the UV filters are shown in the ANOVA table, Table 3. For the sake of simplicity, only F-ratios and p-values are given. The F-ratio measures the contribution of each factor and interaction on the variance of the response. The p-value tests the statistical significance of each factor and interaction. When p-value is lower than 0.05, the factor has a statistically significant effects at the 95% confidence level.

**Table 3.** ANOVA summary table obtained for the micro-matrix solid-phase dispersion (μ-MSPD) procedure.

p-values lower than 0.05 (in bold) denotes statistical significance.

As can be seen, the three studied factors were significant for all the UV filters present in the sample in most cases. The interaction solvent-dispersant (AB) was significant for all the compounds. The other two second order factors (solvent-volume, AC and dispersant-volume, BC) were not significant. Figure 2 shows some selected mean plot graphs, that illustrate the effect of the main factors by showing the mean values as well as the confidence intervals for each level, easily visualizing the most favorable extraction conditions. For all the UV filters, the most efficient solvent was ACN providing higher responses (see Figure 2a). Regarding the dispersing agent, Florisil gave also higher responses for all the analytes (see Figure 2b). As regards the interaction AB, some examples are included in Figure 2c. The two-factor plots display the least squared means at all combinations of two factors, which allows studying the effect of both factors simultaneously. In this case, two different behaviors can be observed. For 2-ethylhexyl 4-methoxycinnamate (2EHMC), 4-methylbenzylidene camphor (4MBC), octocrylene (OCR) and isoamyl-4-methoxycinnamate (IAMC), the use of Florisil provided the highest response regardless of the solvent used (see as example OCR graph in Figure 2c). In the case of ethylhexylsalicylate (EHS) and benzophenone-3 (BP3), the use of sand was more favorable when MeOH or the mixture MeOH/acetone (1:1, v/v) was employed but, in any case, higher responses were obtained using ACN or EtAc with Florisil (see as example BP3 graph in Figure 2c). Regarding solvent volume, 2 mL was initially more favorable, although the differences in the responses were not very high (see Figure 2d).

Since Florisil was the most favorable dispersing agent for all analytes, the results were analyzed considering only the experiments carried out with this sorbent. The ANOVA results were similar for all the analytes and are graphically displayed for IAMC and EHS as example in Figure 3a. The plot shows scaled effects for each factor, so the natural variance of the points in the diagram can be comped to that of the residuals, displayed at the bottom of the plot. By comparing the variability amongst the factors to that of the residuals, it is easy to identify those factors showing differences of a greater magnitude than could be solely accounted by the experimental error. As can be observed, the solvent nature was significant, but the amount of solvent was not a significant factor. The levels of the factors at the right part of the ANOVA plot indicate the conditions that offer higher response and therefore, more efficient extraction. In the mean plot in Figure 3b the influence of the solvent is clearly appreciate. ACN and EtAc provided similar results, whereas for the other solvents the responses were clearly lower.

**Figure 2.** Mean plots (**a**,**b**,**d**) and interaction plots (**c**) of the main factors studied in the multi-factor categorical design for some representative ultraviolet (UV) filters.

Therefore, in view of the results, the selected conditions for the analysis of UV filters comprise the use of Florisil as dispersing agent, and ACN or EtAc as eluting solvent. Under these conditions the amount of solvent was not significant and, therefore, the low solvent volume, 1 mL, was selected. Regarding the other cosmetic ingredients and additives present in the composite sample, including fragrance allergens, preservatives, plasticizers and synthetic musks, the statistical analysis showed as more favourable conditions the once previously selected for the UV filters. Therefore, a general multianalyte method for the determination of all these families of personal care products (PCPs) can be proposed.

**Figure 3.** (**a**,**b**) ANOVA plots showing the main effects for isoamyl-4-methoxycinnamate (IAMC) and ethylhexylsalicylate (EHS).

### *3.3. Method Performance*

The μ-MSPD-GC–MS/MS method was validated in terms of linearity, accuracy and precision. Method performance is summarized in Table 4 for UV filters, and Table 5 for the other compounds.

**Table 4.** μ-MSPD-gas-chromatography tandem mass spectrometry (GC–MS/MS) performance for the UV filters. Linearity, precision, and recovery studies.

a n = 6; b not calculated since the compound was detected in the sample or c below linear range.

The calibration study was performed employing standard solutions prepared in acetonitrile containing the 78 compounds at different levels, covering a concentration range from 0.001 to 10 mg L−1 (see specific ranges for each compound in Tables 4 and 5) with twelve levels and three replicates per level. The method exhibited a direct proportional relationship between the concentration of each analyte and the chromatographic response with determination coefficients R2 ≥ 0.9915 for all compounds. Calibration plots for some representative compounds are shown in Figure S1.

**Table 5.** μ-MSPD-GC–MS/MS performance for the fragrance allergens, preservatives, plasticizers and synthetic musks. Linearity, precision, and recovery studies.

Intra-day, and inter-day precision was also evaluated. The relative standard deviation (RSD) values for the inter-day are shown in Tables 4 and 5, and they were lower than 10% for all the analyzed UV filters, and lower than 14% for the other compounds.

Recovery studies were carried out by implementing the optimized μ-MSPD-GC–MS/MS method to a real cosmetic sample (a moisturizing hand cream). Sample was fortified at three different concentration levels (1, 10 and 100 μg g−1) for the UV filters and the μ-MSPD-GC–MS/MS procedure was performed. Recoveries were calculated as the ratio of concentration found/added considering the responses obtained for each analyte, and they are shown in Table 4 Quantitative recoveries were obtained in all cases, with mean values between 97% and 111%. The precision was also evaluated, and the obtained relative standard deviation (RSD) values were lower than 10% for all the analytes.

Recovery studies were also performed for the fragrance allergens, preservatives, plasticizers and synthetic musks, at two different concentration levels (10 and 100 μg g−1). Results are summarized in Table 5. As can be seen, good recoveries with mean values between 70% and 110% were obtained for all the studied compounds. The RSD values were also lower than 10% in all cases.

#### *3.4. Application to Real Samples*

To show the suitability of the proposed methodology, 13 different cosmetic and personal care products were analyzed, including moisturizing face creams, sunscreens with different solar protection factor (SPF), including products intended from children, blemish base (BB) creams, hair-care products, protection lipsticks, hands cream, make-up, or vitalizing creams. Concentration (μg g−1) of the target UV filters, and the other analyzed PCPs are summarized in Table 6.

Eleven out of the 14 studied UV filters were detected in the analyzed samples. The UV filter most frequently found was 2-EHMC, in 11 of the 13 samples, with concentration levels up to 46,364 μg g −1 (4.6%, w/w) followed by EHS in eight samples. The concentration for this UV filter was higher than 20,000 μg g−1 (2%, w/w) in four samples (S2, S4, S5, and S7). OCR and avobenzone (BMDM) were found in seven samples, at concentrations up to 50,000 μg g−1, excluding BMDM in samples S2, and S4. The other UV filters homosalate (HMS), BP3, benzyl salicylate (BS), and IAMC, were found in six, five, four and three samples, respectively, with concentration ranging from 0.5 to 52,000 μg g−1, whereas 4MBC, DHHB and DRT were only found in one sample each one. Regarding the number of compounds per sample, sample S3 (BB cream) contained eight out of the 11 detected UV filters, followed by sample S2, sample S6 and sample S8, which contained 6 compounds. Highlights especially the high UV filters concentration (between 25,000–99,000 μg g−1) found in Sample S2. This sample was a SPF 50 sunscreen. In the other samples, between 1–5 UV filters were detected. Although for some compounds, while very high concentrations were found, all of them comply with the European requirements according to the Regulation EC No 1223/2009 [1].

Regarding the other studied PCPs, 14 of the 25 target fragrance allergens were found. Highlights the presence of limonene and benzyl alcohol in 12 of the 13 analyzed samples, with concentrations ranging between 0.2 to 213 μg g−1. The other fragrance allergens were found in between 1–4 samples. It is important to note the presence of Lyral®, fragrance which has been recently banned, in one cream at 87 μg g−1. Sample S3, a BB cream, contained the highest number of fragrances, nine of them at also the highest concentration for them, 270 μg g−1 for α-isomethylionone. The other analyzed samples contained between one (sample S2) and six (samples S4 and S9) fragrances.

**Table 6.** *Cont.*

S1: moisturizing facial cream; S2: SPF 50 sunscreen; S3: BB cream; S4: SPF 50 sunscreen intended for children; S5: leave-on hair serum; S6: moisturizing make-up; S7: anti-wrinkle facial cream; S8: solar stick; S9: antiaging hand and nail cream: S10: lipstick; S11: facial cream; S12: make-up; S13: vitalizing cream.

Seven of the 13 target preservatives were found in the analyzed samples. The most frequently found were phenoxyethanol (PhEtOH) and butylhydroxytoluene (BHT) in 92% of the analyzed samples. The highest PhEtOH concentration reached up to 8461 μg g−1, close to its legal limit (10,000 μg g−1), in sample S2, whereas for BHT its concentration was lower than 80 μg g−1 in all cases. Methyl paraben (MeP) was found in nine samples, reaching 3100 μg g−1, also close to its maximum permitted concentration (4000 μg g−1), in sample S1, whereas the other parabens (EtP, PrP, BuP, and iBuP) were found in six, five, and three samples respectively. The samples containing more preservatives were sample S6 and sample S7, containing both seven preservatives, whereas on the other hand, samples S4 and S10 only contained BHT and PhEtOH, respectively.

Regarding the synthetic musks, only celestolide, cashmeran and ambrettolide were detected in the analyzed samples. Galaxolide was found in three samples at concentrations up to 534 μg g−1, whereas the other two were only detected in one sample each one.

Only four plasticizers out of the 15 studied were detected in the analyzed samples. The diethylhexyl adipate (DEHA) was found in nine samples, with concentrations up to 2630 μg g−1. Regarding the other detected phthalates, DEP was found in five samples, whereas two of the phthalates forbidden for their use as ingredients in cosmetics according to the Regulation EC No 1223/2009, dibutyl phthalate (DBP) and diethylhexyl phthalate (DEHP) were found in three and nine samples, respectively. The detected concentrations were lower than 9 μg g−1 in all samples, and the presence of these compounds may be related with a possible transfer between the plastic package and the cosmetic.


1. Introduction

The traditional Proportional Navigation Guidance (PNG) schemes including their extensions have been widely employed in interceptors because of their efficiencies and simplifications (only need line-of-sight information). PNG makes the normal load of interceptor proportional to the line-of-sight (LOS) angular velocity [1]. Nevertheless, the target can add the miss distance by acting evading maneuver because the target maneuvers are ahead of the guidance commands from PNG. For achieving desired interception performances, even for

© 2018 The Author(s). Licensee InTech. 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.

© The Author(s). Licensee InTech. 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 eproduction in any medium, provided the original work is properly cited.

the target maneuver, it is necessary to develop advanced guidance schemes [1, 2]. These advanced guidance schemes usually require more information, like relative speed and distance, target's acceleration, or time-to-go.

Integrated guidance and control (IGC) which is based on the SMC has become an unusual approach for developing a guidance system. The traditional timescale separation method splits the guidance system into an inner loop autopilot and an outer loop command system. The IGC system merges the two loops into a unique loop. Based on self-motion and relative motion states, the IGC produces commands to aero surfaces straight. Zero effort miss is used to be a sliding surface for developing the IGC [10, 11]. Due to the complex coupling between guidance and control states, this method does not spread more widely than an intuitive timescale

Adaptive Robust Guidance Scheme Based on the Sliding Mode Control in an Aircraft Pursuit-Evasion Problem

http://dx.doi.org/10.5772/intechopen.72177

27

Based on the SMC, the guidance scheme with impacting angle constraint is designed to solve the problem of directional impacting. In practical cases, a specific impacting angle is desired to directionally hit the target or to better detect thee target. Under the impacting angle constraint, the result from ideal initial attack conditions can meet the interception requirements for nonmaneuvering and step-maneuvering targets [12–14]. However, the guidance accuracy of

To sum up, although guidance schemes based on the SMC and target's maneuver estimation algorithms act excellently in simulation, the computation degrees of them have become too complex to realize. In fact, one needs a simple-expression guidance scheme based on the SMC, and if not requiring the target acceleration, it will be better. In addition, the discontinuous characteristic induced by the sliding mode part can cause jitter of guidance commands that is detrimental to the aero fins. The coefficient of sliding mode part indicates target acceleration's boundary. Actually, it is hard to get the boundary. If setting the boundary too great, the autopilot might be saturated; if setting the boundary too tiny, the sliding mode's presence cannot be guaranteed. With the target acceleration's unknown boundary, for ensuring the stability, the simplified guidance schemes based on the SMC including the FOSMG, OSMG, and ASMG have greater sliding mode part, which might cause jitter. Adaptive control offers a solution. The unknown parameters can be estimated in the online identification for the uncertain system. Nevertheless, it has no capability to suppress disturbances. Thus, the adaptive control to identify the upper boundary of the system

An interceptor-target pursuit-evasion game which only employs the line-of-sight angular velocity is under consideration in this chapter. The target maneuver is treated as a bounded perturbation. More states are demanded, including initial relative speed and distance and error boundaries of them. It is derived from recursive estimation of relative motion kinematics and obtains approximations of relative speed and distance. A simplified sliding mode guidance scheme is given, which requires target acceleration's boundary and inevitably has jitter phenomenon. For overcoming the above shortcomings, an adaptive parameter is utilized to estimate target acceleration's boundary and to adaptively adjust in terms of the lineof-sight angular velocity; moreover, the Lyapunov stabilization has been analyzed. The proposed guidance scheme's brief characteristic is to decrease the effect of relative speed and distance on the guidance precision and to strengthen the influence of line-of-sight

This chapter's rest part is listed hereafter. The problem statement is given in Section 2. Two robust guidance schemes based on the SMC are presented in Section 3. Section 4 carries out

separation method.

angular velocity.

the target's complicated maneuver will decrease.

uncertainty is merged with the SMC to suppress disturbances [15].

simulations, and conclusions are given in Section 5.

For passive seekers, which are equipped with electro-optical or infrared sensors, the line-ofsight angular velocity can be observed only. If an estimation equation is assumed to estimate target kinematics, relative speed and distance and target's acceleration will be identified. The commonly used estimation model is a Kalman filter. At the same time, one must select a target's motion model, like the current statistical model, the Singer model, or the interactive multi-model scheme [3]. For polishing up the estimating performance of the target's maneuvers, observability of the interception problem with LOS angular velocity measurement is analyzed [4]. It concludes that current homing guidance schemes result in a decrease in observability of tracking the target. Because relative distance cannot be observed from the line-of-sight measurement, it is necessary to use a special type of self-motion to solve this problem. Thus, the method of introducing LOS angular oscillatory motion is presented in [4] to improve the observability. The oscillatory motion of the LOS angle improves observability, but the trajectories generated by the guidance schemes are inevitably influenced by this motion mode and affect final guidance precision. Therefore, the target maneuver estimation is constrained by a lot of practical limitations.

The sliding mode control (SMC) is robust to disturbances. Therefore, it is employed to develop adaptive guidance schemes for target's unpredictable maneuver without requirements to estimate the target's acceleration. Recently, many guidance schemes based on the SMC have been proposed, for instance, the guidance schemes based on the adaptive and optimal SMC [5– 7], the high-order SMC [8, 9], SMC-based integrated guidance and control (IGC) [10, 11], and SMC with impacting angle constraint [12–14].

SMC-based optimal and adaptive guidance schemes have become a focus since the 1990s. An adaptive sliding mode guidance (ASMG) scheme is presented in [5] for target maneuvering and parameter disturbance of the guidance system. In addition, an optimal sliding mode guidance (OSMG) scheme is deduced from the ASMG, and the optimal guidance coefficients are given in [6]. In [7], the Fuzzy OSMG (FOSMG) formulated by the OSMG and PNG is stated by adjusting the weights of the OSMG and PNG using fuzzy logic. It is noted that the FOSMG owns the advantages of the PNG for nonmaneuvering targets and the OSMG for maneuvering targets. The ASMG, OSMG, and FOSMG have practical advantages of simple expressions. Nevertheless, it is essential to identify the target's normal load to adjust weights of the FOSMG.

The higher order sliding mode guidance (HOSMG) scheme is a current research highlight. While the SMC-based first-order guidance is a balance between smoothing jitter and ensuring robustness through switching frequently, the HOSMG generates control commands smoothly to systems with relative degree arbitrarily. A smooth guidance scheme based on a second-order sliding mode is developed for solving the uncertainties of the actuator and the target's maneuver [8]. In [9], a terminal guidance law with known convergent time is proposed by using the finite-time mean-square practical convergence as sliding surfaces. It validates that HOSMG is robust to stochastic noises and bounded uncertainty and does not have high-frequency jitters. The HOSMG's flaw exists in converging slowly for real time due to complex algorithms.

Integrated guidance and control (IGC) which is based on the SMC has become an unusual approach for developing a guidance system. The traditional timescale separation method splits the guidance system into an inner loop autopilot and an outer loop command system. The IGC system merges the two loops into a unique loop. Based on self-motion and relative motion states, the IGC produces commands to aero surfaces straight. Zero effort miss is used to be a sliding surface for developing the IGC [10, 11]. Due to the complex coupling between guidance and control states, this method does not spread more widely than an intuitive timescale separation method.

the target maneuver, it is necessary to develop advanced guidance schemes [1, 2]. These advanced guidance schemes usually require more information, like relative speed and dis-

For passive seekers, which are equipped with electro-optical or infrared sensors, the line-ofsight angular velocity can be observed only. If an estimation equation is assumed to estimate target kinematics, relative speed and distance and target's acceleration will be identified. The commonly used estimation model is a Kalman filter. At the same time, one must select a target's motion model, like the current statistical model, the Singer model, or the interactive multi-model scheme [3]. For polishing up the estimating performance of the target's maneuvers, observability of the interception problem with LOS angular velocity measurement is analyzed [4]. It concludes that current homing guidance schemes result in a decrease in observability of tracking the target. Because relative distance cannot be observed from the line-of-sight measurement, it is necessary to use a special type of self-motion to solve this problem. Thus, the method of introducing LOS angular oscillatory motion is presented in [4] to improve the observability. The oscillatory motion of the LOS angle improves observability, but the trajectories generated by the guidance schemes are inevitably influenced by this motion mode and affect final guidance precision. Therefore, the target maneuver estimation is

The sliding mode control (SMC) is robust to disturbances. Therefore, it is employed to develop adaptive guidance schemes for target's unpredictable maneuver without requirements to estimate the target's acceleration. Recently, many guidance schemes based on the SMC have been proposed, for instance, the guidance schemes based on the adaptive and optimal SMC [5– 7], the high-order SMC [8, 9], SMC-based integrated guidance and control (IGC) [10, 11], and

SMC-based optimal and adaptive guidance schemes have become a focus since the 1990s. An adaptive sliding mode guidance (ASMG) scheme is presented in [5] for target maneuvering and parameter disturbance of the guidance system. In addition, an optimal sliding mode guidance (OSMG) scheme is deduced from the ASMG, and the optimal guidance coefficients are given in [6]. In [7], the Fuzzy OSMG (FOSMG) formulated by the OSMG and PNG is stated by adjusting the weights of the OSMG and PNG using fuzzy logic. It is noted that the FOSMG owns the advantages of the PNG for nonmaneuvering targets and the OSMG for maneuvering targets. The ASMG, OSMG, and FOSMG have practical advantages of simple expressions. Nevertheless, it is essential to identify the target's normal load to adjust weights of the

The higher order sliding mode guidance (HOSMG) scheme is a current research highlight. While the SMC-based first-order guidance is a balance between smoothing jitter and ensuring robustness through switching frequently, the HOSMG generates control commands smoothly to systems with relative degree arbitrarily. A smooth guidance scheme based on a second-order sliding mode is developed for solving the uncertainties of the actuator and the target's maneuver [8]. In [9], a terminal guidance law with known convergent time is proposed by using the finite-time mean-square practical convergence as sliding surfaces. It validates that HOSMG is robust to stochastic noises and bounded uncertainty and does not have high-frequency jitters. The

HOSMG's flaw exists in converging slowly for real time due to complex algorithms.

tance, target's acceleration, or time-to-go.

26 Adaptive Robust Control Systems

constrained by a lot of practical limitations.

SMC with impacting angle constraint [12–14].

FOSMG.

Based on the SMC, the guidance scheme with impacting angle constraint is designed to solve the problem of directional impacting. In practical cases, a specific impacting angle is desired to directionally hit the target or to better detect thee target. Under the impacting angle constraint, the result from ideal initial attack conditions can meet the interception requirements for nonmaneuvering and step-maneuvering targets [12–14]. However, the guidance accuracy of the target's complicated maneuver will decrease.

To sum up, although guidance schemes based on the SMC and target's maneuver estimation algorithms act excellently in simulation, the computation degrees of them have become too complex to realize. In fact, one needs a simple-expression guidance scheme based on the SMC, and if not requiring the target acceleration, it will be better. In addition, the discontinuous characteristic induced by the sliding mode part can cause jitter of guidance commands that is detrimental to the aero fins. The coefficient of sliding mode part indicates target acceleration's boundary. Actually, it is hard to get the boundary. If setting the boundary too great, the autopilot might be saturated; if setting the boundary too tiny, the sliding mode's presence cannot be guaranteed. With the target acceleration's unknown boundary, for ensuring the stability, the simplified guidance schemes based on the SMC including the FOSMG, OSMG, and ASMG have greater sliding mode part, which might cause jitter. Adaptive control offers a solution. The unknown parameters can be estimated in the online identification for the uncertain system. Nevertheless, it has no capability to suppress disturbances. Thus, the adaptive control to identify the upper boundary of the system uncertainty is merged with the SMC to suppress disturbances [15].

An interceptor-target pursuit-evasion game which only employs the line-of-sight angular velocity is under consideration in this chapter. The target maneuver is treated as a bounded perturbation. More states are demanded, including initial relative speed and distance and error boundaries of them. It is derived from recursive estimation of relative motion kinematics and obtains approximations of relative speed and distance. A simplified sliding mode guidance scheme is given, which requires target acceleration's boundary and inevitably has jitter phenomenon. For overcoming the above shortcomings, an adaptive parameter is utilized to estimate target acceleration's boundary and to adaptively adjust in terms of the lineof-sight angular velocity; moreover, the Lyapunov stabilization has been analyzed. The proposed guidance scheme's brief characteristic is to decrease the effect of relative speed and distance on the guidance precision and to strengthen the influence of line-of-sight angular velocity.

This chapter's rest part is listed hereafter. The problem statement is given in Section 2. Two robust guidance schemes based on the SMC are presented in Section 3. Section 4 carries out simulations, and conclusions are given in Section 5.


*Data sets examined*

All data on the olive and oleaster can be analyzed as i) botanical samples to look for a key to differentiate them ;ii) similarity records to try to differentiate the two forms from a statistical point of view, and iii) genetic relationships using Bayesian methods.

The botanical differentiation between the oleaster and the olive, although with numerous attempts, does not reveal key traits neither morphologic nor molecular [31, 47, 67].

Similarity records have been shown more effective in differentiating between the two forms. Clear cut separation has occurred though some trees remained not clustered, which may indicate that there are hybrid forms between trees from the two groups or that all trees did not share all the traits recorded either morphological or molecular. Low frequency markers should be eliminated in such analyses as they may weigh too much and may distort the results. These methods lead to references of phylogenetic relationships between different levels of taxa, even though, they are not accurate for distant taxa (species, genera), but they have shed light on variety relationships for the olive [47, 64, 68, 69].

[57] Breton has examined a wide sampling of about 1900 trees including wild olives (950 from 55 sites), old trees (50) with undetermined status, and cultivars (about 900, either abandoned, feral forms or from collections) sampled in most places around the Mediterranean basin (Figure 3). Using 16 nu-DNA loci (Single Sequence Repeat or SSR) and 3 cp-DNA loci (single base repeats), the comprehensive data set was examined using structure software [63] by different a priori packages made of oleaster trees, cultivars, oleaster and feral trees. All clusters revealed by this study were checked by other aggregation methods (FCA, Dendrograms) to verify their consistency. However, these methods cannot ensure the biological existence of such groups. [70] have examined about 250 cultivars and two oleaster populations with AFLP markers (there are mostly dominant markers) from the central Mediterranean with similar methods. [71] has examined 171 wild trees with 8 SSR from the north-western Mediterranean [30] has studied about 32 cultivars and 70 oleaster trees from Tunisia, with morphological and molecular methods.

12 Olive Germplasm – The Olive Cultivation, Table Olive and Olive Oil Industry in Italy

the end of the last ice age may explain its present distribution.

point of view, and iii) genetic relationships using Bayesian methods.

have shed light on variety relationships for the olive [47, 64, 68, 69].

new information.

*Data sets examined*

dominant markers but are estimated with dominant markers, i.e., Correspondence (FCA) and Hierarchic analyses (leading to dendrograms). Bayesian methods for nuclear DNA (nu-DNA) appeared in 2000 to analyze the data sets and they enable to constitute clusters (based on inferences of allele frequencies) and to check in each individual under examination the proportion of the genome that is coming from the different groups made by the software [63]. These clusters under some hypotheses may correspond to ancestor origins. However, Bayesian method can mix data from nu-, and cp- or mt-DNA. All the methods have contributed in eliciting the olive's origin and they have opened the way to use more adequate methods [64]. Obviously, old data sets could be treated with new methods to get

By the year 2000, after several completed projects (European projects and country projects), the molecular diversity in the wild form appeared deeply structured, that means the geographic distribution of the molecular markers in the wild tree was not homogenous [1, 24, 65, 66]. The genetic structure (estimated by the Fst) was stronger with mt- and cp-DNA markers than with the nu-DNA. Moreover, the mt- and cp-DNA distribution in the eastern and the western halves of the Mediterranean Sea appeared strongly structured. Even if sampling problems for all the studies had biased their data, the trend from the whole data supports that clines for allele frequencies do exist in the wild olive diversity. The clines could be due to different causes and as for other tree species the spread of the wild olive at

All data on the olive and oleaster can be analyzed as i) botanical samples to look for a key to differentiate them ;ii) similarity records to try to differentiate the two forms from a statistical

The botanical differentiation between the oleaster and the olive, although with numerous

Similarity records have been shown more effective in differentiating between the two forms. Clear cut separation has occurred though some trees remained not clustered, which may indicate that there are hybrid forms between trees from the two groups or that all trees did not share all the traits recorded either morphological or molecular. Low frequency markers should be eliminated in such analyses as they may weigh too much and may distort the results. These methods lead to references of phylogenetic relationships between different levels of taxa, even though, they are not accurate for distant taxa (species, genera), but they

[57] Breton has examined a wide sampling of about 1900 trees including wild olives (950 from 55 sites), old trees (50) with undetermined status, and cultivars (about 900, either abandoned, feral forms or from collections) sampled in most places around the Mediterranean basin (Figure 3). Using 16 nu-DNA loci (Single Sequence Repeat or SSR) and 3 cp-DNA loci (single base repeats), the comprehensive data set was examined using

attempts, does not reveal key traits neither morphologic nor molecular [31, 47, 67].

**Figure 3.** Anti Atlas Morocco elevation 1525masl. © Catherine Breton