Dynamic Quantization based Symbolic Abstractions for Nonlinear Control Systems

TL;DR

This paper introduces a dynamic quantization method to construct symbolic abstractions for nonlinear control systems, reducing computational complexity while maintaining approximate bisimulation, demonstrated through mobile robot path planning.

Contribution

It proposes a novel dynamic quantizer and approximation approach for creating efficient symbolic abstractions with guaranteed relations for nonlinear control systems.

Findings

Dynamic quantizer reduces computational complexity.

Approximate bisimulation relation is guaranteed.

Numerical example demonstrates effectiveness in path planning.

Abstract

This paper studies the construction of dynamic symbolic abstractions for nonlinear control systems via dynamic quantization. Since computational complexity is a fundamental problem in the use of discrete abstractions, a dynamic quantizer with a time-varying quantization parameter is first applied to deal with this problem. Due to the dynamic quantizer, a dynamic approximation approach is proposed for the state and input sets. Based on the dynamic approximation, dynamic symbolic abstractions are constructed for nonlinear control systems, and an approximate bisimulation relation is guaranteed for the original system and the constructed dynamic symbolic abstraction. Finally, the obtained results are illustrated through a numerical example from path planning of mobile robots.