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Set membership state estimation with improved zonotopic description of feasible solution set


Correspondence to: Wei Chai, School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, People's Republic of China.



This paper proposes an improved zonotopic method to set membership state estimation for nonlinear discrete-time systems with a bounded description of noise and parameters. According to the previous method, a zonotope containing the uncertain trajectory of the system is computed using interval arithmetic in the time update. In the observation update, an improved intersection algorithm of zonotope and strip is used to obtain a zonotope bounding the intersection of the uncertain trajectory with the region of the state space consistent with the observed output. This obtained zonotope is used to describe the feasible solution set of state. It is proven that the zonotope obtained by the improved algorithm can be tighter than the one obtained by the previous algorithm. Simulation experiments are conducted showing the performance of the improved state estimation method as compared with the previous one. Two types of noise distribution are considered. The results expose the weakness of the previous method and illustrate the effectiveness of the improvement. Copyright © 2012 John Wiley & Sons, Ltd.