Supervisory control using variable lookahead policies

Abstract

This paper deals with the efficient on-line calculation of supervisory controls for discrete event systems (DES's) in the framework of limited lookahead control policies (or LLPs) that we introduced in previous papers. In the LLP scheme, the control action after a given trace of events has been executed is calculated on-line on the basis of an N-step ahead projection of the behavior of the DES. To compute these controls, one must calculate after the execution of each event the supremal controllable sublanguage of a finite language with respect to another finite larger language. In our previous work, we showed how the required supremal controllable sublanguage calculation can be performed by using a backward dynamic programming algorithm over the nodes of the tree representation of these two languages. In this paper, we pursue the same approach for the calculation of LLP controls, but instead we adopt a forward calculation procedure over the N-level tree of interest. This forward procedure improves upon previous work by avoiding the explicit consideration of all the nodes of the N-level tree, while still permitting tree-to-tree recursiveness as enabled events are executed by the system. The forward search ends whenever a control decision can be made unambiguously or whenever the boundary of the N-level tree is reached, whichever comes first. This motivates the name "Variable Lookahead Policy" (or VLP) for this implementation of the LLP supervisory control scheme. This paper presents a general VLP algorithm and studies the properties of several special cases of it. The paper also discusses the implementation of the VLP algorithms and presents computational results regarding the application of these algorithms to a "time-varying" DES. This paper deals with the efficient on-line calculation of supervisory controls for discrete event systems (DES's) in the framework of limited lookahead control policies that we introduced in Chung, Lafortune, and Lin (1992). It builds upon the results presented in Chung, Lin (1992, 1993a) concerning this framework.Consider a DES that is being controlled by dynamically disabling/enabling events after the execution of each event by the controlled system. In supervisory control with limited lookahead policies (or LLPs), the control action after a given trace of events has been executed is calculated on-line on the basis of an N-step ahead projection of the behavior of 238 CHUNG, LAFORTUNE, AND LIN the DES under consideration; this procedure is repeated after the system executes any one of the enabled events. This is in contrast with the "conventional" supervisory control paradigm (cf. Wonham 1988, Ramadge and where the complete control policy is calculated off-line using automaton models of the DES and of the legal behavior. As discussed in Chung, Lafortune, and Lin (1992), LLPs allow to control certain classes of "time-varying" DES's and they also provide a means for dealing with the computational complexity of supervisor synthesis for DES's with large state spaces.Chung, Lafortune, a...

Near-Optimal Online Control of Dynamic Discrete-Event Systems

“…The online controller, (Chung et al, 1994), can be defined as a function γ : L(G) → 2 . For each string which can occur in the system, γ returns the subset of events which should be enabled (all other events will be disabled) so that the system behavior is restricted to strings in K. Note that uc will always be contained in this subset.…”

“…Researchers have worked on various approaches to online control (Chung et al, 1994;Hadj-Alouane et al, 1994, 1996Heymann and Lin, 1994;Kumar et al, 1998). These works propose different methods for how to produce valid control, including the use of online control in systems with partial observability.…”

Decision making in fuzzy discrete event systems

“…How big the tree is depends on the number of forward-looking steps, denoted by L. Looking ahead further will produce better results, but also requires more computation. Also, a variable look-ahead policy may be used by specifying some intelligent terminating conditions [3]. The main difference between a crisp DES tree and the fuzzy DES tree is that there are more branches in the fuzzy DES tree, because the system can now be partially in more than one state and, therefore, more events are possible at each node in the fuzzy DES tree.…”

“…The online approach investigated in this paper can solve such optimal control problems efficiently. Online approaches for controlling crisp DES were first proposed in [2,3,4]. Our control mechanism includes both disablement and enforcement, which is similar to a generalized framework proposed in [6].…”

Properties of continuous Petri nets controlled via model predictive control

“…In the case of discrete event systems (DES), the problem of on-line calculation of supervisory controllers has been introduced in [4] where the framework of limited lookahead control policies is used. For DES modeled by PN, in [6] an integer linear programming formalism is used while, for a particular class of marked graphs, in [12] a control strategy based on Model Predictive Control (MPC) has been studied.…”