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State-Space Solution to Spectral Entropy Analysis and Optimal State-Feedback Control for Continuous-Time Linear Systems

Author

Listed:
  • Victor A. Boichenko

    (V.A. Trapeznikov Institute of Control Sciences of RAS, Moscow 117997, Russia)

  • Alexey A. Belov

    (V.A. Trapeznikov Institute of Control Sciences of RAS, Moscow 117997, Russia)

  • Olga G. Andrianova

    (V.A. Trapeznikov Institute of Control Sciences of RAS, Moscow 117997, Russia)

Abstract

In this paper, a problem of random disturbance attenuation capabilities for linear time-invariant continuous systems, affected by random disturbances with bounded σ -entropy, is studied. The σ -entropy norm defines a performance index of the system on the set of the aforementioned input signals. Two problems are considered. The first is a state-space σ -entropy analysis of linear systems, and the second is an optimal control design using the σ -entropy norm as an optimization objective. The state-space solution to the σ -entropy analysis problem is derived from the representation of the σ -entropy norm in the frequency domain. The formulae of the σ -entropy norm computation in the state space are presented in the form of coupled matrix equations: one algebraic Riccati equation, one nonlinear equation over log determinant function, and two Lyapunov equations. Optimal control law is obtained using game theory and a saddle-point condition of optimality. The optimal state-feedback control, which minimizes the σ -entropy norm of the closed-loop system, is found from the solution of two algebraic Riccati equations, one Lyapunov equation, and the log determinant equation.

Suggested Citation

  • Victor A. Boichenko & Alexey A. Belov & Olga G. Andrianova, 2024. "State-Space Solution to Spectral Entropy Analysis and Optimal State-Feedback Control for Continuous-Time Linear Systems," Mathematics, MDPI, vol. 12(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3604-:d:1523587
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    References listed on IDEAS

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    1. Victor A. Boichenko & Alexey A. Belov & Olga G. Andrianova, 2023. "Axiomatic Foundations of Anisotropy-Based and Spectral Entropy Analysis: A Comparative Study," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
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