Discrete-State Abstractions of Nonlinear Systems Using Multi-resolution Quantizer

Abstract

Abstract. This paper proposes a design method for discrete abstrac-tions of nonlinear systems using multi-resolution quantizer, which is ca-pable of handling state dependent approximation precision requirements. To this aim, we extend the notion of quantizer embedding, which has been proposed by the authors ’ previous works as a transformation from continuous-state systems to discrete-state systems, to a multi-resolution setting. Then, we propose a computational method that analyzes how a locally generated quantization error is propagated through the state space. Based on this method, we present an algorithm that generates a multi-resolution quantizer with a specified error precision by finite refine-ments. Discrete abstractions produced by the proposed method exhibit non-uniform distribution of discrete states and inputs.