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Optimal Stabilization of Linear Stochastic System with Statistically Uncertain Piecewise Constant Drift

Author

Listed:
  • Andrey Borisov

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilova Str., 119333 Moscow, Russia)

  • Alexey Bosov

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilova Str., 119333 Moscow, Russia)

  • Gregory Miller

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilova Str., 119333 Moscow, Russia)

Abstract

The paper presents an optimal control problem for the partially observable stochastic differential system driven by an external Markov jump process. The available controlled observations are indirect and corrupted by some Wiener noise. The goal is to optimize a linear function of the state (output) given a general quadratic criterion. The separation principle, verified for the system at hand, allows examination of the control problem apart from the filter optimization. The solution to the latter problem is provided by the Wonham filter. The solution to the former control problem is obtained by formulating an equivalent control problem with a linear drift/nonlinear diffusion stochastic process and with complete information. This problem, in turn, is immediately solved by the application of the dynamic programming method. The applicability of the obtained theoretical results is illustrated by a numerical example, where an optimal amplification/stabilization problem is solved for an unstable externally controlled step-wise mechanical actuator.

Suggested Citation

  • Andrey Borisov & Alexey Bosov & Gregory Miller, 2022. "Optimal Stabilization of Linear Stochastic System with Statistically Uncertain Piecewise Constant Drift," Mathematics, MDPI, vol. 10(2), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:184-:d:720034
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    Citations

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    Cited by:

    1. Haifeng Huang & Mohammadamin Shirkhani & Jafar Tavoosi & Omar Mahmoud, 2022. "A New Intelligent Dynamic Control Method for a Class of Stochastic Nonlinear Systems," Mathematics, MDPI, vol. 10(9), pages 1-15, April.
    2. Alexey Bosov & Andrey Borisov, 2022. "Comparative Study of Markov Chain Filtering Schemas for Stabilization of Stochastic Systems under Incomplete Information," Mathematics, MDPI, vol. 10(18), pages 1-20, September.
    3. Tudor Sireteanu & Ana-Maria Mitu & Ovidiu Solomon & Marius Giuclea, 2022. "Approximation of the Statistical Characteristics of Piecewise Linear Systems with Asymmetric Damping and Stiffness under Stationary Random Excitation," Mathematics, MDPI, vol. 10(22), pages 1-16, November.

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