On the expressiveness and decidability of o-minimal hybrid systems

Abstract

This paper is driven by a general motto: bisimulate a hybrid system by a finite symbolic dynamical system. In the case of o-minimal hybrid systems, the continuous and discrete components can be decoupled, and hence, the problem reduces in building a finite symbolic dynamical system for the continuous dynamics of each location. We show that this can be done for a quite general class of hybrid systems defined on o-minimal structures. In particular, we recover the main result of a paper by G. Lafferriere, G.J. Pappas, and S. Sastry, on o-minimal hybrid systems. We also provide an analysis and extension of results on decidability and complexity of problems and constructions related to o-minimal hybrid systems.

Reachability in One-Dimensional Controlled Polynomial Dynamical Systems

“…It has been successfully used for proving that certain classes of dynamical and hybrid systems admit finite-state bisimilar models [10,5,8]; for computing combinatorial types of trajectories [9]; for mode switching synthesis [7], etc. In this paper we investigated synthesis of finite control strategy for one-dimentional controlled polynomial dynamical systems while setting up the framework for synthesis of finite control strategies for wider classes of controlled dynamical systems and studying related problems.…”

Formal language properties of hybrid systems with strong resets

“…In this context, an interesting question is to identify expressive classes of hybrid systems which are decidable (for example with respect to the reachability problem). Classes with this property include: linear hybrid automata [2], (initialized) rectangular automata [31], weighted (or priced) timed automata [6,10], and o-minimal hybrid systems [19,36].…”

“…Various nice positive results have been obtained in this class: existence of a finite bisimulation [20,36], decidability of the reachability problem [19], extension to games [12] and to weighted systems [13]. Hybrid systems with strong resets [14] extend o-minimal hybrid systems since they remove the o-minimality hypothesis but keep the restrictions on the discrete transitions.…”

Average-Price-per-Reward Games on Hybrid Automata with Strong Resets

“…Reachability [2][3][4][5] and optimal reachability [6,7] analysis for hybrid automata have been studied. In [6,8] the optimality of infinite behaviours is also addressed.…”