Robust supervisory control of timed discrete event systems under partial observation based on eligible time bounds: The existence conditions ଁ

Abstract This paper addresses a supervisory control problem for uncertain timed discrete event systems (DESs) under partial observation. An uncertain timed DES to be controlled is represented by a set of possible timed models based on the framework of Brandin and Wonham [(1994). Supervisory control of timed discrete event systems. IEEE Transactions on Automatic Control, 39(2), 329-342]. To avoid the state space explosion problem caused by tick events in the timed models, a notion of eligible time bounds is proposed for a single timed model obtained from the set of all possible timed models. Based on this notion, we present the necessary and sufficient conditions for the existence of a robust supervisor achieving a given language specification for the single timed model. Moreover, we show that the robust supervisor can also achieve the specification for any timed model in the set.

Supervisory Control and Analysis of Partially-observed Discrete Event Systems

Nowadays, a variety of real-world systems fall into discrete event systems (DES). In practical scenarios, due to facts like limited sensor technique, sensor failure, unstable network and even the intrusion of malicious agents, it might occur that some events are unobservable, multiple events are indistinguishable in observations, and observations of some events are nondeterministic. By considering various practical scenarios, increasing attention in the DES community has been paid to partially-observed DES, which in this thesis refer broadly to those DES with partial and/or unreliable observations. In this thesis, we focus on two topics of partially-observed DES, namely, supervisory control and analysis. The first topic includes two research directions in terms of system models. One is the supervisory control of DES with both unobservable and uncontrollable events, focusing on the forbidden state problem; the other is the supervisory control of DES vulnerable to sensor-reading disguising attacks (SD-attacks), which is also interpreted as DES with nondeterministic observations, addressing both the forbidden state problem and the liveness-enforcing problem. Petri nets (PN) are used as a reference formalism in this topic. First, we study the forbidden state problem in the framework of PN with both unobservable and uncontrollable transitions, assuming that unobservable transitions are uncontrollable. For ordinary PN subject to an admissible Generalized Mutual Exclusion Constraint (GMEC), an optimal on-line control policy with polynomial complexity is proposed provided that a particular subnet, called observation subnet, satisfies certain conditions in structure. It is then discussed how to obtain an optimal on-line control policy for PN subject to an arbitrary GMEC. Next, we still consider the forbidden state problem but in PN vulnerable to SD-attacks. Assuming the control specification in terms of a GMEC, we propose three methods to derive on-line control policies. The first two lead to an optimal policy but are computationally inefficient for large-size systems, while the third method computes a policy with timely response even for large-size systems but at the expense of optimality. Finally, we investigate the liveness-enforcing problem still assuming that the system is vulnerable to SD-attacks. In this problem, the plant is modelled as a bounded PN, which allows us to off-line compute a supervisor starting from constructing the reachability graph of the PN. Then, based on repeatedly computing a more restrictive liveness-enforcing supervisor under no attack and constructing a basic supervisor, an off-line method that synthesizes a liveness-enforcing supervisor tolerant to an SD-attack is proposed. In the second topic, we care about the verification of properties related to system security. Two properties are considered, i.e., fault-predictability and event-based opacity. The former is a property in the literature, characterizing the situation that the occurrence of any fault in a system is predictable, while the latter is a newly proposed property in the thesis, which describes the fact that secret events of a system cannot be revealed to an external observer within their critical horizons. In the case of fault-predictability, DES are modeled by labeled PN. A necessary and sufficient condition for fault-predictability is derived by characterizing the structure of the Predictor Graph. Furthermore, two rules are proposed to reduce the size of a PN, which allow us to analyze the fault-predictability of the original net by verifying that of the reduced net. When studying event-based opacity, we use deterministic finite-state automata as the reference formalism. Considering different scenarios, we propose four notions, namely, K-observation event-opacity, infinite-observation event-opacity, event-opacity and combinational event-opacity. Moreover, verifiers are proposed to analyze these properties

From Security Enforcement to Supervisory Control in Discrete Event Systems: Qualitative and Quantitative Analyses

Cyber-physical systems are technological systems that involve physical components that are monitored and controlled by multiple computational units that exchange information through a communication network. Examples of cyber-physical systems arise in transportation, power, smart manufacturing, and other classes of systems that have a large degree of automation. Analysis and control of cyber-physical systems is an active area of research. The increasing demands for safety, security and performance improvement of cyber-physical systems put stringent constraints on their design and necessitate the use of formal model-based methods to synthesize control strategies that provably enforce required properties. This dissertation focuses on the higher level control logic in cyber-physical systems using the framework of discrete event systems. It tackles two classes of problems for discrete event systems. The first class of problems is related to system security. This problem is formulated in terms of the information flow property of opacity. In this part of the dissertation, an interface-based approach called insertion/edit function is developed to enforce opacity under the potential inference of malicious intruders that may or may not know the implementation of the insertion/edit function. The focus is the synthesis of insertion/edit functions that solve the opacity enforcement problem in the framework of qualitative and quantitative games on finite graphs. The second problem treated in the dissertation is that of performance optimization in the context of supervisory control under partial observation. This problem is transformed to a two-player quantitative game and an information structure where the game is played is constructed. A novel approach to synthesize supervisors by solving the game is developed. The main contributions of this dissertation are grouped into the following five categories. (i) The transformation of the formulated opacity enforcement and supervisory control problems to games on finite graphs provides a systematic way of performing worst case analysis in design of discrete event systems. (ii) These games have state spaces that are as compact as possible using the notion of information states in each corresponding problem. (iii) A formal model-based approach is employed in the entire dissertation, which results in provably correct solutions. (iv) The approaches developed in this dissertation reveal the interconnection between control theory and formal methods. (v) The results in this dissertation are applicable to many types of cyber-physical systems with security-critical and performance-aware requirements.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/150002/1/jiyiding_1.pd

Observability and Decentralized Control of Fuzzy Discrete Event Systems

Fuzzy discrete event systems as a generalization of (crisp) discrete event systems have been introduced in order that it is possible to effectively represent uncertainty, imprecision, and vagueness arising from the dynamic of systems. A fuzzy discrete event system has been modelled by a fuzzy automaton; its behavior is described in terms of the fuzzy language generated by the automaton. In this paper, we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation. Observability, normality, and co-observability of crisp languages are extended to fuzzy languages. It is shown that the observability, together with controllability, of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor. When a decentralized solution is desired, it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co-observable. Moreover, the infimal controllable and observable fuzzy superlanguage, and the supremal controllable and normal fuzzy sublanguage are also discussed. Simple examples are provided to illustrate the theoretical development.Comment: 14 pages, 1 figure. to be published in the IEEE Transactions on Fuzzy System