具有时滞的随机系统滚动时域控制研究

发布时间：2018-06-15 23:53

本文选题：离散时间 + 连续时间　；参考：《山东大学》2017年博士论文

【摘要】：本文研究了多类具有输入时滞随机系统滚动时域控制(receding horizon control,RHC)问题.分别针对离散时间单输入时滞随机线性定常系统、多输入时滞随机线性定常系统、单输入时滞随机线性时变系统和连续时间单输入时滞随机线性定常系统RHC控制问题进行了深入的研究.主要学术贡献及创新点:一、首次解决了单输入时滞随机线性定常系统(离散时间系统、连续时间系统)RHC镇定问题.通过构造包含两个终端加权矩阵的特殊的性能指标和一组耦合的Lyapunov方程,得到了单输入时滞随机线性定常系统(离散系统、连续系统)RHC镇定的充要条件,在此条件下,推导出了条件期望形式显式的镇定控制器.二、为解决离散时间多输入时滞随机线性定常系统RHC镇定问题,构造了关于控制加权矩阵时变的性能指标,给出了离散时间多输入时滞随机系统RHC镇定的线性矩阵不等式(Linear matrix inequality,LMI)条件.本文构造RHC性能指标的思想对解决其它滚动时域优化镇定问题很有启发.三、首次解决了离散时间单输入时滞随机线性时变系统均方指数镇定问题,给出了离散时间单输入时滞随机时变系统RHC均方指数镇定充要条件及显式的镇定控制器.具体研究内容按照章节顺序包括如下几个方面:1.研究了离散时间单输入时滞随机线性定常系统RHC镇定问题以及耦合的Lyapunov不等式的求解.针对离散时间单输入时滞随机线性定常系统,通过构造包含两个终端加权矩阵的性能指标和分析Riccati-ZXL方程的基础上,基于随机控制理论,首次得到了离散时间单输入时滞随机系统RHC均方镇定的充要条件为两个耦合的Lyapunov不等式有解.针对两个耦合Lyapunov不等式,给出了两种求解算法,一是引入松弛变量得到了不等式求解的迭代算法;二是在对不等式进行转化的基础上,给出了锥补线性化算法(cone complementarity linearization,CCL).在满足可镇定的条件下,利用极值原理优化给定的性能指标得到显式的RHC镇定控制器,该控制器为条件期望的形式,可以通过求解一组耦合的Riccati差分方程得到.2.研究了离散时间多输入时滞随机线性定常系统RHC镇定问题.通过构造一控制加权矩阵为特殊时变的性能指标,得到了系统可镇定的充分条件为性能指标中的两个加权矩阵满足一矩阵不等式,并且该矩阵不等式可以转化成线性矩阵不等式进行求解.给出了离散时间多输入时滞随机系统RHC显式镇定控制器,通过选择适当优化时域,可以求解一组简单的耦合的Riccati差分方程得到RHC控制增益.3.首先研究了离散时间随机线性时变系统RHC镇定问题,得到了系统RHC镇定的充要条件.然后进一步研究了单输入时滞随机线性离散时变系统RHC均方指数镇定问题.结合滚动时域优化处理时变系统的优点及耦合的Riccati差分方程的性质,得到了单输入时滞随机时变系统均方指数镇定的充要条件.充分性通过分析最优性能指标的性质,根据随机Lyapunov稳定性定理得证;必要性通过分析耦合的Riccati差分方程的渐近行为,从而导出了耦合的Lyapunov方程,证明了定理的必要性.在满足可镇定条件下,给出了单输入时滞随机时变系统显式可镇定的RHC控制器.4.首先研究了连续时间随机线性时变系统RHC镇定问题.在此基础上,研究了连续时间单输入时滞随机线性定常系统RHC镇定问题.相比离散时间随机系统,连续时间输入时滞随机系统RHC镇定问题更复杂.通过构造一新的性能指标,首次解决了连续时间单输入时滞随机系统RHC镇定问题,得到了系统RHC均方可镇定当且仅当耦合的Lyapunov不等式有解.在该条件下,得到了系统镇定的显式控制器,该控制器可以通过求解一组耦合的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.
【学位授予单位】：山东大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP13

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