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Optimal Controller for Stochastic Polynomial Systems with State-Dependent Polynomial Input

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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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Authors and Affiliations

  1. Department of Physical and Mathematical Sciences, Autonomous University of Nuevo Leon, Apdo postal 144-F, CP 66450, San Nicolas de los Garza, Nuevo Leon, Mexico

    Michael Basin

  2. Center for Research and Graduate Studies (CINVESTAV), Campus Guadalajara, Av. Cientifica 1145, Zapopan, Jalisco, Mexico

    Alexander Loukianov & Miguel Hernandez-Gonzalez

Authors
  1. Michael Basin
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  2. Alexander Loukianov
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  3. Miguel Hernandez-Gonzalez
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Corresponding author

Correspondence to Michael Basin.

Additional information

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

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