本文選題：離散時間 + 連續(xù)時間��； 參考：《山東大學》2017年博士論文

【摘要】：本文研究了多類具有輸入時滯隨機系統(tǒng)滾動時域控制(receding horizon control,RHC)問題.分別針對離散時間單輸入時滯隨機線性定常系統(tǒng)、多輸入時滯隨機線性定常系統(tǒng)、單輸入時滯隨機線性時變系統(tǒng)和連續(xù)時間單輸入時滯隨機線性定常系統(tǒng)RHC控制問題進行了深入的研究.主要學術貢獻及創(chuàng)新點:一、首次解決了單輸入時滯隨機線性定常系統(tǒng)(離散時間系統(tǒng)、連續(xù)時間系統(tǒng))RHC鎮(zhèn)定問題.通過構造包含兩個終端加權矩陣的特殊的性能指標和一組耦合的Lyapunov方程,得到了單輸入時滯隨機線性定常系統(tǒng)(離散系統(tǒng)、連續(xù)系統(tǒng))RHC鎮(zhèn)定的充要條件,在此條件下,推導出了條件期望形式顯式的鎮(zhèn)定控制器.二、為解決離散時間多輸入時滯隨機線性定常系統(tǒng)RHC鎮(zhèn)定問題,構造了關于控制加權矩陣時變的性能指標,給出了離散時間多輸入時滯隨機系統(tǒng)RHC鎮(zhèn)定的線性矩陣不等式(Linear matrix inequality,LMI)條件.本文構造RHC性能指標的思想對解決其它滾動時域優(yōu)化鎮(zhèn)定問題很有啟發(fā).三、首次解決了離散時間單輸入時滯隨機線性時變系統(tǒng)均方指數(shù)鎮(zhèn)定問題,給出了離散時間單輸入時滯隨機時變系統(tǒng)RHC均方指數(shù)鎮(zhèn)定充要條件及顯式的鎮(zhèn)定控制器.具體研究內(nèi)容按照章節(jié)順序包括如下幾個方面:1.研究了離散時間單輸入時滯隨機線性定常系統(tǒng)RHC鎮(zhèn)定問題以及耦合的Lyapunov不等式的求解.針對離散時間單輸入時滯隨機線性定常系統(tǒng),通過構造包含兩個終端加權矩陣的性能指標和分析Riccati-ZXL方程的基礎上,基于隨機控制理論,首次得到了離散時間單輸入時滯隨機系統(tǒng)RHC均方鎮(zhèn)定的充要條件為兩個耦合的Lyapunov不等式有解.針對兩個耦合Lyapunov不等式,給出了兩種求解算法,一是引入松弛變量得到了不等式求解的迭代算法;二是在對不等式進行轉化的基礎上,給出了錐補線性化算法(cone complementarity linearization,CCL).在滿足可鎮(zhèn)定的條件下,利用極值原理優(yōu)化給定的性能指標得到顯式的RHC鎮(zhèn)定控制器,該控制器為條件期望的形式,可以通過求解一組耦合的Riccati差分方程得到.2.研究了離散時間多輸入時滯隨機線性定常系統(tǒng)RHC鎮(zhèn)定問題.通過構造一控制加權矩陣為特殊時變的性能指標,得到了系統(tǒng)可鎮(zhèn)定的充分條件為性能指標中的兩個加權矩陣滿足一矩陣不等式,并且該矩陣不等式可以轉化成線性矩陣不等式進行求解.給出了離散時間多輸入時滯隨機系統(tǒng)RHC顯式鎮(zhèn)定控制器,通過選擇適當優(yōu)化時域,可以求解一組簡單的耦合的Riccati差分方程得到RHC控制增益.3.首先研究了離散時間隨機線性時變系統(tǒng)RHC鎮(zhèn)定問題,得到了系統(tǒng)RHC鎮(zhèn)定的充要條件.然后進一步研究了單輸入時滯隨機線性離散時變系統(tǒng)RHC均方指數(shù)鎮(zhèn)定問題.結合滾動時域優(yōu)化處理時變系統(tǒng)的優(yōu)點及耦合的Riccati差分方程的性質(zhì),得到了單輸入時滯隨機時變系統(tǒng)均方指數(shù)鎮(zhèn)定的充要條件.充分性通過分析最優(yōu)性能指標的性質(zhì),根據(jù)隨機Lyapunov穩(wěn)定性定理得證;必要性通過分析耦合的Riccati差分方程的漸近行為,從而導出了耦合的Lyapunov方程,證明了定理的必要性.在滿足可鎮(zhèn)定條件下,給出了單輸入時滯隨機時變系統(tǒng)顯式可鎮(zhèn)定的RHC控制器.4.首先研究了連續(xù)時間隨機線性時變系統(tǒng)RHC鎮(zhèn)定問題.在此基礎上,研究了連續(xù)時間單輸入時滯隨機線性定常系統(tǒng)RHC鎮(zhèn)定問題.相比離散時間隨機系統(tǒng),連續(xù)時間輸入時滯隨機系統(tǒng)RHC鎮(zhèn)定問題更復雜.通過構造一新的性能指標,首次解決了連續(xù)時間單輸入時滯隨機系統(tǒng)RHC鎮(zhèn)定問題,得到了系統(tǒng)RHC均方可鎮(zhèn)定當且僅當耦合的Lyapunov不等式有解.在該條件下,得到了系統(tǒng)鎮(zhèn)定的顯式控制器,該控制器可以通過求解一組耦合的Riccati微分方程得到.
[Abstract]:In this paper, we study the receding horizon control (RHC) problem of random linear time-delay systems with input time-delay. For discrete time single input time-delay stochastic linear constant systems, multiple input time-delay stochastic linear constant systems, single input time-delay stochastic linear time-varying systems and continuous time single input time-delay stochastic linear constant systems, respectively. The main academic contributions and innovation points are as follows: first, the RHC stabilization problem of a single input time-delay stochastic linear constant system (discrete time system, continuous time system) is solved for the first time. By constructing a special performance index containing two terminal weighted matrices and a set of coupled Lyapunov equations, the problem is obtained for the first time. A sufficient and necessary condition for RHC stabilization of a single input time-delay stochastic linear constant system (discrete system, continuous system) is given. Under this condition, a conditional formal explicit controller is derived. Two, in order to solve the RHC stabilization problem of a discrete time multi input time-delay stochastic linear constant system, a performance index for the time variation of the weighted matrix is constructed. The condition of linear matrix inequalities (Linear matrix inequality, LMI) for discrete time multi input time-delay stochastic systems RHC is given. The idea of constructing RHC performance indicators in this paper is very enlightening for solving other rolling time domain optimal stabilization problems. Three, the mean square exponential town of discrete time single input time-delay stochastic linear time-varying systems is solved for the first time. The sufficient and necessary conditions for RHC mean square exponential stabilization and explicit stabilization controllers for discrete time single input time-delay stochastic time-delay systems are given. The specific research contents include the following aspects according to the sequence of chapters: 1. the RHC stabilization problem and the coupled Lyapunov inequality for the discrete time single input time-delay stochastic linear constant system are studied. For the discrete time single input time-delay stochastic linear constant system, the necessary and sufficient condition for the RHC mean square stabilization of the discrete time single input time-delay stochastic system is obtained by constructing the performance indexes including two terminal weighted matrices and analyzing the Riccati-ZXL equation, and the sufficient and necessary conditions for the RHC mean square stabilization of the discrete time single input time-delay stochastic systems are for the first time. Two solutions are given for two coupled Lyapunov inequalities. One is an iterative algorithm for solving inequalities by introducing relaxation variables. Two, on the basis of the transformation of inequalities, the cone complement linearization algorithm (cone complementarity linearization, CCL) is given. The value principle optimizes the given performance index to get the explicit RHC stabilization controller. The controller can obtain the RHC stabilization problem of the discrete time multi input time-delay stochastic linear constant system by solving a set of coupled Riccati difference equations. The controller is a conditional expectation form. By constructing a control weighted matrix, it is a special time variable. The sufficient conditions for the stabilization of the system are obtained. The two weighted matrices in the performance index are satisfied with a matrix inequality, and the matrix inequalities can be converted into linear matrix inequalities. The RHC explicit stabilization controller for discrete time multi input time-delay stochastic systems is given. The RHC control gain.3. is obtained by solving a group of simple coupled Riccati difference equations. First, the RHC stabilization problem of discrete time stochastic linear time-varying systems is studied. The sufficient and necessary conditions for the stabilization of the system RHC are obtained. Then, the RHC mean square exponential stabilization problem of the single input time-delay stochastic linear discrete time-varying system is further studied. The sufficient and necessary condition for the mean square exponential stabilization of a stochastic time-varying system with single input time delay is obtained by dealing with the advantages of the time-varying system and the properties of the coupled Riccati difference equation. By analyzing the properties of the optimal performance index, the sufficient property is proved by the stochastic Lyapunov stability theorem, and the necessity has passed the asymptotic behavior of the Riccati differential equation of the analysis coupling. In this way, the coupled Lyapunov equation is derived, and the necessity of the theorem is proved. Under the condition of satisfying the stabilization, the RHC controller.4. explicitly stabilizable for a single input time-delay stochastic time-varying system is given. First, the RHC stabilization problem of a continuous time stochastic linear time-varying system is studied. On this basis, the continuous time single input time-delay random line is studied. RHC stabilization problem of constant time invariant systems. Compared to discrete time stochastic systems, the RHC stabilization problem of continuous time input time-delay stochastic systems is more complex. By constructing a new performance index, the problem of RHC stabilization for continuous time single input time-delay stochastic systems is solved for the first time. The system RHC mean square can be stabilized when and only when the Lyapunov inequality is coupled. Have the solution. In this condition, the explicit stabilization controller system, the Riccati controller can be obtained by solving a set of coupled differential equations.
【學位授予單位】：山東大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：TP13

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