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Optimal linear quadratic Gaussian control method for discrete system

A linear quadratic Gaussian, discrete system technology, applied in the direction of adaptive control, general control system, control/regulation system, etc., can solve the problem that the separation principle is not established, and the optimal LQG control problem has not made any progress.

Active Publication Date: 2020-02-07
SHANDONG UNIV OF SCI & TECH
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Problems solved by technology

[0005] Whereas previous literature has only studied systems with a single input delay and multiplicative noise, for systems with multiple input delays and state / control-dependent noise, to the best of our knowledge little progress has been made on the optimal LQG control problem, and, When the state variables are not fully available, the separation principle does not hold, so the problem of optimal LQG control for this system becomes more challenging

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  • Optimal linear quadratic Gaussian control method for discrete system
  • Optimal linear quadratic Gaussian control method for discrete system
  • Optimal linear quadratic Gaussian control method for discrete system

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Embodiment Construction

[0064] The specific embodiment of the present invention will be further described below in conjunction with accompanying drawing and specific embodiment:

[0065] Discrete system optimal linear quadratic Gaussian control method, discrete linear quadratic Gaussian system with multi-input time delay and state / control related noise is expressed by formula (2.1),

[0066]

[0067] where x k ∈ R n stands for state, u k ∈ R m represents the control variable with delay d>0, v k is zero mean and variance φ 2 scalar white noise, w k ∈ R n is a random variable with zero mean and satisfies matrix C, D. 0 , is a constant matrix of appropriate dimension, v k and w k Irrelevant, initial state x 0 , whose mean is and the control variable u s Known when S=-d,...,-1;

[0068] R n Indicates the n-dimensional real Euclidean space, I indicates the identity matrix of the appropriate dimension, and the superscript 'indicates the transposition of the matrix, represents a ra...

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Abstract

The invention discloses an optimal linear quadratic Gaussian control method for a discrete system and particularly relates to a linear quadratic Gaussian control technology. The method is based on a discrete time optimal linear quadratic Gaussian (LQG) control problem of multi-time-lag and state / control related noise. The method comprises the following steps of deriving a maximum principle of a linear quadratic Gaussian system with multi-time-lag and state / control related noise by using a variational method, obtaining a solution of forward-backward reverse stochastic differential equations (FBSDEs) composed of an adjoint equation and a balance condition through a mathematical induction method, based on the solution of the FBSDEs, sufficient necessary conditions for THE existence of an optimal linear quadratic Gaussian controller are given, and an explicit solution and a minimum quadratic performance index of the optimal controller are obtained.

Description

technical field [0001] The invention relates to a linear quadratic Gaussian control technology, in particular to a discrete system optimal linear quadratic Gaussian control method. Background technique [0002] The linear quadratic Gaussian (LQG) control problem is an optimal stochastic control problem for systems with additive white Gaussian noise and state / control-dependent noise, which combines a linear quadratic regulator for full state feedback and a Kalman filter. In recent years, optimal LQG control has been applied in various fields, such as wind turbines, unmanned aerial vehicles, and industrial machine tools, especially in networked control systems (NCSs). With the rapid development of science and technology, previous LQG control techniques have gradually failed to keep pace with industrial applications, which prompts us to study more complex LQG control systems with multiple input time lags and state / control-related noise. [0003] It is well known that time del...

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Application Information

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IPC IPC(8): G05B13/02
CPCG05B13/024
Inventor 梁笑张琦妍卢晓王海霞张桂林牟宗磊
Owner SHANDONG UNIV OF SCI & TECH
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