Abstract
This paper presents an optimal quadratic-Gaussian controller for stochastic polynomial systems with a state-dependent polynomial control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As an intermediate result, the paper gives a closed-form solution of the optimal regulator (control) problem for polynomial systems with a state-dependent polynomial control input and a quadratic criterion. Performance of the obtained optimal controller is verified in an illustrative example against a conventional linear-quadratic-Gaussian (LQG) controller that is optimal for linearized systems. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.
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The authors thank the Mexican National Science and Technology Council (CONACyT) for financial support under Grants 55584 and 46069 and Sabbatical Fellowship for the first author.
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Basin, M., Loukianov, A. & Hernandez-Gonzalez, M. Optimal Controller for Stochastic Polynomial Systems with State-Dependent Polynomial Input. Circuits Syst Signal Process 30, 1463–1479 (2011). https://doi.org/10.1007/s00034-011-9266-0
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DOI: https://doi.org/10.1007/s00034-011-9266-0