Networked Sliding Mode Control Systems

• Other Authors: Song, Heran (author.)
• Format: Others
• Language: English; Chinese
• Published: 2016
• Online Access: http://repository.lib.cuhk.edu.hk/en/item/cuhk-1292204

本论文以滑膜控制为工具，主要研究了两个问题。 === •对有连续马尔科夫丢包的网络控制系统的滑膜控制。 === 我们首先选取Gilbert-Elliot通道模型来描述丢包之间的时间相关，并假设系统状态可得，提出了一个更新机制来选择滑膜控制器采用的系统状态。我们使用马尔科夫跳线性系统理论中的一项技术解决丢包产生的问题。具体包括：引入李雅谱诺夫函数，该函数的构造依赖于瞬时丢包的指示函数；在满足一组线性矩阵不等式的前提下，证明在均方意义下，推导出的滑膜控制器能够将系统状态轨迹带入之前我们设计的滑面的附近，且系统状态在之后的时间内一直保持在滑面临近区域内。最后我们给出了范例分析，表明了控制律的有效性。 === 然后，我们将Gilbert-Elliot通道模型扩展到一个广泛应用在无线通信系统中的更为普遍和准确的有限状态马尔科夫通道模型，来描述系统丢包之间的时间相关。我们推导出的滑膜控制器能够将系统状态轨迹带入设计的滑面的附近区域，并使系统均方渐进稳定。 === 实际上，丢包系统可看作有两个状态的马尔科夫跳系统。接下来，我们将问题一般化，研究马尔科夫跳系统的控制问题。 === •对有部分未知转移概率的离散时间马尔科夫跳系统的滑膜控制。我们假设系统的未知转移概率是任意有界约束的。首先研究一类特殊的凸集——凸多面体。我们设计了一个积分形的滑面，通过线性矩阵不等式的方法,我们推导出滑膜控制律，在均方意义下将系统状态带入该滑面的临近区域。之后我们提出了一个等效控制律，保证系统状态在随后的时间内一直保持在滑面临近范围内，闭环系统渐进均方稳定。然后我们将凸多面体推广至一般的有界集,找到一个包含有界集的有界凸多面体，使其所有顶点满足一组线性矩阵不等式，得出稳定结果。最后给出了一些仿 === 最后，基于上述研究，我们进一步研究了有连续马尔科夫丢包且系统未知转移概率为凸多面体约束的离散时间马尔科夫跳系统的滑膜控制。结果表明闭环系统可抵抗丢包引起的不确定性，消除系统模式转变、不确定的系统参数以及外界干扰造成的不利影响， 达到渐进均方稳定。 === This thesis mainly investigates two kinds of problems. === • The thesis presents the design of a sliding mode controller for networked control systems subject to successive Markovian packet dropouts. === First, the Gilbert-Elliott channel model is adopted to describe the temporal correlation among packet losses, and an update scheme is proposed to select the assumed available states for use in a sliding mode control law. A technique employed in the theory of discrete-time Markov jump linear systems is applied to tackle the effect of packet losses. This involves introducing a couple of Lyapunov functions dependent on the indicator functions of the instantaneous packet loss, and proving that the sliding mode controller is able to drive the system state trajectories into the neighborhood of the designed integral sliding surface in the mean-square sense given that the corresponding Lyapunov inequalities are satisfied. The system is guaranteed thereafter to remain inside the neighborhood of the sliding surface. Simulated case studies show that the control law can achieve asymptotic stability for discrete-time systems with either successive or single packet dropouts. === Then,the Gilbert-Elliott channel model is generalized to a finite-state Markov channel model, a more generic and accurate model widely used in wireless communication systems. Reachability and asymptotic mean-square stability of the system are ensured by the proposed SMC law. === • The thesis studies the design problem of a sliding mode controller for discrete-time Markovian jump systems subject to partially known transition probabilities. The unknown transition probabilities are assumed to be general constrained, and a special class of bounded sets-convex polytopes is concerned first. By using linear matrix inequalities (LMIs) approach, a sliding mode control law is derived to drive the system state trajectories towards the designed integral sliding surface in the meansquare sense. Next, an equivalent control law is proposed to ensure the system states to remain inside the neighborhood of the sliding surface thereafter, and the closed-loop system is asymptotically mean-square stable. Then the bounded convex polytope is generalized to ageneral bounded set. A bounded convex polytope can be found to cover the bounded set, and the reachability and asymptotic stability of the system are ensured if all the vertices of the bounded convex polytope satisfy a group of LMIs. Simulations are presented to illustrate the effectiveness of the control law. === Finally, based on the above results, further studies on sliding mode control for discrete-time Markovian jump systems with successive packet dropouts and convex-polytope constrained transition probabilities are carried out. The result shows under what === Song, Heran. === Thesis Ph.D. Chinese University of Hong Kong 2016. === Includes bibliographical references (leaves ). === Abstracts also in Chinese. === Title from PDF title page (viewed on …). === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only.