Markov跳变系统的滚动时域鲁棒双模控制  

Robust receding horizon dual-mode control for Markov jump systems

作　　者：闻继伟[1] 刘飞[1] 

机构地区：[1]江南大学自动化研究所,江苏无锡214122

出　　处：《电机与控制学报》2009年第6期919-925,共7页Electric Machines and Control

基　　金：国家自然科学基金(60574001);新世纪优秀人才支持计划(05-0485)

摘　　要：针对一类具有输入和状态联合约束的不确定离散时间Markov跳变系统,提出滚动时域鲁棒双模控制的方法。基于椭圆不变集的性质,在椭圆不变集以外使用滚动时域控制,驱动状态进入椭圆不变集。一旦状态进入椭圆不变集,改为使用线性状态反馈控制以保证状态始终位于椭圆不变集内,并使系统均方稳定。控制器的求解转化为以线性矩阵不等式形式给出的半正定规划问题。为改进半正定规划问题的可行性,将自由终端成本的上界作为椭圆不变集的边界,在优化成本的同时得到一组压缩椭圆集,相对于固定椭圆不变集降低了保守性。仿真实例验证了所提出方法的可行性和有效性。A robust receding horizon dual-mode control method is proposed for a class of uncertain dis- crete-time Markov jump systems subject to input and state constraints by using the property of the invari- ant ellipsoid. Outside the ellipsoid, the receding horizon control is employed. Once the state enters the ellipsoid, the control is switched to a linear state feedback control, which makes the state stay in the el- lipsoid for ever and stabilizes the system in mean square sense. The proposed controller is obtained by u- sing semi-definite programming （SDP） which can be easily solved by means of linear matrix inequalities. To improve the feasibility of the above mentioned SDP problem, the upper-bound of the free terminal cost is regarded as boundary of invariant ellipsoid. A set of shrinking ellipsoids are obtained while the cost function is optimized. It reduces conservativeness of fixed invariant ellipsoid. The simulation example is given to verify the feasibility and efficiency of the proposed method.

关 键 词：MARKOV跳变系统 滚动时域控制 双模控制 输入和状态联合约束 椭圆不变集 半正定规划 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]