一类约束分段仿射系统的鲁棒双模预测控制

Robust dual-model predictive control for a class of piecewise affine systems

研究了具有附加扰动约束的分段仿射(PWA)系统的预测控制问题,提出了PWA系统鲁棒双模预测控制方法.该方法基于不确定演变集,即在任意可能的扰动下,系统的预测状态演变集.把它作为预测控制开环优化问题的状态约束,并选择一个鲁棒正不变集作为终端约束,使得优化问题的可行性保证了系统的鲁棒稳定性,并可利用优化问题的次优解来确保系统的鲁棒稳定性,降低了优化计算的复杂性.数值实例表明,获得的双模控制器在预测时域内可渐近稳定系统状态到鲁棒正不变集,并在局部控制器的作用下保持状态在正不变集内,保证了系统的渐近终端有界.

Model predictive control （MPC） for constrained discrete-time piecewise affine （PWA） systems with additive bounded uncertainties was studied and a robust dual-model predictive control method for PWA systems was presented. The MPC method was based on so-called uncertain evolution sets, which contained the predicted evolution of the uncertain system under any admissible uncertainty. By considering these sets as the state constrain of open-loop formulation of MPC and choosing as terminal constrain a robust positively invariant set, the robust stability was guaranteed by the feasibility of optimization problem.Furthermore, the suboptimal solution of the problem also guaranteed the robust stability, which reduced the complexity of the optimization problem. A numerical example showed that the resulted dual-model controller could asymptotically stabilize the system states to a robust positively invariant set in predictive horizons, and then the local controller kept the states evolution in positively invariant set all the time,which made the controlled system asymptotically ultimately bounded.