Logarithmic Quantization based Symbolic Abstractions for Nonlinear Control Systems

TL;DR

This paper introduces a novel approach for creating symbolic abstractions of nonlinear control systems using logarithmic quantization, enabling effective safety controller synthesis.

Contribution

It proposes a new discrete abstraction method based on logarithmic quantization and establishes a feedback refinement relation for nonlinear systems.

Findings

Successfully constructs symbolic abstractions for nonlinear control systems.

Provides an algorithm for safety controller synthesis using the abstraction.

Demonstrates effectiveness through a numerical example.

Abstract

This paper studies symbolic abstractions for nonlinear control systems using logarithmic quantization. With a logarithmic quantizer, we approximate the state and input sets, and then construct a novel discrete abstraction for nonlinear control systems. A feedback refinement relation between the constructed discrete abstraction and the original system is established. Using the constructed discrete abstraction, the safety controller synthesis problem is studied. With the discrete abstraction and the abstract specification, the existence of a safety controller is investigated, and the algorithm is proposed to compute the abstract controller. Finally, a numerical example is given to illustrate the obtained results.