An Optimal Control Theory for Discrete Event Systems

Sengupta, Raja; Lafortune, Stéphane

doi:10.1137/s0363012994260957

Cited by 97 publications

(125 citation statements)

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“…This function is then used for the computation of the synchronous product, and it can be required that it never goes above or below some fixed maximal or minimal bound, or even that it be maximized or minimized. This is what optimal synthesis does [36,53,50,41,42]. Such an optimization can apply to single transitions [44] or to finite paths.…”

Section: Optimal Discrete Controller Synthesismentioning

confidence: 99%

Automating the addition of fault tolerance with discrete controller synthesis

Girault

Rutten

2009

Form Methods Syst Des

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Abstract. Discrete controller synthesis (DCS) is a formal approach, based on the same state-space exploration algorithms as model-checking. Its interest lies in the ability to obtain automatically systems satisfying by construction formal properties specified a priori. In this paper, our aim is to demonstrate the feasibility of this approach for fault tolerance. We start with a fault intolerant program, modeled as the synchronous parallel composition of finite labeled transition systems; we specify formally a fault hypothesis; we state some fault tolerance requirements; and we use DCS to obtain automatically a program, having the same behavior as the initial fault intolerant one in the absence of faults, and satisfying the fault tolerance requirements under the fault hypothesis. Our original contribution resides in the demonstration that DCS can be elegantly used to design fault tolerant systems, with guarantees on key properties of the obtained system, such as the fault tolerance level, the satisfaction of quantitative constraints, and so on. We show with numerous examples taken from case studies that our method can address different kinds of failures (crash, value, or Byzantine) affecting different kinds of hardware components (processors, communication links, actuators, or sensors). Besides, we show that our method also offers an optimality criterion very useful to synthesize fault tolerant systems compliant to the constraints of embedded systems, like power consumption.

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Section: Optimal Discrete Controller Synthesismentioning

confidence: 99%

Automating the addition of fault tolerance with discrete controller synthesis

Girault

Rutten

2009

Form Methods Syst Des

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“…The (signed) language measure /z could serve as the performance index for synthesis of an optimal control policy (e.g., [11]) that maximizes the performance of a controlled sublanguage. The salient concept is succinctly presented below.…”

Section: Optimal Control Of Regular Languagesmentioning

confidence: 99%

Measure of Regular Languages

Surana

Ray²

2004

Demonstratio Mathematica

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Abstract. This paper reviews and extends the recent work on signed real measure of regular languages within a unified framework. The language measure provides total ordering of partially ordered sets of sublanguages of a regular language to allow quantitative evaluation of the controlled behavior of deterministic finite state automata under different supervisors. The paper presents a procedure by which performance of different supervisors can be evaluated based on a common quantitative tool. Two algorithms are provided for computation of the language measure and their equivalence is established along with a physical interpretation from the probabilistic perspective. IntroductionDeterministic finite-state automata (DFSA) can be represented by a regular languages [2] [5] and are usually capable of capturing the symbolic behavior of physical plants. The concept of discrete-event supervisory control, based on a DFSA plant model, was proposed in the seminal paper of Ramadge and Wonham [8]. The (controlled) sublanguages of the plant language could be different under different supervisors that satisfy their own respective specifications. Such a partially ordered set of sublanguages requires a quantitative measure for total ordering of their respective performance. To address this issue, Wang and Ray [12] formulated a signed measure of regular languages followed by Ray and Phoha [9] who constructed a vector space of formal languages and defined a metric based on the total variation measure of the language. This paper reviews these publications on language measure for discrete-event supervisory control within a unified framework and presents certain clarifications and extensions.The signed real measure for a DFSA is constructed based on assignment of an event cost matrix and a characteristic vector. Two techniques for [12] leads to a system of linear equations whose (closed form) solution yields the language measure vector, the second technique [9] is a recursive procedure with finite iterations. A sufficient condition for finiteness of the signed measure has been established in both cases.In order to induce total ordering on the measure of different sublanguages of a plant language under different supervisors, it is implicit that same strings in different sublanguages must be assigned the same measure. This is accomplished by a quantitative tool that assigns an event cost matrix and a characteristic vector for language measure computation. The clarifications and extensions presented in this paper are intended to enhance development of systematic analytical techniques for synthesis of discrete-event supervisory control systems. For example, Fu et al. [3] [4] have proposed unconstrained optimal control of regular languages where state-based optimal control policies are synthesized by selectively disabling controllable events to maximize performance indices based on a measure of the controlled plant language.The paper is organized in six sections including the present introductory section. Section 2 briefly describes the...

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“…The system to be controlled is modeled as a finite state machine (FSM). Our control problem follows the theory in [8] and is characterized by the presence of uncontrollable events, the notion of occurrence and control costs for events and a worst-case objective function. However, compared to the work in [8] and compared to [3,6], we wish to take into account partial observability.…”

mentioning

confidence: 99%

“…This approximation corresponds to the worst, i.e., the highest, cost of the different unobservable trajectories than can occur between two observable events. In the second step, we use the theory in [8] to synthesize an optimal controller corresponding to the optimal restricted behavior, insofar as it is achievable by an admissible (i.e., physically constructible) supervisor. We use back-propagation from the goal state to generate the supervisor, based on event cost functions.…”

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Optimal control of discrete event systems under partial observation

Marchand

Boivineau²,

Lafortune

Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)

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We are interested in a new class of optimal control problems for Discrete Event Systems (DES). We adopt the formalism of supervisory control theory [7] and model the system as a finite state machine (FSM). Our control problem is characterized by the presence of uncontrollable as well as unobservable events, the notion of occurrence and control costs for events and a worst-case objective function. We first derive an observer for the partially unobservable FSM, which allows us to construct an approximation of the unobservable trajectory costs. We define the performance measure on this observer rather than on the original FSM itself. Further, we use the algorithm of [8] to synthesize an optimal submachine of the observer. This submachine leads to the desired supervisor for the system. Introduction and MotivationWe are interested in a new class of optimal control problems for Discrete Event Systems (DES) [7]. The system to be controlled is modeled as a finite state machine (FSM). Our control problem follows the theory in [8] and is characterized by the presence of uncontrollable events, the notion of occurrence and control costs for events and a worst-case objective function. However, compared to the work in [8] and compared to [3,6], we wish to take into account partial observability. Several concepts and properties of the supervisory control problem under partial observation were studied in [1, 4] among others. However, they only propose a qualitative theory for the control of DESs.

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An Optimal Control Theory for Discrete Event Systems

Cited by 97 publications

References 9 publications

Automating the addition of fault tolerance with discrete controller synthesis

Automating the addition of fault tolerance with discrete controller synthesis

Measure of Regular Languages

Optimal control of discrete event systems under partial observation

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