Markovian跳变非线性系统的自适应输出跟踪控制研究

发布时间：2018-09-05 07:06

【摘要】：Markovian跳变系统是一类特殊的随机混杂系统,广泛存在于诸如化工过程、电力系统、飞行器系统、船舶导航系统等实际工程领域。其中Markovian跳变非线性系统的控制研究是当前控制理论研究的热点和难点,跳变行为使系统动态变得异常复杂,增加了这类系统的控制难度和复杂程度。本文分别针对具有模态转移率部分未知、未建模动态、时变时滞、输入饱和等特性的Markovian跳变非线性系统,展开了输出跟踪控制问题的研究。主要工作如下:首先,研究了一类模态转移率部分未知的Markovian跳变非线性系统的输出反馈跟踪控制问题。基于T-S模糊双线性模型,设计了动态输出反馈控制器;利用Lyapunov稳定性理论和线性矩阵不等式方法,给出了闭环系统均方渐近稳定的充分条件;通过求解一组线性矩阵不等式得到了控制器增益矩阵。最后通过仿真验证了所设计控制器的有效性。其次,研究了一类具有未建模动态的严格反馈Markovian跳变非线性系统的自适应跟踪控制问题。利用RBF神经网络逼近系统的未知综合非线性函数,并结合自适应估计方法设计了神经网络自适应跟踪控制器。所设计的控制器只需一个自适应参数在线调整,降低了计算的复杂性。理论分析证明了所设计的控制器能够保证闭环系统所有状态的一致最终有界性。再次,研究了一类严格反馈Markovian跳变非线性时滞系统的预设性能自适应跟踪控制问题。通过误差等效变换将预设性能跟踪控制问题转化为稳定性问题;通过构造合适的Lyapunov泛函抵消了不确定时滞项;采用神经网络逼近方法和自适应估计技术设计了预设性能自适应跟踪控制器。仿真结果表明所设计控制器能有效提高系统的输出跟踪性能。最后,进一步考虑执行器存在饱和约束,研究了一类严格反馈Markovian跳变非线性关联大系统的抗饱和预设性能自适应跟踪控制问题。采用RBF神经网络逼近系统的未知综合非线性函数,并结合自适应估计方法设计了一种抗饱和预设性能自适应分散控制器;通过引入一个动态补偿信号参与控制器的设计,降低了抗饱和控制器的设计难度。仿真结果验证了所设计的具有抗饱和作用的控制器对改善系统跟踪控制性能的有效性。
[Abstract]:Markovian jump system is a kind of special stochastic hybrid system, which is widely used in practical engineering fields such as chemical process, power system, aircraft system, ship navigation system and so on. The control of Markovian jump nonlinear systems is a hot and difficult point in the current control theory research. The jump behavior makes the system dynamic become extremely complex, which increases the control difficulty and complexity of this kind of systems. In this paper, the output tracking control problem for Markovian jump nonlinear systems with some unknown modal transfer rates, unmodeled dynamics, time-varying delays and input saturation is studied. The main work is as follows: firstly, the output feedback tracking control problem for a class of Markovian jump nonlinear systems with partially unknown modal transfer rate is studied. Based on T-S fuzzy bilinear model, a dynamic output feedback controller is designed, and a sufficient condition for the mean square asymptotic stability of the closed-loop system is given by using Lyapunov stability theory and linear matrix inequality (LMI) method. The controller gain matrix is obtained by solving a set of linear matrix inequalities. Finally, the effectiveness of the designed controller is verified by simulation. Secondly, the adaptive tracking control problem for a class of strict feedback Markovian jump nonlinear systems with unmodeled dynamics is studied. An adaptive tracking controller based on RBF neural network is designed by using RBF neural network to approximate the unknown comprehensive nonlinear function of the system and the adaptive estimation method. The designed controller only needs one adaptive parameter online adjustment, which reduces the complexity of calculation. It is proved by theoretical analysis that the designed controller can guarantee the uniform ultimate boundedness of all states of the closed-loop system. Thirdly, the preset performance adaptive tracking control problem for a class of strictly feedback Markovian jump nonlinear time-delay systems is studied. The preset performance tracking control problem is transformed into a stability problem by error equivalent transformation, and the uncertain time-delay term is offset by constructing appropriate Lyapunov functional. The adaptive tracking controller with preset performance is designed by using neural network approximation method and adaptive estimation technique. Simulation results show that the designed controller can effectively improve the output tracking performance of the system. Finally, considering the saturation constraint of the actuator, the adaptive tracking control problem for a class of nonlinear interconnected large-scale systems with strict feedback Markovian jump is studied. An adaptive decentralized controller with anti-saturation presupposition performance is designed by using RBF neural network to approximate the unknown comprehensive nonlinear function of the system, and an adaptive decentralized controller with anti-saturation presupposition is designed by introducing a dynamic compensation signal to participate in the design of the controller. The design difficulty of anti-saturation controller is reduced. The simulation results verify the effectiveness of the designed controller with anti-saturation effect on improving the tracking control performance of the system.
【学位授予单位】：燕山大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP13

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