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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。
Aiming at a class of piecewise affine systems with bounded additional perturbations, a robust low-complexity robust predictive control method is proposed - robust minimum time control. Firstly, the maximum robust positive invariant set of the system and the related local stability control law are calculated. Then based on the maximum robust positive invariant set, a robust one-step system of offline iterative computing system is constructed through multi-parameter programming. The minimum time controller is obtained. Robust and stable set. The proposed robust minimum time control ensures that the system states enter a robust invariant set within the minimum time, thus ensuring robust feasibility and stability. Numerical examples verify the effectiveness and low complexity of the method.