Sliding mode mean square filter design for linear stochastic time delay systems |
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Institution: | 1. Institute of Automation, Bohai University, Jinzhou, Liaoning, 121013, China;2. College of Engineering, Bohai University, Jinzhou, Liaoning, 121013, China |
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Abstract: | This paper investigates the mean-square filtering problem for a linear time delay systems with Gaussian white noises. The obtained solution contains a sliding mode term, signum of the innovations process. It is demonstrated that the estimate produced by the designed filter generates the mean-square estimate, which has the same minimum estimation-error variance as the best estimate given by the classical Kalman–Bucy filter. The theoretical result is applied to an illustrative example: the tryptophan operon of E. coli, verifying the performance of the designed filter. It is demonstrated that the estimates produced by the designed sliding-mode mean-square filter and the Kalman–Bucy filter yield the same estimation-error variance. Simulation graphs demonstrate the better performance of the designed sliding-mode filter and show the potential of the proposed new filter. |
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