约束分段仿射系统的鲁棒最小时间控制

Robust Minimum-Time Control for Constrained Piecewise Affine Systems with Bounded Disturbances

针对一类有界附加扰动的分段仿射系统,提出了一种离线低复杂性的鲁棒预测控制方法-鲁棒最小时间控制。首先计算系统的最大鲁棒正不变集和相关的局部稳定控制律,然后基于最大鲁棒正不变集通过多参数规划离线迭代计算系统的鲁棒一步集,得到的最小时间控制器覆盖最大鲁棒可稳定集。提出的鲁棒最小时间控制确保系统状态在最小时间内进入鲁棒正不变集内,从而保证了鲁棒可行性和稳定性。数值例子验证了方法的有效性和低复杂性。

A robust low complexity predictive control scheme, referred to as robust minimum-time control, for constrained piecewise affine（PWA） systems with bounded disturbances is proposed in this paper. Firstly, the maximal robust posltively invarlant set of the system associated with a local stabilizing control law is computed. Secondly, the robust one-step set based on the maximal robust positively invariant set is iteratively computed off-line using multi-parametric programming and the resulting controller cover the maximal robust stabilizable set. The proposed robust minimum-time control guarantees that the states within the maximal robust stabilizable set enter the positively invariant set in minimum time. Numerical examples show the validity and low complexity of the scheme compared to the existing one.