Optimal control of discrete event systems under partial observation

Abstract

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.

Modeling Fault-tolerant Distributed Systems for Discrete Controller Synthesis

“…It is also possible to consider weights assigned to the states and/or inputs/outputs of P, and to specify that some upper or lower bound must never be reached. Optimal controller synthesis [16] can then be used to control transitions so as to minimize/maximize, in one step (or on bounded paths), some function w.r.t. these weights; i.e., go only to next states with optimal weight.…”

On optimal control of a class of partially observed discrete event systems

“…The supervisor is synthesized in a manner that gives them optimal substructure, consistent with the notion of DP-optimality by Sengupta and Lafortune (1998). Due to space limitations, proofs and examples of the results presented in this paper had to be omitted; they are available in Marchand, Boivineau, and Lafortune (2000).…”

Optimal supervisory control under partial observation

“…In supervisory control theory, there have been many studies in which the control objective is to restrict the system behaviour so that a certain cost function defined on the system is optimized (Passino and Antsaklis 1989, Ionescu and Lin 1995, Kumar and Garg 1995, Sengupta and Lafortune 1998, Cho and Lim 1999, Lee and Lim 2001, Marchand et al 2001. In Passino and Antsaklis (1989) and Ionescu and Lin (1995), the cost function is defined on the set of events, and their control objective is to find the optimal path from the initial state to the final state.…”

“…The OSCP studied in Sengupta and Lafortune (1998) is extended to the partial observation cases in Marchand et al (2001), but the optimal supervisor is designed to minimize the cost function under the worst-case assumption. Although, in Kumar and Garg (1995), the OSCP under partial observation is solved with modification of the plant and the control cost of the events, the proposed method cannot guarantee the optimality of the designed supervisor because the parsimoniousness is no longer the necessary condition for the optimality in the partial observation cases.…”