含控制时滞系统的实时故障诊断和最优容错控制

研究含有控制时滞的线性系统的故障诊断方法和最优容错控制问题.给出了最优容错控制律的存在唯一性条件,提出了最优容错控制律的设计算法.通过构造增广的降维状态观测器,设计了在线诊断故障的故障诊断器并同时实现了系统状态的观测,解决了最优容错控制的物理不可实现问题.利用观测器的输出得到物理可实现的动态最优容错控制律.仿真实例验证了故障诊断方法和动态最优容错控制律的有效性.     

一类具有漂移、扩散及停时的奇异型随机控制

以随机分析的知识和最优控制理论为基础,推广了一类带停时的奇异型随机控制中的折扣费用模型,主要在受控状态过程中增加了漂移因子和扩散因子,使其为一随机微分方程的解,并将费用函数一般化.通过求解一组变分方程,证明了最优控制及最优停时的存在性,并给出了最优费用函数的解析表达式.     

一类大时滞非线性网络控制系统的H∞保成本控制

本文研究一类大时滞不确定非线性网络控制系统的H∞保成本控制问题. 首先将具有随机大时滞的网络控制系统模型化为具有不确定系数的离散时间系统模型. 然后利用Lyapunov稳定性理论和线性矩阵不等式方法, 给出H∞保成本控制律的存在条件和H∞保成本控制器的设计方法. 进而通过求解凸优化问题得到最优鲁棒H∞保成本控制器. 最后仿真结果验证了该控制算法的有效性.     

状态和输入受限的切换奇异布尔控制网络的最优控制

本文研究了状态和输入均受限的切换奇异布尔控制网络的最优控制问题.利用矩阵半张量积方法获得受限切换奇异布尔控制网络的等价代数形式.然后通过类似针变化得到了存在最优控制的必要条件,并且提出了一个算法设计切换序列和控制策略使收益函数最大化.最后给出例子验证所得结果的有效性.     

社交网络影响的不良信息扩散建模及最优控制策略

针对已有不良信息传播模型没有考虑不同社交网络间信息扩散情况,利用图论中的连通性原理,建立了多个社交网络间不良信息扩散的动力学模型,并且将优化控制理论应用到模型中。通过最优控制原理,证明了最优控制策略的存在性,进一步得到了不良信息扩散的优化控制模型。实验结果表明,引入优化控制措施可以有效抑制不良信息扩散规模,而且控制策略的强度可以根据需要进行动态调整。另外,通过模拟不同社交网络间是否有信息相互传递,发现社交网络间的信息传递会增大不良信息扩散的规模和速度。     

LQG control of networked control systems with access constraints and delays

We explore the LQG control of a networked control system (NCS) in which a linear plant is controlled remotely over a network or other shared communication medium. The medium provides a limited number of simultaneous connections, so that only a subset of the plant's sensors and actuators may communicate with the controller at any one time, subject to known transmission delays. Instead of insisting on jointly optimal control and medium access policies, we reduce the infinity of possible access sequences down to those which preserve the stabilisability and detectability of the underlying plant, and are periodic. Our choice of communication and NCS model effect a kind of ‘decoupling’ of the LQG problem, in the sense that the medium access policy can be selected independently of the controller. This guarantees the existence of a stabilising LQG controller which is optimal for the communication policy of choice, and which is then combined with a delay compensator. We include simulations that illustrate our approach.     

计算机病毒的最优控制模型*

提出一个带有最优控制的SAIC模型,让感染病毒的节点数目和系统消耗保持在较低的水平。运用最优控制理论的相关原理和方法,证明了最优控制的存在性,并给出了刻画最优控制的最优系统。数值仿真结果表明,使用适当的控制策略后,计算机病毒的传播得到了有效的控制。所提的方法有望成为一种有用的工具来控制计算机病毒的传播。     

控制时滞系统基于观测器的最优扰动抑制

研究在持续外界扰动作用下含有控制时滞线性系统的最优扰动抑制问题. 首先利用模型转换将控制时滞系统转化为无时滞系统. 然后证明最优控制律的存在唯一性, 并通过求解Riccati方程和Sylvester方程设计含前馈补偿器和控制记忆项的最优控制律, 其中的前馈控制项和控制记忆项分别补偿了扰动和控制时滞对系统的影响. 通过构造扰动状态观测器, 解决了前馈补偿器的物理不可实现问题. 仿真实例验证了所设计的最优控制律的有效性.     

Optimal control of LTI systems over unreliable communication links

In this paper, optimal control of linear time-invariant (LTI) systems over unreliable communication links is studied. The motivation of the problem comes from growing applications that demand remote control of objects over Internet-type or wireless networks where links are prone to failure. Depending on the availability of acknowledgment (ACK) signals, two different types of networking protocols are considered. Under a TCP structure, existence of ACK signals is assumed, unlike the UDP structure where no ACK packets are present. The objective here is to mean-square (m.s.) stabilize the system while minimizing a quadratic performance criterion when the information flow between the controller and the plant is disrupted due to link failures, or packet losses. Sufficient conditions for the existence of stabilizing optimal controllers are derived.     

Parametric optimal control for uncertain linear quadratic models

In recent few decades, linear quadratic optimal control problems have achieved great improvements in theoretical and practical perspectives. For a linear quadratic optimal control problem, it is well known that the optimal feedback control is characterized by the solution of a Riccati differential equation, which cannot be solved exactly in many cases, and sometimes the optimal feedback control will be a complex time-oriented function. In this paper, we introduce a parametric optimal control problem of uncertain linear quadratic model and propose an approximation method to solve it for simplifying the expression of optimal control. A theorem is given to ensure the solvability of optimal parameter. Besides, the analytical expressions of optimal control and optimal value are derived by using the proposed approximation method. Finally, an inventory-promotion problem is dealt with to illustrate the efficiency of the results and the practicability of the model.     

Stochastic optimal control of networked control systems with control packet dropouts

This paper considers the stochastic optimal control problem for networked control systems(NCSs)with control packet dropouts.The proportional plus up to the third-order derivative(PD3)compensation strategy is adopted to compensate for control packet dropouts at the actuator by using the past control packets stored in the buffer.Based on the strategy,a new NCS structure model with packet dropouts is provided,where the packet dropout is assumed to obey the Bernoulli random binary distribution.In terms of the given model,the stochastic optimal control law is proposed. Numerical examples illustrate the effectiveness of the results.     

A note on the existence and optimal control for mixed Volterra–Fredholm-type integrodifferential dispersion system of third order

The optimal control problem consists of a performance index subject to a set of differential equations that describes the path of the control and state variables. The main aim of this article is to prove the existence and uniqueness of a mild solution, optimal control, and time-optimal control of a mixed Volterra–Fredholm-type third-order dispersion system. By applying the strongly continuous semigroup theory and the Banach fixed-point theorem, we prove the existence and uniqueness of the considered system. The optimal control results are proved by using Mazur's lemma, Gronwall's inequality, and the minimizing sequence technique. The discussion on the time-optimal control of the third-order dispersion system is also presented.     

基于Stackbelberg博弈的认知无线网络速率控制模型

提出了基于Stackelberg博弈的认知无线单跳网络流量速率控制模型。应用反向归纳法对提出的流量速率Stackelberg博弈模型纳什均衡进行了分析,证明了提出的模型纳什均衡存在性及唯一性,并给出了Stackelberg博弈模型纳什均衡解的具体形式。仿真验证了提出的模型正确性,仿真结果表明在模型的纳什均衡处网络总体效用是最优的,且网络效用最大时认知结点可获得最优数据传输速率。     

Optimal control problem for stochastic evolution equations in Hilbert spaces

In this article, we consider an optimal control problem in which the controlled state dynamics is governed by a stochastic evolution equation in Hilbert spaces and the cost functional has a quadratic growth. The existence and uniqueness of the optimal control are obtained by the means of an associated backward stochastic differential equations with a quadratic growth and an unbounded terminal value. As an application, an optimal control of stochastic partial differential equations with dynamical boundary conditions is also given to illustrate our results.     

Bilinear optimal control of a Kirchhoff plate

We consider the problem of optimal control of a Kirchhoff plate. A bilinear control is used as a force to make the plate close to a desired profile taking into the account, a quadratic cost of control. We prove the existence of an optimal control and characterize it uniquely through the solution of an optimality system.     

受扰线性离散系统的前馈2反馈最优控制

研究具有已知动态特性但未知初始条件的持续外界扰动的线性离散系统最优控制问题。给出了前馈一反馈最优控制律的存在唯一性条件，并提出了最优控制律的设计算法．通过降维扰动观测器解决了前馈一反馈最优控制律的物理不可实现问题．对近海结构物振动控制的实例仿真表明，该设计算法易于实现，在抑制外部持续扰动和鲁棒性方面优于经典的状态反馈最优控制。     

Rate of convergence for the Legendre pseudospectral optimal control of feedback linearizable systems

Pseudospectral (PS) computational methods for nonlinear constrained optimal control have been applied to many industrial-strength problems, notably, the recent zero-propellant-maneuvering of the international space station performed by NASA. In this paper, we prove a theorem on the rate of convergence for the optimal cost computed using a Legendre PS method. In addition to the high-order convergence rate, two theorems are proved for the existence and convergence of the approximate solutions. Relative to existing work on PS optimal control as well as some other direct computational methods, the proofs do not use necessary conditions of optimal control. Furthermore, we do not make coercivity type of assumptions. As a result, the theory does not require the local uniqueness of optimal solutions. In addition, a restrictive assumption on the cluster points of discrete solutions made in existing convergence theorems is removed.     

双时滞系统的故障诊断和动态最优容错控制

对含有状态时滞和控制时滞的线性时滞系统, 研究系统发生不可直接测量的传感器故障和执行故障时的故障诊断和最优容错控制问题. 首先基于时滞系统的线性变换, 利用Riccati矩阵方程和Sylvester方程设计了故障情况下的最优容错控制律, 并证明了最优容错控制律的存在唯一性. 然后通过构造一种新的含有故障的增广系统的降维状态观测器, 实现了故障的实时在线诊断和系统状态的观测, 解决了最优容错控制的物理不可实现问题. 最后利用故障诊断的结果给出了物理可实现的动态最优容错控制律. 仿真实例验证了故障诊断方法和动态最优容错控制方法的可行性和有效性.     

An optimal control based approach to designing plantwide control system architectures

An approach to designing decentralized plantwide control system architectures is presented. The approach is based on splitting the optimal controller gain matrix that results from solving an output optimal control problem into feedback and feedforward parts. These two parts are then used to design and evaluate decentralized control systems. Results for the application of the methodology to a realistic, 4 by 4 reactor with recycle process are given. For this system, the optimal control based approach suggests feedback pairings that are significantly different than those suggested by the steady state RGA. The approach presented can give an indication if MPC is preferred over a decentralized approach to plantwide control. Comparison of the results produced by the best decentralized plantwide system and a model predictive control system are presented.