随机非线性系统的控制器设计与分析

【作者】 李武全；

【导师】 解学军；

【作者基本信息】 曲阜师范大学 ， 运筹学与控制论， 2007， 硕士

【摘要】 本文主要研究了一类高阶次随机非线性系统的逆最优镇定问题和一类高阶次随机非线性系统的输出反馈镇定问题．全文分为以下两部分：一、一类高阶次随机非线性系统的逆最优镇定问题．考虑如下的高阶次随机非线性系统：dx_i=(x_i+1^pi+f_i（x_i）)dt+g_i^T（x_i）dω,i=1，…，n-1，dx_n=(u^pn+f_n（x_n）)dt+g_n^T（x_n）dω，其中z=[x₁…，x_n]^T∈Rⁿ和u∈R分别是系统的可测状态和控制输入；ω∈R^r是独立标准Wiener过程向量；p_i≥1，i=1，…，n，是奇数；f_i：Rⁱ→R和g_i：Rⁱ→R^r是满足如下假设1的光滑函数且f_i（0）=0，g_i（0）=0．假设1：对f_i（x_i）∈R和g_i（x_i）∈R^r，i=1，…，n，x_i=[x₁，…，x_i]^T∈Rⁱ（i=1，…，n），存在已知的非负光滑函数f_il（·）和g_i1（·），i=1，…，n，使得|f_i（x_i）|≤(|x₁|^pi+…+|x_i|^pi)f_i1（x_i），|g_i（x_i）|≤(|x₁|^pi+…+|x_i|^pi)g_i1（x_i），i=1，…，n．p_i≥1，i=1，…，n，是满足假设2的奇数．假设2：p₁≥…≥p_n≥1．该部分的控制目标是在假设1，2的条件下，设计一个光滑的状态反馈控制器，使得闭环系统在概率意义下是全局渐近稳定的，并且是逆最优稳定的．二、一类高阶次随机非线性系统的输出反馈镇定问题．考虑如下的随机非线性系统：dζ_i=ζ_i+1^p dt+φ_i^T（ζ_i）dω，i=1，…，n-1，dζ_n=v^pdt+φ_n^T（ζ_n）dω，y=ζ₁，其中ζ=[ζ₁，…，ζ_n]^T∈Rⁿ，v∈R和y∈R分别是系统的不可量测的状态向量，控制输入和可测的输出；ω∈R^m是独立标准Wiener过程向量；p≥1是奇数．φ_i（（?）_i）∈R^r是满足如下假设3的光滑函数且φ_i（0）=0．假设3：对φ_i（（?）_i），i=1，…，n，存在常数k>0使得[φ_i（（?）_i）|≤k|y|^p+1/2．控制目标是在假设3的条件下，设计一个观测器和一个输出反馈控制器：（?）=（?）（x），u=μ（x），保证闭环系统在概率意义下的全局渐近稳定性．更多还原

【Abstract】 Inverse optimal stabilization for a class of high-order stochastic nonlinear systems, and output-feedback stabilization for high-order stochastic nonlinear systems are considered in the paper, which is composed of the following two parts.1. The problem of Inverse optimal stabilization for a class of high-order stochastic nonlinear systems.Consider the following high-order stochastic nonlinear systems described by:dx_i=(x_i+1^pi+f_i（x_i）)dt+g_i^T（x_i）dω,i=1,…,n-1,dx_n=(u^pn+f_n（x_n）)dt+g_n^T（x_n）dω,where x = [x₁,…,x_n]^T∈Rⁿ and u∈R are the measurable state and control input, respectively;ω∈R^r is independent standard Wiener process vector; P_i≥1, i = 1,…,n, are odd integers. The functions f_i : Rⁱ→R and g_i : Rⁱ→R^r, i = 0,1,…, n, are assumed to be smooth which satisfies the following Assumption 1, vanished at the origin.Assumption 1: There are nonnegative smooth functions f_i1（x_i） and g_i1（x_i）,i=1,…,n, such that |f_i（x_i）|≤(|x₁|^pi+…+|x_i|^pi)f_i1（x_i），|g_i（x_i）|≤(|x₁|^pi+…+|x_i|^pi)g_i1（x_i）, i=1,…,n．p_i≥1,i=1,…,n,are odd integers satisfying Assumption 2.Assumption 2:p₁≥…≥p_n≥1．The objective of this part is to design a smooth state-feedback controller under Assumption 1 and 2, such that the closed-loop system is globally asymptotically stable in probability and inverse optimal stabilization in probability.2. The problem of output-feedback stabilization for high-order stochastic nonlinear systems.Consider the following stochastic nonlinear systems:dζ_i=ζ_i+1^p dt+φ_i^T（ζ_i）dω,i=1,…,n-1,dζ_n=v^pdt+φ_n^T（ζ_n）dω,y=ζ₁,where x = [x₁,…,x_n]^T∈Rⁿ, u∈R and y∈E are unmeasurable state vector, control input and measurable output, respectively;ω∈R^m is independent standard Wiener process vector; p > 0 is an odd integer,φ_i : Rⁱ→R^r, i = 1,…, n, are C¹ functions which satisfy the following Assumption 3 andφ_i（0） = 0.Assumption 2:φ_i（x_i）,i= 1,…,n, there exists a real number k > 0 such that for all i= 1,…n,[φ_i（（?）_i）|≤k|y|^p+1/2The objective is to design an observer and an output-feedback controller:（?）=（?）（x）, u=μ（x）,under Assumption 3, such that the closed-loop system is globally asymptotically stable in probability.更多还原