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

Victor A. Boichenko, Alexey A. Belov and Olga G. Andrianova ()
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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

Mathematics, 2024, vol. 12, issue 22, 1-19

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.

Keywords: linear systems; spectral entropy; optimal control; robust control; algebraic Riccati equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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