Petri Nets at Modelling and Control of Discrete-Event Systems Containing Nondeterminism - Part 1

Discrete-Event Systems are discrete in nature, driven by discrete events. Petri Nets are one of the mostly used tools for their modelling and control synthesis. Place/Transitions Petri Nets, Timed Petri Nets, Controlled Petri Nets are suitable when a modelled object is deterministic. When the system model contains uncontrollable/unobservable transitions and unobservable/unmeasurable places or other failures, such kinds of Petri Nets are insufficient for the purpose. In such a case Labelled Petri Nets and/or Interpreted Petri Nets have to be used. Particularities and mutual differences of individual kinds of Petri Nets are pointed out and their applicability to modelling and control of Discrete-Event Systems are described and tested

Formal techniques for the procedural control of industrial processes

Imperial Users onl

DESIGN OF OPTIMAL PROCEDURAL CONTROLLERS FOR CHEMICAL PROCESSES MODELLED AS STOCHASTIC DISCRETE EVENT SYSTEMS

This thesis presents a formal method for the the design of optimal and provably correct procedural controllers for chemical processes modelled as Stochastic Discrete Event Systems (SDESs). The thesis extends previous work on Procedural Control Theory (PCT) [1], which used formal techniques for the design of automation Discrete Event Systems (DESs). Many dynamic processes for example, batch operations and the start-up and shut down of continuous plants, can be modelled as DESs. Controllers for these systems are typically of the sequential type. Most prior work on characterizing the behaviour of DESs has been restricted to deterministic systems. However, DESs consisting of concurrent interacting processes present a broad spectrum of uncertainty such as uncertainty in the occurrence of events. The formalism of weighted probabilistic Finite State Machine (wp-FSM) is introduced for modelling SDESs and pre-de ned failure models are embedded in wp-FSM to describe and control the abnormal behaviour of systems. The thesis presents e cient algorithms and procedures for synthesising optimal procedural controllers for such SDESs. The synthesised optimal controllers for such stochastic systems will take into consideration probabilities of events occurrence, operation costs and failure costs of events in making optimal choices in the design of control sequences. The controllers will force the system from an initial state to one or more goal states with an optimal expected cost and when feasible drive the system from any state reached after a failure to goal states. On the practical side, recognising the importance of the needs of the target end user, the design of a suitable software implementation is completed. The potential of both the approach and the supporting software are demonstrated by two industry case studies. Furthermore, the simulation environment gPROMS was used to test whether the operating speci cations thus designed were met in a combined discrete/continuous environment

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

Supervisor Synthesis for Discrete Event Systems under Partial Observation and Arbitrary Forbidden State Specifications

In this paper, we consider the forbidden state problem in discrete event systems modeled by partially observed and partially controlled Petri nets. Assuming that the reverse net of the uncontrollable subnet of the Petri net is structurally bounded, we compute a set of weakly forbidden markings from which forbidden markings can be reached by firing a sequence of uncontrollable/unobservable transitions. We then use reduced consistent markings to represent the set of consistent markings for Petri nets with structurally bounded unobservable subnets. We determine the control policy by checking if the firing of a certain controllable transition will lead to a subsequent reduced consistent marking that belongs to the set of weakly forbidden markings; if so, we disable the corresponding controllable transition. This approach is shown to be minimally restrictive in the sense that it only disables behavior that can potentially lead to a forbidden marking. The setting in this paper generalizes previous work by studying supervisory control for partially observed and partially controlled Petri nets with a general labeling function and a finite number of arbitrary forbidden states. In contrast, most previous work focuses on either labeling functions that assign a unique label to each observable transition or forbidden states that are represented using linear inequalities. More importantly, we demonstrate that, in general, the separation between observation and control (as considered in previous work) may not hold in our setting

Control Synthesis for Multi-Agent Systems under Metric Interval Temporal Logic Specifications

This paper presents a framework for automatic synthesis of a control sequence for multi-agent systems governed by continuous linear dynamics under timed constraints. First, the motion of the agents in the workspace is abstracted into individual Transition Systems (TS). Second, each agent is assigned with an individual formula given in Metric Interval Temporal Logic (MITL) and in parallel, the team of agents is assigned with a collaborative team formula. The proposed method is based on a correct-by-construction control synthesis method, and hence guarantees that the resulting closed-loop system will satisfy the specifications. The specifications considers boolean-valued properties under real-time. Extended simulations has been performed in order to demonstrate the efficiency of the proposed controllers.Comment: 8 pages version of the accepted paper to IFAC World Congres

A branch and bound approach for the design of decentralized supervisors in Petri net models

The paper addresses the design of compact and maximally permissive decentralized supervisors for Petri nets, based on generalized mutual exclusion constraints. Decentralization constraints are formulated with respect to the net transitions, instructing each local supervisor to detect and disable transitions of its own control site only. A solution is characterized in terms of the states it allows and its feasibility is assessed by means of two separate tests, one checking the required behavioral properties (e.g., liveness, reversibility and controllability) of the induced reachability subgraph and the other ensuring the existence of a decentralized supervisor enforcing exactly the considered set of allowed states. The second test employs an integer linear programming formulation. Maximal permissivity is ensured by efficiently exploring the solution space using a branch and bound method that operates on the reachable states. Particular emphasis is posed on the obtainment of the controllability property, both in the structural and the behavioral interpretation

Modular control-loop detection

This paper presents an efficient algorithm to detect control-loops in large finite-state systems. The proposed algorithm exploits the modular structure present in many models of practical relevance, and often successfully avoids the explicit synchronous composition of subsystems and thereby the state explosion problem. Experimental results show that the method can be used to verify industrial applications of considerable complexity