**3. The @qua approach**

The European Union has defined a key objective for his industrial development on interoperability of systems. This approach is dedicated to various domain including environment and water. In order to support this vision, the European Commission has launched a Thematic Network called @qua under the CIP-ICT PSP Programme. The ICT Policy Support Programme (ICT PSP) under the Competitiveness and Innovation Programme (CIP) aims at stimulating innovation and competitiveness through the wider uptake and best use of ICT by citizens, governments and businesses, particularly Small and Medium-sized Enterprises (SMEs). The approach is based on leveraging innovation in response to growing societal demands.

In his programme frame of ICT Policy Support Programme (ICT PSP) 2011, the General Direction Information Society (DG INFSO) of the European Commission has launched a new theme network dedicated to Innovation Communication Technologies for water management. This domain represents a sector which the European Union wishes to develop during the next 10 years and it's contemplated in different initiatives of the Digital Agenda for Europe 2020 which will allow at the same time improving the user's services quality and developing a sustainable management of resources. These objectives will be achieved with the improvement of already available technologies, adaptation of the existing solutions and the identification of R&D axes to work on the next years.

@qua Innovation Network (http://www.a-qua.eu), founded by 17 partners and managed by Nice Sophia Antipolis University gathers thus ICT and water services leading actors from SME to majors, research entities developing competences in both sectors, local and regional authorities directly responsible for water policy and water management. Partners have developed significant expertise about the interface of ICT and water and at the same time, covering the full spectrum of the water related domain. @qua provides a forum to exchange and to share expertise in deploying innovative ICT solutions for water management, studies feasibility of standardized ICT solutions and interoperability in the field of water management across the EU and develops specifications and guidelines according to a jointly defined "level of sharing" among representatives of professional sectors. Focus of @qua is on gathering and sharing experiences on how to overcome barriers to the introduction of ICT solutions for innovative water management and on how to ensure their wider uptake and best use. Partners have the ambition to develop and to promote the interoperability principle and the use of common standards in the water industry. In a holistic and consistent approach, @qua addresses all the issues of the water management from resources to societal changes, using a wide range of ICT solutions: data acquisition, numerical modelling, real-time monitoring and field operation management.

#### **3.1 The @qua methodology**

The @qua thematic network members have developed a general methodology based around few steps which can be summarized as follow:

ICT for Water Efficiency 421

wavelength, to in depth R&D development like the use of alternative energy sources for power supply in waste water monitoring actions. The partners of the @qua network have significant experience of implementation and development actions. The spectrum of their expertise is covering most the business processes involved in the water domain. From this experience and according to their identified needs in innovative ICT solutions, they define, for each technology identified as a priority, the requested level for developing an efficient interface between the different components involved into the business process. Such work represents a major output for the @qua network and constitutes clearly an added value provision by the network to various professional communities. It is clear that in a wide community as the European water profession, the status of the various Information Systems has a very high variety. This step will analyse the "IS/IT context" parameters in the profession: maturity of the IS, level of integration (integration of the IS itself as well as integration in the business processes), level of alignment with the strategy, and the local parameters (ERP/ software already installed, other relevant IT projects, trends of the local IS/IT market, etc.). This step proposes the ideal "level of sharing", i.e. the level which will maximize the effectiveness and efficiency of the new ICT tools by taking into account the actual current IT/IS situation. This output defines the outcomes of the @qua network, which could go from the very theoretical methodologies, data models, architectures, principles of standardization, etc. - to the very concrete elements such as list of devices compliant with the selected telecom standards,

deployment of a common software and instructions of customization, etc.

most of the business processes involved in all water uses and domains.

use which where both expectations and possibilities are the highest:

Real time information of customers and stakeholders;

Installation of leak detectors in the network;

**3.2 The expected results and impacts**

conductivity, RedOx, etc.); Sensors at all Points Of Use (POU);

decision support systems.

a. Real time monitoring

In a final step, the production of the guidelines and specifications whose needs are identified in the previous steps. According to the results of the previous step, these results can go from very generic guidelines to more precise technical specifications such as hardware requirement for sensors, software architecture, strategy for implementation and deployment in water services, metadata architecture, business process description and standards. A similar approach has been partly applied with HarmonIT project (http://www.harmonit.org) on the specific field of the hydroinformatic systems interoperability and the development of the OpenMI standards (http://www.openmi.org). In the case of the @qua approach, the spectrum is much more wider because it's addressing

The water domain - and water stakeholders - is very wide and covers a huge number of business processes especially if all domains and activities are considered. This situation legitimates the mapping process and the prioritization of gaps that need to be bridged. Clearly the efforts have to be focused on five major areas directly linked to the urban water

Specially real time networks monitoring including Automated Meter Reading(AMR);

Real time quality management (disinfectant, turbidity, pH, temperature,

 Related technologies such as Supervisory Control And Data Acquisition (SCADA), GIS, telecommunications, sensors (especially low cost sensors), inverse models,

Step 4. Produce guidelines, standards and specifications on specific ICT solutions needed by the water domain in order to achieve a more efficient water management.

The two main characteristics of the defined approach are:

Fig. 4. The @qua methodology.

The initial step, led by water utilities and water engineering companies, is dedicated to the analysis of the business processes, both for the artificial cycle and the natural cycle of water, and both for design and for operations. The business processes are described at a macro scale, where the tiny differences between entities are not seen and where just the common "backbone" is visible. These business models are used as "base maps" in order to show the unequipped - or poorly equipped - steps in terms of ICT. A special attention is turned to the analysis of added value of these unequipped steps. The diagnostic characterizes the added value not only on the economic point of view, but also on sociological and ecological dimensions. In addition to the common map of the water business processes itself, the result of this step is the list of the steps / processes that "deserve" to be equipped with new ICT tools. This effort of analysis according to the business processes vision represents an essential input in the water domain. Until now this diagnostic was not established for several reasons and especially due to the low maturity of water industrial domain regarding ICT solutions and uses.

The second step is led by the ICT sector representatives and consists in a technologic analysis of the needs and requests written by the water companies' representatives. The step includes not only the assessment of the feasibility, the potential availability and the cost of the requests, but it will also propose other tracks, unimagined or not foreseen during the previous step. The water companies have a partial vision of ICT solutions and they need a better knowledge of the current trends of the ICT industry / market. Alternating the leadership of the steps between the "water people" - water companies and other stakeholders - and the "ICT people" brings an efficient synergy.

The third step is focused on the determination of the "level of sharing". This concept is a central element which is developed and used by the @qua network. For the time being, the use and the implementation of existing ICT solutions in the water domain is made case by case, with a quite variable customization which is covering a simple technical adaptation like

Step 4. Produce guidelines, standards and specifications on specific ICT solutions needed by the water domain in order to achieve a more efficient water management.

the definition and the use of concept of "level of sharing" to decide which ICT

• Water business processes and ICT solutions: identification of gaps and

Step 2 • Identification and validation of innovative ICT solutions & bridge the gaps

standards, architecture and roadmap for implementation issues

• Develop the "level of sharing" of each ICT solution and address interoperability,

• Produce guidelines, standards and specifications on ICT solutions needed by the

The initial step, led by water utilities and water engineering companies, is dedicated to the analysis of the business processes, both for the artificial cycle and the natural cycle of water, and both for design and for operations. The business processes are described at a macro scale, where the tiny differences between entities are not seen and where just the common "backbone" is visible. These business models are used as "base maps" in order to show the unequipped - or poorly equipped - steps in terms of ICT. A special attention is turned to the analysis of added value of these unequipped steps. The diagnostic characterizes the added value not only on the economic point of view, but also on sociological and ecological dimensions. In addition to the common map of the water business processes itself, the result of this step is the list of the steps / processes that "deserve" to be equipped with new ICT tools. This effort of analysis according to the business processes vision represents an essential input in the water domain. Until now this diagnostic was not established for several reasons and especially due to the low maturity of water industrial domain regarding

The second step is led by the ICT sector representatives and consists in a technologic analysis of the needs and requests written by the water companies' representatives. The step includes not only the assessment of the feasibility, the potential availability and the cost of the requests, but it will also propose other tracks, unimagined or not foreseen during the previous step. The water companies have a partial vision of ICT solutions and they need a better knowledge of the current trends of the ICT industry / market. Alternating the leadership of the steps between the "water people" - water companies and other

The third step is focused on the determination of the "level of sharing". This concept is a central element which is developed and used by the @qua network. For the time being, the use and the implementation of existing ICT solutions in the water domain is made case by case, with a quite variable customization which is covering a simple technical adaptation like

stakeholders - and the "ICT people" brings an efficient synergy.

the global analysis based on "business processes" and associated added value;

innovations could be widely disseminated throughout the water profession.

The two main characteristics of the defined approach are:

Fig. 4. The @qua methodology.

water domain

expectations

Step 1

Step 3

Step 4

ICT solutions and uses.

wavelength, to in depth R&D development like the use of alternative energy sources for power supply in waste water monitoring actions. The partners of the @qua network have significant experience of implementation and development actions. The spectrum of their expertise is covering most the business processes involved in the water domain. From this experience and according to their identified needs in innovative ICT solutions, they define, for each technology identified as a priority, the requested level for developing an efficient interface between the different components involved into the business process. Such work represents a major output for the @qua network and constitutes clearly an added value provision by the network to various professional communities. It is clear that in a wide community as the European water profession, the status of the various Information Systems has a very high variety. This step will analyse the "IS/IT context" parameters in the profession: maturity of the IS, level of integration (integration of the IS itself as well as integration in the business processes), level of alignment with the strategy, and the local parameters (ERP/ software already installed, other relevant IT projects, trends of the local IS/IT market, etc.). This step proposes the ideal "level of sharing", i.e. the level which will maximize the effectiveness and efficiency of the new ICT tools by taking into account the actual current IT/IS situation. This output defines the outcomes of the @qua network, which could go from the very theoretical methodologies, data models, architectures, principles of standardization, etc. - to the very concrete elements such as list of devices compliant with the selected telecom standards, deployment of a common software and instructions of customization, etc.

In a final step, the production of the guidelines and specifications whose needs are identified in the previous steps. According to the results of the previous step, these results can go from very generic guidelines to more precise technical specifications such as hardware requirement for sensors, software architecture, strategy for implementation and deployment in water services, metadata architecture, business process description and standards. A similar approach has been partly applied with HarmonIT project (http://www.harmonit.org) on the specific field of the hydroinformatic systems interoperability and the development of the OpenMI standards (http://www.openmi.org). In the case of the @qua approach, the spectrum is much more wider because it's addressing most of the business processes involved in all water uses and domains.

#### **3.2 The expected results and impacts**

The water domain - and water stakeholders - is very wide and covers a huge number of business processes especially if all domains and activities are considered. This situation legitimates the mapping process and the prioritization of gaps that need to be bridged. Clearly the efforts have to be focused on five major areas directly linked to the urban water use which where both expectations and possibilities are the highest:

	- Specially real time networks monitoring including Automated Meter Reading(AMR);
	- Installation of leak detectors in the network;
	- Real time quality management (disinfectant, turbidity, pH, temperature, conductivity, RedOx, etc.);
	- Sensors at all Points Of Use (POU);
	- Real time information of customers and stakeholders;
	- Related technologies such as Supervisory Control And Data Acquisition (SCADA), GIS, telecommunications, sensors (especially low cost sensors), inverse models, decision support systems.

ICT for Water Efficiency 423

A sensor is any device that can take a stimulus, such as heat, light, magnetism, or exposure to a particular chemical, and convert it to a signal. Sensors have certainly been around for a very long time with scales (weight sensors), thermometers (temperature sensors) and barometers(pressure sensors). More recently, scientists and engineers have come up with devices to sense light (photocells), sound (microphones), ground vibrations (seismometers), and force (accelerometers), as well as sensors for magnetic and electric fields, radiation,

While the concept of sensors is nothing new, the technology of sensors is undergoing a rapid transformation. Indeed, the forces that have already revolutionized the computer, electronics, and biotech industries are converging on the world of sensors from at least three different

Smaller. Rapid advances in fields such as nanotechnology and (micro electro-mechanical systems (MEMS)) have not only led to ultra-compact versions of traditional sensors, but have inspired the creation of sensors based on entirely new principles. The reduced size fits perfectly with the constraints of the water supply and open possibilities into the monitoring

Smarter. The exponentially increasing power of microelectronics has made it possible to create sensors with built-in "intelligence." In principle, at least, sensors today can store and process data on the spot, selecting only the most relevant and critical items to report. One of the emerging concepts in this domain is the ubiquitous computing paradigm. This approach is highly relevant for the water domain especially for all warning and monitoring systems

More Mobile. The rapid proliferation of wireless networking technologies has cut the tether. Today, many sensors send back their data from remote locations, or even while they're in

In the urban water domain, the new sensors are already deeply impacting several business processes with Automated Meter Readers (AMR), water quality control devices and operating supervision. Such trend is following the recent evolution observed in energy distribution sector. An emblematic evolution is the one taking place with the introduction of

Water meters reading remains one of the core business process of water utilities or public services in charge of drinking water supply. This activity requests a good level of organization and a good management of the devices. To date, water meters have been accumulation meters, pulse meters or interval meters which are all mechanical devices. The data are collected directly regularly on the field. This process can report about consumption and can detect some leakages into the network. However, reactivity is low due to the limited visits on the field. The past decade has seen an evolution of conceptual design of advanced or smart metering and its terminology. Driven by electricity investment, metering has evolved from accumulation meters to interval meters with simple communications, to advanced or smart metering with an increased range of metering functionality. This increase in electricity meter functionality and

Interval metering is comparatively more expensive than pulse metering, as the interval meter is required to constantly monitor the water flows through the meter and record this volume at the expiration of the metering interval. By using a fine pulse quantum and analysing the time stamps of these pulses, pulse metering data can be used to approximate

strain, acidity, and many other phenomena.

which may avoid the centralized design.

the smart metering concept for water consumption monitoring.

complexity has started to be mirrored in the water industry.

**4.2 From mechanical meters to smart metering**

directions:

motion.

and operating activities.

	- In the current vision , there is an absolute need of generalized ICT in the operation of the cities of the future, or sustainable cities, or water-sensitive cities;
	- Cascading usages of water (incl. re-use and recycling), rainwater harvesting, storm water management, desalination, managed aquifer recharge, micro treatment plants, etc. are the core techniques of the cities of the future These techniques need a very high level of monitoring and thus, a sophisticated density of ICT;
	- Leakage reduction in distribution networks;
	- Improving water efficiency in cities.
	- In-pipe and "through road" condition assessment sensing technologies;
	- Continuous performance, condition and risk assessment sensors and prediction models;
	- Optimised network operation and "just in time" repairs and investment programmes;
	- GIS/GPS information;
	- Buried asset electronic identification and tagging devices, wireless communication through road materials;
	- "Wearable computers" for field workers, giving access in real time to all data bases of the company, with interfaces consistent with field conditions.
	- Smart grid in water distribution systems (real time management of pumping strategy, refined demand forecast, optimization of network management and of operating costs);
	- Tools for energy saving in treatment plants;
	- Real time status monitoring (open/closed) of manual valves (cf. above : equipment of field operators);
	- Monitoring and control of heat recovery in wastewater;
	- Tools for Smart Metering / Smart Pricing (e.g. condition-based tariffs).
	- Improving water efficiency in cities;
	- Improving water efficiency in agriculture, including detection of illegal abstraction;
	- Ecosystems and land-use management in perspective of project scope and available resources.


**2.1. Petri nets2**

52 Petri Nets – Manufacturing and Computer Science

reachability graph isomorphic to the original TS.

special nets only.

redundant MTSIs cannot be entirely avoided for large FMS cases.

controllers are not ordinary (i.e. they contain weighted arcs).

5 gives the comparisons. Conclusions are made in Section 6.

of siphons3-6. Li & Zhou propose an elementary siphon control policy (ESCP) to reduce the redundant siphons to obtain structurally simpler controllers9-10. However, they cannot obtain optimal ones. Reachability graph methods are used to obtain the live system behavior11-14. Without confining to a certain class of FMS, they can provide an optimal deadlock controller by adopting the theory of regions15. The theory is originally developed for a transition system (TS). A state-based representation with arcs labeled with symbols from an alphabet of events in a TS can be mapped into a PN model. For an elementary TS (ETS) there exists a PN with minimum transition count (one transition for each label) with a

Uzam12 follows the theory of regions15 to define a deadlock-zone (DZ) and deadlock-free zone (DFZ) for preventing deadlocks. Hence, the concept of DZ and DFZ is used to solve ESSPs. An optimal controller can be obtained but suffers from many redundant control places. Ghaffari *et al.*13 propose a unique interpretation of the theory of regions and define *MF* (*forbidden marking*), *MD* (*dangerous marking*), *ML* (*legal marking*), and (the set of *marking*/*transition-separation instances* or MTSI). An optimal PN controller synthesis method for FMS is proposed based on both MTSI and the theory of regions. Unfortunately,

To reduce redundant control places, Li *et al.*16 adopt a combined algorithm based on siphon control and the theory of regions15. Its advantage is that the number of separation instances is significantly reduced after some sets of elementary siphons of a system are controlled. However, it fails to determine all sets of MTSIs and its application seems limited to some

Uzam and Zhou propose an iterative control policy of liveness enforcement for PNs based on the theory of regions17. Less computation is required to obtain a controller. However, as indicated by Li et al18, it requires the repeated calculation of reachability graphs. Piroddi *et al.* propose a combined selective siphons and critical markings in a reachability graph algorithm to obtain optimal controllers via iterations19. They successfully identify the critical uncontrolled siphons and control them to make a deadlock-prone PN live. However, their algorithm also requires the repeated calculation of reachability graphs. Eventually, the

This work in this chapter aims to develop a computationally more efficient optimal deadlock control policy by using the theory of regions. It focuses on dead markings in a reachability graph. The concept of a crucial MTSI (CMTSI) is proposed to synthesize optimal controllers. The proposed method can reduce the computational burden of the MTSI method13 and redundant control places12-13. The experimental results indicate that it is the

Section 2 presents the basic definitions and properties of PNs and the theory of regions. Section 3 describes the proposed policy. Section 4 presents the experimental results. Section

most efficient policy among all known ones12-13, 16 that can design optimal controllers.

A Petri net (*PN*) is a 5-tuple *N =* (*P, T, F, W, M*0) where *P* is a finite set of places; *T* is a finite set of transitions, with *P T* ≠ and *P T* = ; *F*  (*P*×*T*) (*T*×*P*) is the set of all directed arcs, *W*: (*P*×*T*) (*T*×*P*) → is the weight function where = { 0, 1, 2, …}, and *M*0: *P* → is the initial marking. A *PN* is said to be ordinary, denoted as (*P, T, F*), if *f F*, *W*(*f*) = 1. [*N*]*+*(*p, t*) *= W*(*p, t*) is the input function that means the multiplicity of a directed arc from *p* to *t* if (*p*, *t*)*F*. [*N*]*-* (*p, t*) *= W*(*t, p*) is the output function that means the multiplicity of a directed arc from *t* to *p* if (*t*, *p*)*F*. The set of input (resp., output) transitions of a place *p* is denoted by •*p* (resp., *p*•). Similarly, the set of input (resp., output) places of a transition *t* is denoted by •*t* (resp., *t*•). A PN structure *(P, T, F, W)* is denoted by *N*. A PN with a given initial marking is denoted by (*N, M*0).

A PN is said to be pure if no place is both input and output places of the same transition. The so-called incidence matrix [*N*] of a pure Petri nets is defined as [*N*] = [*N*]- [*N*]+. A transition *t* is said to be enabled at marking *M*, if *p* •*t, M*(*p*)  *W*(*p, t*)*, or p* is marked with at least *W*(*p*, *t*) tokens, as denoted by *M*[*t*>. A transition may fire if it is enabled. In an ordinary net, it is enabled iff *p* •*t*, *M*(*p*) 1. Firing *t* at *M* gives a new marking *M*such that *p P*, *M*(*p*) = *M*(*p*) – *W*(*p*, *t*) + *W*(*t*, *p*). It is denoted as *M*[*t*>*M*. *M* indicates the number of tokens in each place, which means the current state of the modeled system. When *Mn* can be reached from *M*0 by firing a sequence of transitions σ, this process is denoted by *M* [σ > *Mn* and satisfies the *state equation Mn* = *M* + [*N*] . Here, is a vector of non-negative integers, called a *firing vector*, and ( )*t* indicates the algebraic sum of all occurrences of *t* in . The set of all reachable markings for a PN given *M*0 is denoted by *R*(*N*, *M*0). Additionally, a definition of linearized reachability set (using the state equation) is defined as ( *R N*, *M*0)={*M*: *M* = *M*0 +[*N*](• )}. This definition is suitable for the incorporation of the state equation into a set of linear constraints. The markings in ( *R N*, *M*0) - *R*(*N*, *M*0) are called *spurious ones* (with respect to the state equation)20*.* They may also be the solutions of the state equation but not reachable markings. In this work, ones just focus on the reachable markings.

A transition *t* is said to be *live* if for any *M R*(*N*, *M*0), there exists a sequence of transitions whose firing leads to *M'* that enables *t*. A PN is said to be *live* if all the transitions are live. A PN contains a *deadlock* if there is a marking *M R*(*N*, *M*0) at which no transition is enabled.  Deadlock situations are as a result of inappropriate resource allocation policies or exhaustive use of some or all resources. Liveness of a PN means that for each marking *M R*(*N*, *M*0) reachable from *M*0, it is finally possible to fire *t*, *t T* through some firing sequence. (*N, M*0) is said to be *reversible*, if *M R*(*N*, *M*0), *M*0 *R*(*N*, *M*). Thus, in a reversible net it is always possible to go back to initial marking (state) *M*0. A marking *M* is said to be a *home state*, if for each marking *M R*(*N*, *M*0), *M* is reachable from *M*. Reversibility is a special case of the home state property, i.e. if the home state *M*= *M*0, then the net is reversible.

#### **2.2. Theory of regions and synthesis problem13**

The theory of regions is proposed for the synthesis of pure nets given a finite TS15, which can be adopted to synthesize the liveness-enforcing net supervisor (LENS) for a plant model12-13. For convenience, our method follows the interpretation of the theory of regions in13.

 Assume that there exists a node *v* in *G* such that there exists a path from it to any node. The objective of the theory of regions is to find a pure PN (*N*, *M*0), having *T* as its set of transitions and characterized by its incidence matrix [*N*](*p*, *t*) and its initial marking *M*0, such that its reachability graph is *G* and the marking of node *v* is *M*0. In the following, *M* denotes both a reachable marking and its corresponding node in *G*.

Consider any marking *M* in net (*N*, *M*0). Because (*N*, *M*0) is pure, *M* can be fully characterized by its corresponding incidence vector [*N*](*p*, ) *M* where *M* is the firing vector of path *M* . For any transition *t* that is enabled at *M*, i.e., *t* is the label of an outgoing arc of the node *M* in *G*

$$M'(p) = M(p) + [N](p\_\prime \cdot) \vec{\Gamma}\_{M \to M'}, \forall \{M, M'\} \in G \land M \mid t \ge M' \tag{1}$$

Consider now any oriented cycle of a reachability graph. Applying the state equation to a node in and summing them up give the following cycle equation:

$$\sum\_{t \in T} [N](p, t)\vec{\gamma}(t) = 0, \forall \gamma \in \mathbb{C} \tag{2}$$

A Computationally Improved Optimal Solution

for Deadlocked Problems of Flexible Manufacturing Systems Using Theory of Regions 55

The above equation (4) is called the event separation condition of (*M*, *t*). The set of all possible pairs (*M*, *t*) where *M* is a reachable marking and *t* is not enabled at *M* is called the *set of event separation instances* or *marking/transitions-separation instances* (MTSI)13. Symbol is used to represent the set of MTSI in this paper. To solve the control problem, is identified. The corresponding control places can then be found to prevent the transitions of the

In this section, an efficient controller synthesis method is developed based on the theory of regions. Please note that all transitions of the PN models are regarded as controllable

It is assumed that a deadlock-prone PN model contains at least a dead marking in its reachability graph at which no transition is enabled. Its reachability graph contains dead and live zones. Consequently, this study attempts to propose a method to prevent the

A dead marking cannot enable any transition and thus cannot go to any other markings.

 If there is no dead zone in a

The goal of the work is to control a deadlock-prone system such that it is live. All markings of a reachability graph can be divided into three groups: legal markings (*ML*), quasi-dead

*Definition 3*: The set of *quasi-dead markings MQ* = {*MR*(*N*, *M*0)| *M* must eventually evolve to a

*Definition 4*: A zone consisting of all quasi-dead markings is called a *quasi-dead zone*, denoted

*Definition 5*: A zone consisting of all quasi-dead and dead markings, i.e., *ZI* = *ZD ZQ*, is

Markings except quasi-dead and dead markings are legal ones. Once a legal marking is

*Definition 6*: A zone consisting of all legal markings is called a *legal zone*, i.e., *ZL* = *R*(*N*, *M*0) - *ZI*. Ramadge and Wonham show that a system has the maximally permissive behavior if the system behavior equals *ZL*21. In other words, one must remove all the markings in illegal

enforced into the illegal zone, the net will eventually become deadlock.

*Definition 1*: The set of *dead markings MD* = {*M R*(*N*, *M*0)| at *M*, no transition is enabled}. *Definition 2*: A zone consisting of all dead markings is called a *dead zone*, denoted by *ZD*.

controlled system from firing in order to keep all legal markings only.

**3. Controller synthesis method**

**3.1. Supervisory control problem**

controlled systems from entering a dead zone/marking.

We can formally define the dead marking *MD* as follows.

reachability graph, the system is called a live one.

dead one regardless of transition firing sequences}.

markings (*MQ*), and dead markings (*MD*).

ones.

by *ZQ*.

called an *illegal zone*.

where is an oriented cycle of *G*, ( )*t* is a firing vector corresponding to *,* and *C* is the set of oriented cycles of *G.*

According to the definition of *G*, there exists an oriented path *M* from *M*0 to *M*. Applying (1) along the path leads to *M*(*p*) = *M*0(*p*) + [*N*](*p*,) *M* . There are several paths from *M*0 to *M*. Under the cycle equations, the product [*N*](*p*,) *M* is the same for all these paths. As a result, *M* can be arbitrarily chosen. The reachability of any marking *M* in *G* implies that

$$M(p) = M\_0(p) + [N](p\_\prime \cdot) \vec{\Gamma}\_M \ge 0, \forall M \in G \tag{3}$$

The above equation is called the reachability condition. Notably, (3) is necessary but not sufficient. Hence, spurious markings are beyond this paper.

It is clear that the cycle equations and reachability conditions hold for any place *p*. For each pair (*M*, *t*) such that *M* is a reachable marking of *G* and *t* is a transition not enabled at *M*, *t* should be prevented from happening by some place *p*. Since the net is pure, *t* is prevented from happening at *M* by a place *p* iff

$$[M\_0(p) + [N](p\_\prime \cdot)]\vec{\Gamma}\_M + [N](p\_\prime t) \le -1\tag{4}$$

The above equation (4) is called the event separation condition of (*M*, *t*). The set of all possible pairs (*M*, *t*) where *M* is a reachable marking and *t* is not enabled at *M* is called the *set of event separation instances* or *marking/transitions-separation instances* (MTSI)13. Symbol is used to represent the set of MTSI in this paper. To solve the control problem, is identified. The corresponding control places can then be found to prevent the transitions of the controlled system from firing in order to keep all legal markings only.


*<IP_ADDRESS> Immune check point inhibitors*

The creation of antibodies capable of blocking coinhibitory immune cell receptors, or "immune checkpoints" — T-cell surface receptors that, when activated by specific ligands, limit the T-cytotoxic cell's immunological response — is a hopeful improvement in cancer treatment. Tumour cells tend to overexpress the ligands that activate these inhibitory receptors, allowing them to evade the immunological response of T cells and proliferate freely. Despite the fact that over two dozen individual costimulatory receptors have been identified, two of them — CTLA-4 and programmed cell death 1 (PD-1), have been the focus of antibody-based immune checkpoint blockade (ICB) treatments [76].