WSEAS Transactions on Signal Processing
Print ISSN: 1790-5052, E-ISSN: 2224-3488
Volume 19, 2023
Linear H-Infinity Tracking Control in Discrete-Time Stochastic Systems with Uncertain Parameters
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Abstract: In linear discrete-time stochastic systems with uncertain parameters, this study proposes an H-infinity tracking control strategy based on an H-infinity tracking controller and a robust recursive least-squares Wiener filter. A linear H-infinity tracking control algorithm for quantity $$u(k)$$, whose components are the control and exogenous inputs, was proposed for discrete-time deterministic systems without input and observation noise. Based on the separation principle between control and estimation, this study presents equations for $$u(k)$$ in linear discrete-time stochastic systems with uncertain parameters as a counterpart to the equations in deterministic systems. The H-infinity tracking control algorithm in linear discrete-time stochastic systems with uncertain parameters is derived in the same manner as the H-infinity tracking control algorithm in linear discrete-time deterministic systems. The filtering estimate $$\hat{\overleftrightarrow{x}}(k)$$ of the degraded system state $${\overleftrightarrow{x}}(k)$$ is used to calculate the estimate $${\hat{u}}(k)$$ of $$u(k)$$. The robust RLS Wiener filter calculates the filtering estimate $$\hat{\overleftrightarrow{x}}(k)$$ of the system state $${\overleftrightarrow{x}}(k)$$ for degraded stochastic systems with uncertain parameters. With knowledge of the estimate $${\hat{u}}(k-1)$$ of $$u(k-1)$$, the degraded observed value $$\mathord{\stackrel{\smallsmile}{y}}(k)$$, and the filtering estimate $$\hat{\mathord{\stackrel{\smallsmile}{x}}}(k)$$ of the degraded state $${\mathord{\stackrel{\smallsmile}{x}}}(k-1)$$, $$\hat{\overleftrightarrow{x}}(k)$$ is updated from $$\hat{\overleftrightarrow{x}}(k-1)$$.
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Keywords: H-infinity tracking control, control input, exogenous input, robust recursive least-squares Wiener filter, discrete-time stochastic systems with uncertain parameters
Pages: 41-52
DOI: 10.37394/232014.2023.19.5