一种基于闭环优化的新型鲁棒预测控制方法

Novel Robust predictive control algorithm based on closed-loop optimization.

针对带约束的凸多面体线性不确定模型,提出了一种新型鲁棒预测控制方法.它采用离散化的不确定模型构造最小一最大优化控制问题,并在其中直接引入状态反馈机制.与其他最小-最大预测控制方法相比,这种方法等效于增加了控制序列的长度,为优化问题增加了更多的自由度,从而扩大了可行域.作为最小化目标的是离散化不确定系统在整个预测时域上二次型成本函数的最大值,而不是各预测阶段对应成本项的上界之和,从而减少了与最小-最大优化相关的方程个数,有利于降低计算复杂性.文中进一步证明了不确定系统的闭环稳定性取决于优化问题在初始时刻的可行性,并将优化问题转化为线性矩阵不等式形式.最后,以数值仿真例子验证了方法的有效性.

A novel robust predictive control scheme was presented for constrained linear time-varying systems with polytopic uncertainty. Compared with other similar methods, it has the following characteristics. Firstly, the min-max optimal control problem is formulated using the discretized uncertain models and the state feedback mechanism is also introduced directly to it. Thus more freedom is added to the constrained optimal problem and the feasible region is effectively enlarged. Secondary, the minimization object is the cost on the whole predictive horizon, not the sum of the upper bounds of stepwise cost. This leads to a notable reduction in number of equations pertaining to min-max optimization. Furthermore , the robust stability is proved to depend on the feasibility of the optimization problem at the initial time and the optimization problem is formulated in terms of LMls. Finally, a numerical example was used to verify the effectiveness of the presented method.