约束分段仿射系统的鲁棒一步预测控制

Robust One Step Predictive Control for Constrained Piecewise Affine Systems

针对一类具有附加有界扰动的离散时间约束分段仿射系统,提出了一种鲁棒低复杂性的模型预测控制方法,即鲁棒一步控制.首先,基于最大鲁棒正不变集,计算系统的最大鲁棒可稳定集并作为第一步预测状态的约束集,使得产生的滚动时域控制器可以在较小的预测时域内控制最大鲁棒可稳定集.然后,在最大鲁棒正不变集外,通过构建线性矩阵不等式来分析其鲁棒稳定性.两个步骤分别确保控制器的可行性和闭环系统的鲁棒稳定性.大量的数值例子表明,和已有的控制方法相比,所得的鲁棒一步控制器具有更低的复杂性.

A robust low complexity model predictive control（MPC） scheme,referred to as robust one-step control,is proposed for a class of constrained discrete-time piecewise affine（PWA） systems with bounded additive disturbance.First, based on the maximal robust positively invariant set,the maximal robust stabilizable set is computed and chosen as the constraint set of the first predicted state in MPC formulation,such that the resulting receding horizon（RH） controller can control maximal robust stabilizable set with shorter prediction horizons.Second,the robust stability is analyzed via linear matrix inequalities（LMIs） outside of maximal robust positively invariant set.The combination of these two components guarantees the robust feasibility of the controller and stability of closed-loop system.Extensive numerical examples show that the controller with lower complexity can be obtained with one-step control scheme compared with existing ones.