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

This paper proposes a design method for discrete abstractions of nonlinear systems using multi-resolution quantizer, which is capable 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 refinements. Discrete abstractions produced by the proposed method exhibit non-uniform distribution of discrete states and inputs.