Control of discrete-time periodic linear systems with input saturation via multi-step periodic invariant set
Control of discrete-time periodic linear systems with input saturation via multi-step periodic invariant set
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DOI：
10.1002/rnc.3076
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
Bin Zhou;Dewei Li;Zongli Lin
中科院分区：
文献类型：
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作者：
Bin Zhou;Dewei Li;Zongli Lin
本文利用多步周期不变集方法研究了输入饱和的离散线性周期系统的局部控制问题。多步周期不变集是指所有轨迹经过有限步后都将进入一个周期不变集，并永远保持在那里，最终随着时间的推移而收敛到原点的集合。考虑了吸引域的鲁棒估计、鲁棒局部镇定和干扰抑制等问题。与传统的周期不变集方法相比，该方法通过在集合不变条件下引入更多的辅助变量，能够显著降低保守性.此外，新方法允许设计与开环系统周期相同的（鲁棒）稳定周期控制器，这不同于现有的周期增强方法，即控制器的周期是开环系统周期的倍数。数值算例表明了该方法的有效性。
This paper studies local control of discrete-time periodic linear systems subject to input saturation by using the multi-step periodic invariant set approach. Multi-step periodic invariant set refers to a set from which all trajectories will enter a periodic invariant set after finite steps, remain there forever, and eventually converge to the origin as time approaches infinity. A couple of problems including the (robust) estimation of domain of attraction, (robust) local stabilization, and disturbance rejection are considered. Compared with the conventional periodic invariant set approach which has been used in the literature for local stability and stabilization of discrete-time periodic linear systems subject to input saturation, this new invariant set approach is capable of significantly reducing the conservatism by introducing more auxiliary variables in the set invariance conditions. Moreover, the new approach allows to design (robust) stabilizing periodic controller whose period is the same as the open-loop system, which is different from the existing periodic enhancement approach by which the period of the controller is multiple times of the period of the open-loop system. Several numerical examples are worked out to show the effectiveness of the proposed approach.