Symbolic Abstractions for Nonlinear Control Systems via Feedback Refinement Relation

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.

9 pages, 8 figures

References in corpus (3)

• Approximately bisimilar symbolic models for nonlinear control systems
• Logarithmic Quantization based Symbolic Abstractions for Nonlinear Control Systems
• Symbolic models for nonlinear time-delay systems using approximate bisimulations