Alternating approximately bisimilar symbolic models for nonlinear control systems affected by disturbances

Abstract

Symbolic models of continuous and hybrid systems provide a formal approach to solve control problems where software and hardware interact with the physical world. Symbolic models are abstract descriptions of continuous systems in which one symbol corresponds to an “aggregate” of continuous states. In this paper, we address the construction of symbolic models for nonlinear control systems affected by disturbances. The main contribution of this paper is in proposing symbolic models that can be effectively constructed and that are alternating approximately bisimilar to incrementally stable nonlinear control systems, with arbitrarily good accuracy.