On the decidability of problems in liveness of controlled Discrete Event Systems modeled by Petri Nets

A Discrete Event System (DES) is a discrete-state system, where the state changes at discrete-time instants due to the occurrence of events. Informally, a liveness property stipulates that a 'good thing' happens during the evolution of a system. Some examples of liveness properties include starvation freedom -- where the 'good thing' is the process making progress; termination -- in which the good thing is for an evolution to not run forever; and guaranteed service -- such as in resource allocation systems, when every request for resource is satisfied eventually. In this thesis, we consider supervisory policies for DESs that, when they exist, enforce a liveness property by appropriately disabling a subset of preventable events at certain states in the evolution of DES. One of the main contributions of this thesis is the development of a system-theoretic framework for the analysis of Liveness Enforcing Supervisory Policies (LESPs) for DESs. We model uncertainties in the forward- and feedback-path, and present necessary and sufficient conditions for the existence of Liveness Enforcing Supervisory Policies (LESPs) for a general model of DESs in this framework. The existence of an LESP reduces to the membership of the initial state to an appropriately defined set. The membership problem is undecidable. For characterizing decidable instances of this membership problem, we consider a modeling paradigm of DESs known as Petri Nets, which have applications in modeling concurrent systems, software design, manufacturing systems, etc. Petri Net (PN) models are inherently monotonic in the sense that if a transition (which loosely represents an event of the DES) can fire from a marking (a non-negative integer-valued vector that represents the state of the DES being modeled), then it can also fire from any larger marking. The monotonicity creates a possibility of representing an infinite-state system using what can be called a "finite basis" that can lead to decidability. However, we prove that several problems of our interest are still undecidable for arbitrary PN models. That is, informally, a general PN model is still too powerful for the analysis that we are interested in. Much of the thesis is devoted to the characterization of decidable instances of the existence of LESPs for arbitrary PN models within the system-theoretic framework introduced in the thesis. The philosophical implication of the results in this thesis is the existence of what can be called a "finite basis" of an infinite state system under supervision, on which the membership tests can be performed in finite time; hence resulting in the decidability of problems and finite-time termination of algorithms. The thesis discusses various scenarios where such a finite basis exists and how to find them

Robust State-Based Supervisory Control of Hierarchical Discrete-Event Systems

Model uncertainty due to unknown dynamics or changes (such as faults) must be addressed in supervisory control design. Robust supervisory control, one of the approaches to handle model uncertainty, provides a solution (i.e., supervisor) that simultaneously satisfies the design objectives of all possible known plant models. Complexity has always been a challenging issue in the supervisory control of discrete-event systems, and different methods have been proposed to mitigate it. The proposed methods aim to handle complexity either through a structured solution (e.g. decentralized supervision) or by taking advantage of computationally efficient structured models for plants (e.g., hierarchical models). One of the proposed hierarchical plant model formalisms is State-Tree-Structure (STS), which has been successfully used in supervisor design for systems containing up to 10^20 states. In this thesis, a robust supervisory control framework is developed for systems modeled by STS. First, a robust nonblocking supervisory control problem is formulated in which the plant model belongs to a finite set of automata models and design specifications are expressed in terms of state sets. A state-based approach to supervisor design is more convenient for implementation using symbolic calculation tools such as Binary Decision Diagrams (BDDs). In order to ensure that the set of solutions for robust control problem can be obtained from State Feedback Control (SFBC) laws and hence suitable for symbolic calculations, it is assumed, without loss of generality, that the plant models satisfy a mutual refinement assumption. In this thesis, a set of necessary and sufficient conditions is derived for the solvability of the robust control problem, and a procedure for finding the maximally permissive solution is obtained. Next, the robust state-based supervisory framework is extended to systems modeled by STS. A sufficient condition is provided under which the mutual refinement property can be verified without converting the hierarchical model of STS to a flat automaton model. As an illustrative example, the developed approach was successfully used to design a robust supervisor for a Flexible Manufacturing System (FMS) with a state set of order 10^8

Safety in Supervisory Control for Critical Systems

Part 10: Control and DecisionInternational audienceRecent studies show the designs of automated systems are becoming increasingly complex to meet the global competitive market. Additionally, organizations have focused on policies to achieve people’s safety and health, environmental management system, and controlling of risks, based on standards. In this context, any industrial system in the event of a fault that is not diagnosed and treated correctly could be considered to pose a serious risk to people’s health, to the environment and to the industrial equipment. According to experts, the concept of Safety Instrumented Systems (SIS) is a practical solution to these types of issues. They strongly recommend layers for risk reduction based on control systems organized hierarchically in order to manage risks, preventing or mitigating faults, or to bringing the process to a safe state. Additionally, the concept of Risk and Hazard Control can be applied to accomplish the required functionalities. It is based on problem solving components and considers a cooperative way to find a control solution. In this context, the software architecture can be based on a service-oriented architecture (SOA) approach. This paper initially proposes a new architecture for design of safety control systems for critical systems, based on Safety Supervisory Control Architecture, in accordance with standards IEC 61508 and IEC 61511. Furthermore, a method is also proposed for design the control layer of risk prevention within Safety Supervisory Control Architecture

Review of selection criteria for sensor and actuator configurations suitable for internal combustion engines

This literature review considers the problem of finding a suitable configuration of sensors and actuators for the control of an internal combustion engine. It takes a look at the methods, algorithms, processes, metrics, applications, research groups and patents relevant for this topic. Several formal metric have been proposed, but practical use remains limited. Maximal information criteria are theoretically optimal for selecting sensors, but hard to apply to a system as complex and nonlinear as an engine. Thus, we reviewed methods applied to neighboring fields including nonlinear systems and non-minimal phase systems. Furthermore, the closed loop nature of control means that information is not the only consideration, and speed, stability and robustness have to be considered. The optimal use of sensor information also requires the use of models, observers, state estimators or virtual sensors, and practical acceptance of these remains limited. Simple control metrics such as conditioning number are popular, mostly because they need fewer assumptions than closed-loop metrics, which require a full plant, disturbance and goal model. Overall, no clear consensus can be found on the choice of metrics to define optimal control configurations, with physical measures, linear algebra metrics and modern control metrics all being used. Genetic algorithms and multi-criterial optimisation were identified as the most widely used methods for optimal sensor selection, although addressing the dimensionality and complexity of formulating the problem remains a challenge. This review does present a number of different successful approaches for specific applications domains, some of which may be applicable to diesel engines and other automotive applications. For a thorough treatment, non-linear dynamics and uncertainties need to be considered together, which requires sophisticated (non-Gaussian) stochastic models to establish the value of a control architecture

Decentralized and Fault-Tolerant Control of Power Systems with High Levels of Renewables

Inter-area oscillations have been identified as a major problem faced by most power systems and stability of these oscillations are of vital concern due to the potential for equipment damage and resulting restrictions on available transmission capacity. In recent years, wide-area measurement systems (WAMSs) have been deployed that allow inter-area modes to be observed and identified.Power grids consist of interconnections of many subsystems which may interact with their neighbors and include several sensors and actuator arrays. Modern grids are spatially distributed and centralized strategies are computationally expensive and might be impractical in terms of hardware limitations such as communication speed. Hence, decentralized control strategies are more desirable.Recently, the use of HVDC links, FACTS devices and renewable sources for damping of inter-area oscillations have been discussed in the literature. However, very few such systems have been deployed in practice partly due to the high level of robustness and reliability requirements for any closed loop power system controls. For instance, weather dependent sources such as distributed winds have the ability to provide services only within a narrow range and might not always be available due to weather, maintenance or communication failures.Given this background, the motivation of this work is to ensure power grid resiliency and improve overall grid reliability. The first consideration is the design of optimal decentralized controllers where decisions are based on a subset of total information. The second consideration is to design controllers that incorporate actuator limitations to guarantee the stability and performance of the system. The third consideration is to build robust controllers to ensure resiliency to different actuator failures and availabilities. The fourth consideration is to design distributed, fault-tolerant and cooperative controllers to address above issues at the same time. Finally, stability problem of these controllers with intermittent information transmission is investigated.To validate the feasibility and demonstrate the design principles, a set of comprehensive case studies are conducted based on different power system models including 39-bus New England system and modified Western Electricity Coordinating Council (WECC) system with different operating points, renewable penetration and failures