Integrated symbolic control design for nonlinear systems with infinite states specifications

TL;DR

This paper develops an integrated approach for symbolic control design of nonlinear continuous systems with infinite state specifications, combining abstraction construction and controller synthesis into a unified algorithm.

Contribution

It introduces a novel algorithm that simultaneously constructs discrete abstractions and designs symbolic controllers for nonlinear systems modeled by differential equations.

Findings

Algorithm effectively integrates abstraction and control design.

Complexity analysis compares favorably with traditional methods.

Examples demonstrate practical applicability of the approach.

Abstract

Discrete abstractions of continuous and hybrid systems have recently been the topic of great interest from both the control systems and the computer science communities, because they provide a sound mathematical framework for analysing and controlling embedded systems. In this paper we give a further contribution to this research line, by addressing the problem of symbolic control design of nonlinear systems with infinite states specifications, modelled by differential equations. We first derive the symbolic controller solving the control design problem, given in terms of discrete abstractions of the plant and the specification systems. We then present an algorithm which integrates the construction of the discrete abstractions with the design of the symbolic controller. Space and time complexity analysis of the proposed algorithm is performed and a comparison with traditional approaches currently available in the literature for symbolic control design, is discussed. Some examples are included, which show the interest and applicability of our results.