Discrete Abstractions of Nonlinear Systems Based on Error Propagation Analysis

• Published in: IEEE transactions on automatic control Vol. 57; no. 3; pp. 550 - 564
• Main Authors: Tazaki, Y., Imura, J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aerospace electronics; Algorithms; Applied sciences; Approximation methods; Automatic control; Automation; Computational modeling; Computer science; control theory; systems; Computer systems performance. Reliability; Concrete; Discrete abstraction; Dynamical systems; Exact sciences and technology; Iterative methods; Mathematical analysis; Mathematical model; Mathematical models; Nonlinear dynamics; nonlinear systems; Quantization; quantized systems; Software; Trajectory; Error estimation; Refinement method; Abstract interpretation; Iterative method; Linear programming; Finite automaton; Nonlinear dynamical systems; Dynamical system; Abstraction; Modeling; quantized systems; Program verification; nonlinear systems; Equations of state; Bisimulation; Signal quantization; Concurrency; Non linear model; Discrete time; Feasibility; Discrete abstraction; Growth of error
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2011.2161789

This paper proposes a computational method for the feasibility check and design of discrete abstract models of nonlinear dynamical systems. First, it is shown that a given discrete-time dynamical system can be transformed into a finite automaton by embedding a quantizer into its state equation. Under this setting, a sufficient condition for approximate bisimulation in infinite steps of time between the concrete model and its discrete abstract model is derived. The condition takes the form of a set of linear inequalities and thus can be checked efficiently by a linear programming solver. Finally, the iterative refinement algorithm, which generates a discrete abstract model under a given error specification, is proposed. The algorithm is guaranteed to terminate in finite iterations.