Controlling Stochastic Sensitivity by Feedback Regulators in Nonlinear Dynamical Systems with Incomplete Information

Irina Bashkirtseva
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Irina Bashkirtseva: Institute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, Russia

Mathematics, 2021, vol. 9, issue 24, 1-12

Abstract: The problem of synthesis of stochastic sensitivity for equilibrium modes in nonlinear randomly forced dynamical systems with incomplete information is considered. We construct a feedback regulator that uses noisy data on some system state coordinates. For parameters of the regulator providing assigned stochastic sensitivity, a quadratic matrix equation is derived. Attainability of the assigned stochastic sensitivity is reduced to the solvability of this equation. We suggest a constructive algorithm for solving this quadratic matrix equation. These general theoretical results are used to solve the problem of stabilizing equilibrium modes of nonlinear stochastic oscillators under conditions of incomplete information. Details of our approach are illustrated on the example of a van der Pol oscillator.

Keywords: control; feedback regulator; random disturbances; incomplete information; stochastic sensitivity; nonlinear oscillators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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