Dynamic Quantization based Symbolic Abstractions for Nonlinear Control Systems

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.