离散时间Itˆo 型跳变系统Lyapunov 方程的有限次迭代求解算法

针对离散时间Itˆo 型马尔科夫跳变系统Lyapunov 方程的求解给出一种迭代算法. 经证明, 在误差允许的范围内, 该算法可以在确定的有限次数内收敛到系统的精确解, 收敛速度较快, 具有良好的数值稳定性, 并且该算法为显式迭代, 可避免迭代过程中求解其他矩阵方程对结果精度产生的影响. 最后通过一个数值算例对该算法的有效性进行了验证.

     

事件驱动的网络化系统最优控制

针对随机事件驱动的网络化控制系统, 研究其中的有限时域和无限时域内最优控制器的设计问题. 首先, 根据执行器介质访问机制将网络化控制系统建模为具有多个状态的马尔科夫跳变系统; 然后, 基于动态规划和马尔科夫跳变线性系统理论设计满足二次型性能指标的最优控制序列, 通过求解耦合黎卡提方程的镇定解, 给出最优控制律的计算方法, 使得网络化控制系统均方指数稳定; 最后, 通过仿真实验表明了所提出方法的有效性.

     

求解多处理器任务调度问题的改进差分进化算法

针对多处理器系统任务调度复杂问题, 在自适应差分进化算法基础上增加惯性速度分项, 提出一种称为惯性速度差分进化(IVDE) 的改进算法, 以避免陷入局部最优解. 结合启发式任务列表, 对算法的状态编码提出了处理器列表(PL)、部分偏序任务列表(PTL) 和全部任务列表(CTL) 等3 种形式. 通过求解随机生成的任务调度标准图和真实求解任务问题, 进行了数值仿真验证, 其中PTL-IVDE 算法相比蚁群优化(ACO) 算法、混合遗传算法(TLPLC-GA), 能快速求得更好的任务调度方案.

     

乘性随机离散系统的最优控制

基于对系统随机不确定因素的分析,文中定义了一种新型随机离散系统--乘性随机 离散系统,并研究该类系统的线性二次型(LQ)最优控制问题.首先给出了该类系统的有限时间 和无限时间LQ最优控制律,并着重分析、证明了无限时间LQ最优控制问题的Riccati方程的 正定矩阵解的存在性及相应数值求解算法与收敛性,以及闭环系统的稳定性等问题.仿真结果 表明了该方法的有效性.     

一类非线性动态系统基于强化学习的最优控制制

提出一类非线性不确定动态系统基于强化学习的最优控制方法. 该方法利用欧拉强化学习算法估计对象的未知非线性函数, 给出了强化学习中回报函数和策略函数迭代的在线学习规则. 通过采用向前欧拉差分迭代公式对学习过程中的时序误差进行离散化, 实现了对值函数的估计和控制策略的改进. 基于值函数的梯度值和时序误差指标值, 给出了该算法的步骤和误差估计定理. 小车爬山问题的仿真结果表明了所提出方法的有效性.

     

基于灵敏度分析的含比例型手续费的投资组合优化

研究含比例型手续费的离散时间投资组合优化问题. 基于马尔可夫决策过程模型和性能灵敏度分析方法, 推导两个不同投资策略之间的资产长期平均增值率的差分公式, 利用差分公式的结构特点, 证明了最优性方程, 并设计出可在线应用的策略迭代算法. 仿真实例验证了所提出算法的有效性.

     

求解大规模系统可靠性问题的修正和声搜索算法

针对大规模系统可靠性问题, 提出一种修正和声搜索(MHS) 算法. 该算法修改了和声搜索(HS) 算法的搜索机制, 以当前最优解为研究对象, 随机选取不同维数进行即兴创作, 并修正步长(BW) 的调整方式, 均衡算法的全局搜索和局部搜索. 对经典的大规模系统可靠性问题进行求解, 数值结果表明, 所提出算法优于其他文献中的6 种和声搜索算法. 与最近提出的求解此类问题的各种算法进行实验对比, 实验结果表明所提出算法在整体上具有良好的优化性能.

     

转移概率部分未知的随机Markov 饱和切换系统的非脆弱镇定

研究一类转移概率部分未知的随机Markov饱和切换系统的非脆弱镇定问题. 基于参数依赖型Lyapunov函数, 设计非脆弱状态反馈控制器以保证闭环饱和系统的随机稳定性, 在此基础之上, 通过求解线性矩阵不等式, 得到均方意义下的最大不变吸引域. 数值仿真验证了所提出方法的有效性.

     

时变概率随机拓扑条件下高阶群系统一致性分析

在时变连接概率的随机拓扑条件下, 研究了离散时间高阶线性群系统的一致性问题. 首先, 给出一个依赖于相邻主体间拓扑连接概率和各个主体自身信息的随机控制协议; 然后, 应用状态空间分解法分析离散时间高阶线性群系统的一致性, 给出了在连接概率时变的随机拓扑条件下以概率为1 实现一致的充分必要条件; 进而, 确定了随机拓扑条件下离散时间高阶线性群系统的一致函数; 最后, 通过数值分析验证了所得出结论的正确性.

     

一种改进的输出反馈特征结构配置方法在飞翼飞机增稳系统设计中的应用

针对常规输出反馈特征结构配置方法不能完全保证闭环系统稳定性的问题, 提出一种改进的输出反馈特征结构配置方法. 该改进的算法通过引入二次型性能指标, 将闭环系统的稳定性问题转化为线性二次型最优控制问题,从而保证闭环系统的稳定性; 考虑到采用特征结构配置方法所设计的闭环系统鲁棒性不强, 给出保证系统鲁棒性的条件, 以解决系统鲁棒性问题. 最后, 通过在飞翼飞机上的仿真结果验证了所提出算法的有效性.

     

Data-driven policy iteration algorithm for continuous-time stochastic linear-quadratic optimal control problems

This paper studies a continuous-time stochastic linear-quadratic (SLQ) optimal control problem on infinite-horizon. Combining the Kronecker product theory with an existing policy iteration algorithm, a data-driven policy iteration algorithm is proposed to solve the problem. In contrast to most existing methods that need all information of system coefficients, the proposed algorithm eliminates the requirement of three system matrices by utilizing data of a stochastic system. More specifically, this algorithm uses the collected data to iteratively approximate the optimal control and a solution of the stochastic algebraic Riccati equation (SARE) corresponding to the SLQ optimal control problem. The convergence analysis of the obtained algorithm is given rigorously, and a simulation example is provided to illustrate the effectiveness and applicability of the algorithm.     

Robust stabilization of stochastic systems based on the LQ controller

The robust exponential stability in mean square for a class of linear stochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we have designed an optimal controller which guarantees the exponential stability of the system. Actually, we employed Lyapunov fimction approach and the stochastic algebraic Riccati equation (SARE) to have shown the robusmess of the linear quadratic(LQ) optimal control law.And the algebraic criteria for the exponential stability on the linear stochastic uncertain closed-loop systems are given.     

Robust stabilization of stochastic systems based on the LQ cont roller

The robust exponential stability in mean square for a class of linear stochastic uncertain control systems is dealt with. For the uncertain stochastic systems ,we have designed an optimal controller which guarantees the exponential stability of the system. Actually ,we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to have shown the robustness of the linear quadratic (LQ) optimal control law. And the algebraic criteria for the exponential stability on the linear stochastic uncertain closed- loop systems are given.     

Linear matrix inequalities, Riccati equations, and indefinitestochastic linear quadratic controls

This paper deals with an optimal stochastic linear-quadratic (LQ) control problem in infinite time horizon, where the diffusion term in dynamics depends on both the state and the control variables. In contrast to the deterministic case, we allow the control and state weighting matrices in the cost functional to be indefinite. This leads to an indefinite LQ problem, which may still be well posed due to the deep nature of uncertainty involved. The problem gives rise to a stochastic algebraic Riccati equation (SARE), which is, however, fundamentally different from the classical algebraic Riccati equation as a result of the indefinite nature of the LQ problem. To analyze the SARE, we introduce linear matrix inequalities (LMIs) whose feasibility is shown to be equivalent to the solvability of the SARE. Moreover, we develop a computational approach to the SARE via a semi-definite programming associated with the LMIs. Finally, numerical experiments are reported to illustrate the proposed approach     

Infinite horizon indefinite stochastic linear quadratic control for discrete-time systems

This paper discusses discrete-time stochastic linear quadratic (LQ) problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefinite. The problem gives rise to a generalized algebraic Riccati equation (GARE) that involves equality and inequality constraints. The well-posedness of the indefinite LQ problem is shown to be equivalent to the feasibility of a linear matrix inequality (LMI). Moreover, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQ problem. All the optimal controls are obtained in terms of the solution to the GARE. Finally, we give an LMI -based approach to solve the GARE via a semidefinite programming.     

Policy iteration based feedback control

It is well known that stochastic control systems can be viewed as Markov decision processes (MDPs) with continuous state spaces. In this paper, we propose to apply the policy iteration approach in MDPs to the optimal control problem of stochastic systems. We first provide an optimality equation based on performance potentials and develop a policy iteration procedure. Then we apply policy iteration to the jump linear quadratic problem and obtain the coupled Riccati equations for their optimal solutions. The approach is applicable to linear as well as nonlinear systems and can be implemented on-line on real world systems without identifying all the system structure and parameters.     

线性离散奇异系统的不定二次最优控制问题: Krein空间方法

The finite time horizon indefinite linear quadratic(LQ) optimal control problem for singular linear discrete time-varying systems is discussed. Indefinite LQ optimal control problem for singular systems can be transformed to that for standard state-space systems under a reasonable assumption. It is shown that the indefinite LQ optimal control problem is dual to that of projection for backward stochastic systems. Thus, the optimal LQ controller can be obtained by computing the gain matrices of Kalman filter. Necessary and sufficient conditions guaranteeing a unique solution for the indefinite LQ problem are given. An explicit solution for the problem is obtained in terms of the solution of Riccati difference equations.     

Solvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems

A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the “equivalent cost functional method”, is introduced by Yu (2013) in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefinite stochastic Riccati equations. As the response, this paper continues to develop the equivalent cost functional method by extending it to the Riccati equation setup. Our analysis is featured by its introduction of some equivalent cost functionals which enable us to have the bridge between the indefinite and positive-definite stochastic LQ problems. With such bridge, some solvability relation between the indefinite and positive-definite Riccati equations is further characterized. It is remarkable the solvability of the former is rather complicated than the latter, hence our relation provides some alternative but useful viewpoint. Consequently, the corresponding indefinite linear quadratic problem is discussed for which the unique optimal control is derived in terms of state feedback via the solution of the Riccati equation. In addition, some example is studied using our theoretical results.