时滞线性区间系统的鲁棒稳定与鲁棒镇定

利用一个微分不等式给出了几类具有区间 系数的时滞系统的鲁棒稳定和鲁棒镇定的充分条件,这些条件只需判断一个常数矩阵是否为 M矩阵,使用方便．     

时变不定机器人控制系统的鲁棒镇定

本文讨论了含有时变参量或扰动的机器人系统的鲁棒稳定问题，给出了该类不确定的机器人系统可鲁棒稳定化的充分条件，并且构造了一个静态可稳化鲁棒控制器。     

不确定时滞系统时滞相关鲁棒镇定

文章研究了线性不确定时滞系统的时滞相关反馈镇定问题。基于系统的状态反馈给出系统可反馈镇定的控制规律。利用线性矩阵不等式(LMI)给出了系统可反馈镇定的充分条件,最后用实例验证了所得结论的正确性。     

带有非线性不确定参数的线性系统的鲁棒稳定性和鲁棒镇定问题

研究带有非线性不确定参数的线性系统的鲁棒稳定性和鲁棒镇定问题。讨论一种有很强实际应用背景并允许带有二次不确定参数的模型,研究该系统的鲁棒稳定性和鲁棒镇定问题。以ＬＭＩ的形式给出了判据,并举例证明了该方法的优越性。     

鲁棒镇定区间系统族的一个充分条件

讨论了区间系统族的鲁棒镇定问题,给出存在控制器鲁棒镇定区间系统族的一个充分条件,并且当这个条件成立时,得到了鲁棒镇定区间系统族的控制器的参数化公式.     

分数阶系统线性矩阵不等式稳定判据的改进与鲁棒镇定: 0<α<1的情况

针对确定的分数阶系统,通过发掘其稳定区域与线性矩阵不等式(LMI)之间的联系,提出改进的LMI稳定判据.与已有结果相比,该判据形式简洁,求解变量少,且不含复矩阵变量,能够直接应用于控制器设计而不带来任何保守性,克服了原判据存在的主要缺点.然后基于该判据,进一步研究了当分数阶系统具有多胞型不确定时的鲁棒镇定控制器的设计方法.最后,仿真结果表明该方法的有效性.     

多模态Hto随机系统的均方稳定性与鲁棒镇定

研究由连续时间Ｍａｒｋｏｖ链所确定的多模态Ｉｔｏ随机系统的均方稳定性与鲁棒镇定,得到了一般多模态Ｉｔｏ随机系统的ｋ阶距指数稳定性定理,线性不确定系统的均方稳定性定理,给出了线性不确定系统的鲁棒镇定控制器。     

基于观测器的分散鲁棒镇定控制

对一类系统的状态、输入和输出均含有不确定性,不确定性不满足匹配条件的关联大系统,给出了其可分散观测器状态反馈镇定的充分条件,即一级线性矩阵不等式（ＬＭＩ）有解。通过求解一凸优化问题,可方便地获得分散观测器和状态反馈增益矩阵。文中的仿真示例说明了该方法的有效性和优越性。     

具有结构式混合不确定性系统的鲁棒镇定

研究具有结构式混合不确定性系统的鲁棒镇定问题。根据两类不确定性的不同特点，先用ｕ分解原理和线性分式变换模型，依据未建模动态所对应的子系统确定能鲁棒镇定含未建模动态系统的控制器集合Ψ（Ｋ（ｓ），Ｕ），再根据混ｕ理论从Ψ（Ｋ（ｓ），Ｕ）中确定所需的鲁棒镇定控制器Ψ（Ｋ（ｓ），Ｕ（ｓ））。     

不确定离散线性系统的鲁棒镇定

针对一类具有范数有界时变不确定性的离散性线系统,研究其二次稳定化状态反馈控制律的设计问题。推导出二次稳定化控制律存在一个充分必要条件,该条件被塌一步等价地表示成一个线性矩阵不等式的可解性问题。后者可用现有方法方便地求解,且它的解提供了所有二次稳定定化控制律的一个参数化表示。     

Weighted Nash equilibrium of incomplete-profile networked evolutionary games with multiple payoffs

This paper investigates the existence and convergence of weighted Nash equilibrium for incomplete-profile networked evolutionary games with multiple payoffs. First, the incomplete-profile networked evolutionary game under probabilistic myopic best response adjustment rule is transformed into an algebraic form based on the semi-tensor product of matrices. Second, a method for calculating weighted Nash equilibrium is presented, and the relationship between weighted Nash equilibrium and positive-probability fixed point is derived. Furthermore, a criterion is provided to verify whether the profiles in the feasible profile set can converge to the set of weighted Nash equilibriums with probability one. Finally, an illustrative example is given to support the new results obtained in this paper.     

布尔控制网络的输出稳定与镇定

矩阵的半张量积是将逻辑变量转化为向量研究的主要工具.本文利用半张量积把逻辑控制系统表示为离散时间仿射线性系统,在逻辑系统的状态空间框架下研究了以布尔控制网络为代表的逻辑动态系统的输出稳定与镇定.首先给出布尔网络输出稳定的定义,研究了布尔网络输出稳定的充要条件;其次讨论了布尔控制网络的输出镇定,分别得到了布尔控制网络由常值输入变量、自由控制序列、状态反馈控制序列输出镇定的条件.本文讨论的系统输出稳定与镇定是(部分)变量稳定与镇定的推广.     

Stability and stabilization of evolutionary games with time delays via matrix method

This paper studies the stability and stabilization of a class of evolutionary games (EGs) with time delays via the semi‐tensor product (STP) method. First, the matrix expression of the EGs with time delays is given, and then it is converted into the form without delay equivalently. By designing Lyapunov function, a necessary and sufficient condition for the global stability of delayed EGs is obtained. To deal with the delayed EGs with multiple equilibriums, the controlled EGs with time delays is investigated. An intermittent state feedback control is proposed, in which the controller works only at certain strategy profiles. Based on the intermittent control, two necessary and sufficient conditions are provided to assure the stabilization of the controlled EGs with time delays. Some examples are worked out to illustrate the effectiveness of the theoretical results.     

A Matrix Approach to the Modeling and Analysis of Networked Evolutionary Games With Time Delays

Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games (NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic expression is formulated for the networked evolutionary games with finite memories, based on which the behavior of the corresponding evolutionary game is analyzed. Secondly, under a proper assumption, the existence of Nash equilibrium of the given networked evolutionary games is proved and a free-type strategy sequence is designed for the convergence to the Nash equilibrium. Finally, an illustrative example is worked out to support the obtained new results.      

Modelling and strategy consensus for a class of networked evolutionary games

Using the semi-tensor product method, this paper investigates the algebraic formulation and strategy consensus for a class of networked evolutionary games (NEGs) with ‘unconditional imitation updating rule’, and presents a number of new results. First, the given NEG is converted to an algebraic form via the semi-tensor product method, and an algorithm is established to obtain the algebraic expression of the considered game. Second, based on the algebraic form, the behaviours of the players in the given evolutionary games are analysed, and some meaningful results are presented. Finally, the strategy consensus problem is considered by adding a pseudo-player to the game, and a free-type control sequence is designed to make the given NEG reach strategy consensus. The study of an illustrative example shows that the new results obtained in this paper work very well.     

局部信息约束下网络演化博弈的动力学与优化

网络演化博弈的优化问题是混合值逻辑网络的一个自然推广.本文研究了一类网络演化博弈的优化控制问题,其中每个控制个体在极大化自己的收益时只能获取到邻域信息.首先,利用矩阵的半张量积,将局部信息约束下控制网络演化博弈的动力学转化为相应的代数形式.然后得到了局部信息约束下确定型网络演化博弈的最优控制序列.最后,基于动态规划的解,研究了局部信息约束下概率型网络演化博弈的优化控制问题,得到了最优控制序列的简单计算公式.两个数值例子验证了本文的理论结果.     

Robust stability and stabilisation of Boolean networks with disturbance inputs

This paper deals with the problems of robust stability analysis and robust stabilisation control design for Boolean networks with disturbance inputs. The main tool used in this paper is the semi-tensor product of matrices. First, a necessary and sufficient condition is presented for the robust stability of Boolean networks based on the algebraic representation of Boolean networks with disturbance inputs. Second, the concept of one-step robust reachability is defined for Boolean control networks (BCNs) with disturbance inputs, based on which a constructive procedure is proposed for the robust stabilisation control design of BCNs. The study of an illustrative example demonstrates the effectiveness of the obtained new results.     

On finite-time stability and stabilization of nonlinear port-controlled Hamiltonian systems

The finite-time stability and stabilization of nonlinear port-controlled Hamiltonian(PCH)systems are investigated in this paper,and a number of new results are proposed.Firstly,by exploiting the Hamiltonian structural properties,a proper form of the Hamiltonian function is obtained,based on which a finite-time stability criterion is then presented for a class of Hamiltonian systems.Secondly,using the obtained stability criterion and the so-called"energy shaping plus damping injection"technique,the continuous finite-time stabilization problem is studied for the PCH system,and several global stabilization results are provided.Finally,the continuous robust finite-time stabilization of the PCH system with external disturbances is investigated,and two results on designing global robust finite-time stabilizers are obtained.Study of several examples with numerical simulations shows that the control design approach developed in this paper works very well.     

Modelling and strategy optimisation for a kind of networked evolutionary games with memories under the bankruptcy mechanism

This paper investigates the evolutionary dynamic and strategy optimisation for a kind of networked evolutionary games whose strategy updating rules incorporate ‘bankruptcy’ mechanism, and the situation that each player's bankruptcy is due to the previous continuous low profits gaining from the game is considered. First, by using semi-tensor product of matrices method, the evolutionary dynamic of this kind of games is expressed as a higher order logical dynamic system and then converted into its algebraic form, based on which, the evolutionary dynamic of the given games can be discussed. Second, the strategy optimisation problem is investigated, and some free-type control sequences are designed to maximise the total payoff of the whole game. Finally, an illustrative example is given to show that our new results are very effective.     

N人合作博弈的Nash及演化均衡稳定策略分析

在有限理性的基础上,对N人合作博弈的对称Nash均衡进行了分析,并引入演化博弈理论分析了参与人的演化均衡稳定策略,得到了不同策略选择下的均衡点。进而应用生物复制动态理论对离散时间及连续时间下的复制动态稳定集进行了研究。最后通过实例说明了该方法在博弈均衡选择上的有效性。