基于收缩序列集的约束PWA系统鲁棒预测控制

Robust predictive control of constrained piecewise affine systems based on a contractive sequence of sets

针对一类有附加有界扰动的约束离散时间分段仿射系统,提出了一种具有鲁棒稳定性保证的模型预测控制方法。通过多参数规划采用一步预测时域法离线计算具有收缩性质的鲁棒可稳定集系列,把它们作为优化问题的稳定约束,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即保证了系统的鲁棒稳定性。仿真实例表明提出的控制方法可使系统渐近稳定到鲁棒正不变集。

A robust MPC （model predictive control） scheme with stability guaranteed is proposed for a class discrete time PWA （piecewise affine） systems subject to constraints on states and inputs with additional bound ed disturbances. A contractive sequence of robust stabilizable sets are computed off-line using multi-parametric programming with one-step predictive horizon. By incorporating this sequence as a stabilizing constraint in the optimization problem and choosing a robust positively invariant set as a terminal constraint, the feasibility of the optimization problem guarantees the robust stability. A numerical example shows that the proposed controller asymptotically stabilizes the system to a robust positively invariant set.