Robust observer design and Nash-game-driven fuzzy optimization for uncertain dynamical systems

Abstract The estimation of system state is pivotal especially when system state can't be directly measured. In this paper, an optimal robust observer is proposed for uncertain dynamical systems. The fuzzy set theory is utilized to interpret the uncertainty bound. Unlike fuzzy-logic based observer, the proposed observer is not IF-THEN fuzzy rules-based. The uniform boundedness and ultimate uniform boundedness of estimation error are guaranteed. Then, the optimal design problem of the two tunable parameters is formulated under the framework of a two-player Nash game. The fuzzy-set theoretic cost functions of the two players are associated with the observer performance. We prove that the Nash equilibria does exist, and provide procedures in solving this optimal problem. Numerical simulations are conducted on an inverted pendulum using MATLAB/Simulink. The theory is illustrated by the observer design for an inverted pendulum subject to the earthquake excitation. The novelty of this work is an integrated framework for optimal robust observer design, which creatively blends the state estimation theory, the fuzzy set theory and the Nash game theory.