随机系统输出概率密度函数的有限时间镇定

针对一类含有限能量未知扰动的随机动态系统,研究基于随机分布函数的有限时间控制问题．通过Ｂ 样条逼近建立了输出概率密度函数（ＰＤＦ）与权值之间的对应关系,利用线性矩阵不等式,给出了基于观测器的ＰＤＦ 有限时间控制器的参数化设计方法．采用该方法设计的控制器,可使系统对所有满足条件的未知扰动是随机有限时间有界和随机有限时间镇定的．仿真实例验证了所提出方法的有效性．

     

Markov跳变系统的有限时间状态反馈镇定

讨论一类含有限能量未知扰动的线性Markov跳变系统的有限时间镇定问题.针对连续系统和离散系统两种情况,利用构造的Lyapunov-Krasovskii函数,并结合线性矩阵不等式方法,分别证明并给出了跳变系统有限时间镇定控制器有解的充分条件.采用该方法设计的镇定控制器可使连续系统和离散系统对所有满足条件的未知扰动是有限时问有界和有限时间镇定的.最后通过数值示例表明了该设计方法的有效性.     

基于输出反馈和滑模控制的一类二阶非线性系统有限时间镇定方法

本文研究了一类具有不确定非线性动力学和未知外部扰动的二阶非线性系统的全局有限时间输出镇定问 题. 首先, 提出了一种全局状态反馈有限时间控制器, 实现了二阶非线性系统的有限时间镇定. 为了解决只有系统输 出可用这种更有挑战性的情况, 采用了一种新颖的设计思想, 即非分离原理. 构造了一个有限时间收敛的状态观测 器来估计未知状态. 在此观测器的基础上, 提出了一种基于输出的有限时间复合控制器. 基于李雅普诺夫方法, 证明 了整个闭环系统的全局有限时间稳定性. 仿真结果表明了理论的有效性.     

基于扩张状态观测器的二质量系统非奇异快速终端滑模控制

针对含未知负载信息的二质量伺服系统,提出一种基于有限时间扩张状态观测器的非奇异快速终端滑模控制方法.首先,利用电机侧位置信息设计有限时间扩张状态观测器估计系统的扰动,并将估计值融入到控制器中作为前馈项对系统的未知扰动进行补偿;然后,引入一种新型的滑模趋近律,该趋近律能够避免传统滑模控制中存在的奇异性问题,据此设计非奇异快速终端滑模控制器,保证系统状态在有限时间内收敛到原点,并根据李雅普诺夫稳定性理论分析闭环系统的稳定性;最后,通过仿真和实验验证所提出方法的优越性.结果表明,与传统的PID等控制相比较,所提出的基于扩张状态观测器的有限时间滑模控制方法能够提高系统的跟踪性能,并有效增强二质量伺服系统的抗扰动能力.     

Markov跳变系统的有限时间状态反馈镇定

讨论一类含有限能量未知扰动的线性Markov跳变系统的有限时间镇定问题.针对连续系统和离散系统两种情况,利用构造的Lyapunnov-Krasovskii函数,并结合线性矩阵不等式方法,分别证明并给出了跳变系统有限时间镇定控制器有解的充分条件.采用该方法设计的镇定控制器可使连续系统和离散系统对所有满足条件的未知扰动是有限时间有界和有限时间镇定的.最后通过数值示例表明了该设计方法的有效性.

     

随机马尔科夫跳跃系统有限时间控制

研究了转移概率部分信息未知的随机马尔科夫跳跃系统的有限时间控制问题.首先,介绍了有限时间随机稳定性与随机镇定性的概念;然后,利用矩阵变换、数学期望以及Gronwall不等式等方法,给出了系统为有限时间随机稳定的判定准则.利用上述结果,得出了系统状态输出反馈随机镇定的充分条件;进一步,考虑到实际工程中系统状态的不完全可测性,给出了保证系统有限时间随机镇定的动态输出反馈控制器设计方式,并求得了此控制器存在的判定条件.最后,用一个数值算例说明了控制器设计方法的有效性.     

Buck型变换器自适应有限时间降压控制算法研究

针对负载未知情况下Buck型DC-DC变换器系统, 基于有限时间控制技术和自适应控制技术, 提出了一种新的快速降压控制算法.首先, 基于时间尺度变换, 对系统的平均状态空间方程进行变换; 然后, 利用饱和有限时间控制理论设计出一类新的快速降压控制算法, 以实现输出电压在有限时间内收敛到参考电压.由于控制器设计过程中考虑了饱和约束条件, 使得变换器的占空比函数满足0到1之间的约束条件.对于负载未知情况, 设计了有限时间观测器以估计未知负载, 最终得到自适应式的有限时间控制算法.与PI控制结果进行了仿真对比, 验证了所提出的控制算法既具有快速的调节性能, 又具有较强的抗负载变化性能.     

基于扩展状态观测器的随机隐Markov正跳变系统有限时间异步控制

针对一类含不匹配扰动的随机隐Markov跳变系统, 本文研究了基于扩展状态观测器(ESO)的有限时间异步 控制问题. 首先, 引入一组扩展变量将隐Markov跳变系统转换成一组新的随机扩展系统, 补偿不匹配扰动对系统控 制输出的影响. 基于Lyapunov–Krasovskii泛函方法, 给出使得基于ESO的闭环随机隐Markov增广跳变系统是正系 统, 且有限时间有界的充分条件. 进而得到直接求解观测器增益和控制器增益的线性矩阵不等式. 最后, 通过仿真结 果验证了本文所设计的异步状态反馈控制器和观测器的有效性和可行性.     

T-S模糊系统的有限时间控制

面向具有强非线性的复杂工业过程,利用T-S模糊模型逼近原非线性系统,把T-S模糊模型逼近非线性系统存在的误差描述成有界时变的扰动,进而提出带扰动的T-S模糊系统的有限时间控制方法.首先,给出线性系统有限时间有界性的一个充分条件,与现有结果相比,该条件具有较小的保守性,并可以处理扰动是时变的情况;然后,提出T-S模糊系统有限时间镇定控制器的设计方法;最后,给出基于线性矩阵不等式(LMI)的控制器设计算法,并通过数值算倒演示所给方法的有效性.     

高速列车非线性系统的分数阶有限时间控制器设计

针对具有输入非线性, 不确定的气动阻力, 未知的车间力, 外部扰动以及未知的执行器故障等特征的高速列车非线性系统, 结合分数阶稳定性原理以及有限时间控制理论, 本文设计了一种分数阶有限时间控制器以实现高速列车更快速且更高精度的跟踪控制. 该控制器能够直接补偿高速列车的不确定性和非线性以及执行器故障而不需任何“试错”过程, 且稳定时间可由控制参数的不同选择来调整. 仿真研究验证了所设计控制器的有效性和优越性.     

Finite‐Time Stability and Stabilization of Linear Itô Stochastic Systems with State and Control‐Dependent Noise

In this paper, finite‐time stability and stabilization problems for a class of linear stochastic systems are studied. First, a new concept of finite‐time stochastic stability is defined for linear stochastic systems. Then, based on matrix inequalities, some sufficient conditions under which the stochastic systems are finite‐time stochastically stable are given. Subsequently, the finite‐time stochastic stabilization is studied and some sufficient conditions for the existence of a state feedback controller and a dynamic output feedback controller are presented by using a matrix inequality approach. An algorithm is given for solving the matrix inequalities arising from finite‐time stochastic stability (stabilization). Finally, two examples are employed to illustrate the results.     

Nonsmooth Stabilization of a Class of Markovian Jump Stochastic Nonlinear Systems with Parametric and Dynamic Uncertainties

In this paper, we investigate the finite‐time stabilization of Markovian jump stochastic nonlinear (SNL) systems with dynamic uncertainties. Firstly, a proper criterion on finite‐time globally asymptotically stability in probability (FGSP) and some useful lemmas are introduced. Then, overcoming the influence of coupled item which determined by Markovian switching, by adding a power integrator technique and induction method, a state‐feedback finite‐time controller is explicitly constructed. It is proven that, the system state of the closed‐loop systems is FGSP. Simulation examples illustrate the effectiveness of our method.     

Finite‐Time Stabilization of Stochastic High‐Order Nonlinear Systems

This paper considers the problem of global finite‐time stabilization in probability for stochastic high‐order nonlinear systems in which the power order is greater than or equal to one and the drift and diffusion terms satisfy weaker growth conditions. Based on stochastic Lyapunov theorem on finite‐time stability, via the combined adding one power integrator and sign function method, constructing a Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed‐loop system globally finite‐time stable in probability.     

Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay

Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method.     

Semiglobal finite‐time synchronization of complex networks with stochastic disturbance via intermittent control

This paper focuses on the problem of semiglobal finite‐time synchronization of stochastic complex networks via an intermittent control strategy. By establishing a finite‐time criterion condition and a novel finite‐time ‐operator differential inequality, combined with convex techniques, some sufficient conditions are obtained to ensure finite‐time synchronization for stochastic complex networks with time delays. An effective controller is given to guarantee inner finite‐time synchronization, especially for a nondelayed dynamic system. This paper provides a simple controller. Finally, a numerical simulation is given to demonstrate the effectiveness of our results.     

输出概率密度函数鲁棒弹性最优跟踪控制

研究了一类随机动态系统的鲁棒弹性最优跟踪控制问题。在采用B样条神经网络模型逼近随机动态系统的输出概率密度函数(PDF)的基础上,同时考虑系统模型和控制器增益不确定性,结合Lyapunov稳定性理论和线性矩阵不等式(LMI)技术,引入增广控制作用,设计基于广义状态反馈的鲁棒弹性最优跟踪控制器,目的是使系统的输出PDF跟踪给定PDF。通过求解LMI,所得控制器不仅能实现跟踪目的,而且能确保该随机动态系统全局稳定并满足一定的线性二次型性能指标上界。仿真结果表明该方法简单易行,且无需任何设计参数调整。     

Finite‐time stabilization of stochastic low‐order nonlinear systems with FT‐SISS inverse dynamics

This paper studies finite‐time stabilization problem for stochastic low‐order nonlinear systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with finite‐time stochastic input‐to‐state stability, combining the Lyapunov function and adding a power integrator technique, and using the stochastic finite‐time stability theory, a state feedback controller is designed to guarantee global finite‐time stability in probability of stochastic low‐order nonlinear systems with finite‐time stochastic input‐to‐state stability inverse dynamics.     

Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation

This paper presents a method for the dynamic analysis of structures with stochastic parameters to random excitation. A procedure to derive the statistical characteristics of the dynamic response for structure is proposed by using dynamic Neumann stochastic finite element method presented herein. Random equation of motion for structure is transformed into a quasi-static equilibrium equation for the solution of displacement in time domain. Neumann expansion method is developed and applied to the equation for deriving the statistical solution of the dynamic response of such a random structure system, within the framework of Monte Carlo simulation. Then, the results from Neumann dynamic stochastic finite element method are compared with those from the first- and second-order perturbation stochastic finite element methods and the direct Monte Carlo simulation with respect to accuracy, convergence and computational efficiency. Numerical examples are examined to show that the approach proposed in this paper has a very high accuracy and efficiency in the analysis of compound random vibration.     

基于不同加权因子的随机多模型自适应控制

针对一类噪声方差未知的随机系统,基于不同加权因子设计多个参数辨识器辨识模型参数,在此基础上,构成多模型自适应控制器.在每个采样时刻基于指标切换函数选择最佳辨识模型.并将基于此最佳模型设计的控制器切换为当前控制器.同时,证明了多个模型控制器之间相互切换时整个闭环系统是全局收敛的.仿真结果表明,同单一自适应模型控制器相比,这种基于多个不同加权因子的多模型自适应控制器在模型参数发生跳变时可很好地改善被控对象的控制品质.     

Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H_∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.