采用输出反馈的执行器饱和跳变系统H_∞控制

H_∞ Control of Jump Systems with Saturated Actuator Using Output Feedback

针对一类具有饱和执行器的马尔可夫跳变系统的H∞控制问题,提出一种基于模态跳变的动态输出反馈控制器的设计方法,并在保证闭环系统随机稳定的基础上,设计出了动态输出H∞控制器.通过将非线性饱和约束转化为特殊的线性约束,使具有饱和执行器的控制器求解问题转化为线性约束控制器的求解问题,利用位于闭环系统吸引域内的不同模态下椭圆不变集的交集来保证系统的随机稳定性,此时控制器的求解可等效为线性矩阵不等式的可解性问题.采用该设计方法设计的动态输出反馈H∞控制器能够保证闭环系统随机稳定,并且满足一定的H∞衰减水平.数值仿真结果表明,所设计的控制器使得闭环系统在椭圆不变集中的初始状态随机稳定,同时系统对干扰有很强的抑制能力.

In order to solve the H∞ control problem for a class of Markov jump systems with saturated actuator, a design method based on dynamic output feedback controller of mode-jumping is proposed, and the H∞ dynamic output feedback controller is then designed on the basis of the guarantee that the closed-loop system is random stable. By transforming the nonlinear saturation constraint into the special linear constraint, the problem of solving the feedback controller with saturated actuator is converted to the design of controller with linear constraint. The stochastic stability is ensured by using the intersection of ellipsoid invariant set of different modes existing in the attraction domain of the closed loop system. In this case, solving controllers can be equivalent to a solvability problem of linear matrix inequalities. With the above method, the stochastic stability of the closed-loop system can be guaranteed by the designed controller which satisfies a certain level of H∞ disturbance attenuation. Simulation results demonstrate that the proposed method is valid and the system has strong restraint ability against disturbance.