WSEAS Transactions on Circuits and Systems
Print ISSN: 1109-2734, E-ISSN: 2224-266X
Volume 21, 2022
H-Infinity Tracking Controller for Linear Discrete-Time Stochastic Systems with Uncertainties
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Abstract: For linear discrete-time stochastic systems with uncertainties, this paper proposes a tracking control method based on the H-infinity tracking controller and the robust recursive least-squares (RLS) Wiener filter. In linear discrete-time deterministic systems without input and observation noises, the equations for the quantity $$u(k)$$ with the components of the control and exogenous inputs are as previously described. In Section 2, we show that $$u(k)$$ satisfies the same equations for linear discrete-time stochastic systems with white input and observation noises as for deterministic systems, based on the separation principle of control and estimation. The results show that the H-infinity tracking control algorithm for linear discrete-time stochastic systems is the same as that for linear discrete-time deterministic systems. The filtered estimate $$\hat{x}(k)$$ of the system state $$x(k)$$ is used to compute the estimate $$\hat{u}(k)$$ of $$u(k)$$. The robust RLS Wiener filter of Theorem 2 computes the filtered estimate $$\hat{x}(k)$$ of the system state x(k) for degraded stochastic systems with uncertainties in the system and observation matrices. $$\hat{x}(k)$$ is updated from $$\hat{x}(k-1)$$with the degraded observed value $$\breve{y}(k)$$, the filtered estimate $$\hat{\breve{x}}(k-1)$$ of the degraded state $$\breve{x}(k-1)$$, and the estimate $$\hat{u}(k-1)$$ of $$u(k-1)$$.
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Keywords: H-infinity tracking controller, control input, exogenous input, robust recursive least-squares Wiener filter, discrete-time stochastic systems, uncertain parameters, separation principle
Pages: 238-248
DOI: 10.37394/23201.2022.21.26