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Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises

Author

Listed:
  • Mikhail Kamenshchikov

    (Department of Nonlinear Dynamical Systems and Control Processes, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia
    Laboratory of Terminal Control Systems, V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 117997 Moscow, Russia
    Department of Engineering Cybernetics, National University of Science and Technology «MISiS», 119049 Moscow, Russia)

Abstract

The problem of constructing functional optimal observers (filters) for stochastic control systems with additive noises in discrete time are studied in this work. Under the assumption that there is no filter of the first order, necessary and sufficient conditions for the existence of filters of the second and third order are obtained in the canonical basis. Analytical expressions of the transfer function matrix from the input noise to the estimation error are presented. A numerical example is given to compare the performance of filters by the quadratic criterion in the steady state.

Suggested Citation

  • Mikhail Kamenshchikov, 2022. "Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises," Mathematics, MDPI, vol. 10(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:370-:d:733645
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