Symbolic models for nonlinear control systems affected by disturbances

Abstract

Abstract. In the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems. Symbolic models are abstract descriptions of continuous systems where one symbol corresponds to an "aggregate" of continuous states. In this paper we face the problem of deriving 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 approximate nonlinear control systems affected by disturbances in the sense of alternating approximate bisimulation.

A modal characterization of alternating approximate bisimilarity

“…Pola and Tabuada adopt alternating transition systems to model the samples of control systems with disturbances and their finite abstractions, and introduce the notion of alternating approximate bisimilarity to capture the equivalence between these systems [25] [26]. Based on the modal characterization of alternating approximate bisimilarity obtained in this paper, we provide the transformation function T r ε from LTL + -specifications to LTL ε +specifications.…”

“…This subsection recalls some notions and results about control systems with disturbances and their finite abstractions provided by [25] [26]. Before doing so, we introduce some useful notations.…”

“…A control system is said to be forward complete if and only if every trajectory is defined on an interval of the form ]a, ∞[. [25] [26], we assume that 0 ∈ X, X ⊆ R n is a bounded polytopic sets with non-empty interior, and the control system Σ is forward complete .…”

“…For such systems, Pola and Tabuada adopt a variety of alternating transition systems as models of their sampling systems and finite abstractions [25] [26].…”

“…To overcome these defects, a number of theories are provided to describe approximate behavioral equivalence [5][6] [7][10] [11] [13][15] [25] [26] [32]. In these work, two different approaches have been adopted.…”