Symbolic Abstractions for Nonlinear Control Systems via Feedback Refinement Relation

TL;DR

This paper develops methods to create symbolic models for nonlinear control systems with and without time delays, using feedback refinement relations to ensure accurate abstraction and reduce computational complexity.

Contribution

It introduces new approximation techniques with static and dynamic quantizers for constructing symbolic models of nonlinear control systems, including those with time delays.

Findings

Successful construction of symbolic models satisfying feedback refinement relations

Reduction in computational complexity through static quantizer approximation

Extension to time-delay systems with dynamic quantizers

Abstract

This paper studies the construction of symbolic abstractions for nonlinear control systems via feedback refinement relation. Both the delay-free and time-delay cases are addressed. For the delay-free case, to reduce the computational complexity, we propose a new approximation approach for the state and input sets based on a static quantizer, and then a novel symbolic model is constructed such that the original system and the symbolic model satisfy the feedback refinement relation. For the time-delay case, both static and dynamic quantizers are combined to approximate the state and input sets. This leads to a novel dynamic symbolic model for time-delay control systems, and a feedback refinement relation is established between the original system and the symbolic model. Finally, a numerical example is presented to illustrate the obtained results.