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Abstract <p>This general algorithm obtained in Part I of this article is presented for the time-sequential synthesis of a mean-optimal fast dynamic controller of a determinable order, designed for the case of inaccurate output measurements of a nonlinear stochastic controlled plant. Its application is demonstrated for a particular control problem for a linear–Gaussian plant with a variable performance criterion that is quadratic in the control input and the controller’s state, but quadratic–biquadratic in the plant’s state. It is shown that the optimal nonlinear structural functions of the controller’s state equation and its output formula in this case are expressed in terms of the first three initial moments of the conditional probability density obtained by solving the Cauchy problem for a nonlinear partial differential equation obtained from the Fokker–Planck–Kolmogorov equation. To find the approximate analytical form of these functions, the Gaussian approximation method is used, which reduces the problem to obtaining the coefficients of some nonlinearities, which depend only on time, by the sequential Monte Carlo method. It is shown that the biquadraticity of the criterion leads to a useful polynomial form up to the third degree for the structural functions of the Gaussian controller, whereas for the quadratic criterion, a linear controller satisfying Wonham’s separation theorem is obtained, and its order is equal to the plant’s order.</p>

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Operationally Optimal Finite-Dimensional Dynamic State Controller for a Stochastic Differential Plant Based on Its Output: II. Linear–Gaussian Plant with Inaccurate State Measurements and a Quadratic–Biquadratic Criterion

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • E. A. Rudenko

摘要

Abstract

This general algorithm obtained in Part I of this article is presented for the time-sequential synthesis of a mean-optimal fast dynamic controller of a determinable order, designed for the case of inaccurate output measurements of a nonlinear stochastic controlled plant. Its application is demonstrated for a particular control problem for a linear–Gaussian plant with a variable performance criterion that is quadratic in the control input and the controller’s state, but quadratic–biquadratic in the plant’s state. It is shown that the optimal nonlinear structural functions of the controller’s state equation and its output formula in this case are expressed in terms of the first three initial moments of the conditional probability density obtained by solving the Cauchy problem for a nonlinear partial differential equation obtained from the Fokker–Planck–Kolmogorov equation. To find the approximate analytical form of these functions, the Gaussian approximation method is used, which reduces the problem to obtaining the coefficients of some nonlinearities, which depend only on time, by the sequential Monte Carlo method. It is shown that the biquadraticity of the criterion leads to a useful polynomial form up to the third degree for the structural functions of the Gaussian controller, whereas for the quadratic criterion, a linear controller satisfying Wonham’s separation theorem is obtained, and its order is equal to the plant’s order.