Games for synthesis of controllers with partial observation

Abstract

The synthesis of controllers for discrete event systems, as introduced by Ramadge and Wonham, amounts to computing winning strategies in parity games. We show that in this framework it is possible to extend the specifications of the supervised systems as well as the constraints on the controllers by expressing them in the modal µ-calculus. In order to express unobservability constraints, we propose an extension of the modal µ-calculus in which one can specify whether an edge of a graph is a loop. This extended µ-calculus still has the interesting properties of the classical one. In particular it is equivalent to automata with loop testing. The problems such as emptiness testing and elimination of alternation are solvable for such automata. The method proposed in this paper to solve a control problem consists in transforming this problem into a problem of satisfiability of a µ-calculus formula so that the set of models of this formula is exactly the set of controllers that solve the problem. This transformation relies on a simple construction of the quotient of automata with loop testing by a deterministic transition system. This is enough to deal with centralized control problems. The solution of decentralized control problems uses a more involved construction of the quotient of two automata. This work extends the framework of Ramadge and Wonham in two directions. We consider infinite behaviours and arbitrary regular specifications, while the standard framework deals only with specifications on the set of finite paths of processes. We also allow dynamic changes of the set of observable and controllable events.

Symbolic Control of Linear Systems Based on Symbolic Subsystems

“…Theorem 5.5 shows that existence of a controller for immediately leads to a controller for . Furthermore, when is finite existing supervisory control [10], [25], [30] and controller synthesis [5], [13], [26], [33], [44], [45] techniques can be immediately used for the construction of . In addition to provide a new computational approach to controller synthesis problems for continuous control systems, Theorem 5.5 also shows that it is now possible to design controllers based on specifications that, traditionally, have not been considered for continuous systems such as regular languages, transitions systems, temporal logics, etc.…”

Approximately bisimilar symbolic models for nonlinear control systems

“…In fact from the analysis point of view, symbolic models provide a unified framework for describing continuous systems as well as, hardware and software interacting with the physical environment. Furthermore, the use of symbolic models allows one to leverage the rich literature on supervisory control [RW87] and algorithmic approaches to game theory [AVW03], for controller design. After the pioneering work of Alur and Dill [AD94] that showed existence of symbolic models for timed automata, researchers tried to identify more general classes of continuous systems admitting finite bisimulations.…”

Permissive strategies: from parity games to safety games

“…A correct controller is a winning strategy in such a game (see [1]). There may be many winning strategies in a given game.…”

“…Finding a winning strategy in a given parity game is a prominent problem in computer aided verification as many model checking problems can be effectively reduced to it [6,12]. Here, we are interested in the synthesis problem when the interaction of a controller and an environment is described by a parity game [17,1].…”