扩大约束分段仿射系统鲁棒预测控制的吸引域

Enlarging domain of attraction of robust predictive control for constrained piecewise affine systems

针对一类具有附加有界扰动的约束离散时间分段仿射(PWA)系统,提出一种扩大其鲁棒模型预测控制吸引域的新方法.计算系统的最大鲁棒正不变集以及相关的局部稳定控制律.基于最大鲁棒正不变集,通过多参数规划,采用一步预测时域来离线计算一序列具有收缩性质的鲁棒可稳定集,构成收缩序列集,并将它们作为优化问题的预测状态终端约束集.得到的预测控制器可以鲁棒调节收缩序列集内的状态到鲁棒正不变集,从而确保系统的鲁棒稳定,并扩大了鲁棒预测控制的吸引域.通过数值实例验证了方法的有效性.

Aimed at a class of constrained discrete-time piecewise affine （PWA） systems with addictive bounded disturbances, a new method for enlarging the domain of attraction of robust model predictive control （MPC） was presented. The maximal robust positively invariant set and the associated local stable control law were computed. Based on the maximal robust positively invariant set, a contractive sequence of robust stabilizable sets were computed off-line using multi-parametric programming with one-step predictive horizon. By considering this sequence as terminal constraint of predictive states in the optimization problem, the resulting controller can robustly steer the states in the contractive sequence of sets to the maximal robust positively invariant set. Hence the stability and the enlargement of domain of attraction of robust predictive control were guaranteed. A numerical example showed the validity of the proposed method.