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离散Markov跳变系统的滚动时域H_∞跟踪控制

Receding Horizon H_∞ Tracking Control for Discrete-time Markov Jump Systems
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摘要 针对离散Markov跳变系统,研究滚动时域H∞跟踪控制问题。为便于工程应用,假定系统当前时刻的状态和模态总是可测的,而系统未来时刻的模态是不可知的。利用庞特里亚金极小值原理,构造哈密尔顿函数,求解min-max优化问题,得到当前采样时刻的最优控制作用以及最严峻的外界扰动。控制器的求解可等效为在一组线性矩阵不等式约束条件下,迭代方程的可解性问题。控制律采用滚动时域结构,每次仅施加当前采样时刻计算得到的控制作用,在下一采样时刻将重新计算控制作用。该控制律保证系统在给定H∞扰动抑制水平的情形下,获得最优线性二次型性能指标以及良好的输出跟踪性能。最后仿真示例验证了该方法的可行性和有效性。 To the discrete-time Markov jump linear system, a receding horizon tracking control scheme is presented. In terms of engineering application, the current state and jump mode are assumed to be completely observed, and the future modes are naturally supposed unavailable. The min-max problem is solved by using pontryaging minimum principle through constructing Hamilton function. The optimal control at current sampling time and the worst disturbance are obtained. The controller can be constructed through numerical solution of an iterative equation subject to a set of linear matrix inequalities. Only the first computed control move at current sampling time is implemented. At the next sampling time, the optimization is solved again with new measurement of the plant. The control scheme make the system obtain an optimal linear quadratic cost function and good tracking performance while H∞ disturbance attenuation is also satisfied. The simulation result shows the feasibility and effectiveness of the proposed method.
作者 闻继伟 刘飞
机构地区 江南大学自动化研究所
出处 《控制工程》 CSCD 北大核心 2010年第1期67-70,共4页 Control Engineering of China
基金 国家自然科学基金资助项目(NSFC:60974001) 江苏省"六大人才高峰"基金资助项目
关键词 MARKOV跳变系统 滚动时域 跟踪控制 跳变模态 H∞扰动抑制水平 Markov jump systems receding horizon tracking control jump mode H∞ disturbance attenuation
分类号 TP13 [自动化与计算机技术—控制理论与控制工程]
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参考文献9

  • 1Boukas E K, Shi P, Nguang S K. Robust H∞ control for linear Markovian jump systems with unknown nonlinearities [ J ]. Journal of Mathematical Analysis and Application, 2003, 282( 1 ) : 241-255.
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二级参考文献10

  • 1Hu T S, Lin Z L, Chen B M. Analysis and design for discretetime linear systems subject to actuator saturation[J]. Systems Control Lett. ,2002. 45(2) : 97 - 112.
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  • 9Park B G, Kwon W H, Lee J W. Robust receding horizon control of discrete-time Markovian jump uncertain systems. IEICE Trans. on Fundamentals, 2001, E84-A(9):2272-2279.
  • 10Cao Y Y, Lin Z I., Shamash Y. Set invariance analysis and gainscheduling control for LPV systems subject to actuator saturation [J]. Systems and Control Letters. 2002, 46 (2) : 137 - 151.

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控制工程
2010年 第1期

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