论文标题
对模型预测控制的比例综合投影梯度方法
Proportional-Integral Projected Gradient Method for Model Predictive Control
论文作者
论文摘要
最近，人们对模型预测控制（MPC）的原始偶对偶的方法越来越兴趣，这需要在每次迭代中最大程度地减少（增强）拉格朗日语。对于MPC，我们提出了一种新颖的一阶原始偶对偶偶联方法，称为\ emph {比例综合投影梯度方法}，其中基础有限的地平线最佳控制问题既具有状态和输入约束。我们方法的每次迭代都没有最大程度地减少（增强的）拉格朗日，而只能计算出对状态和输入约束集的单个投影。我们的方法可确保按照平均迭代序列，如果目标函数为凸，则最佳距离和约束违规的距离以\（o（1/k）\）的速率收敛到零，其中\（k \）是迭代号。如果目标函数强烈凸出，则可以将此速率提高到\（O（1/k^2）\），以达到最佳的距离，并且\（O（1/k^3）\）以违反约束。我们通过轨迹规划的示例与现有方法与现有方法进行比较，并与共有的保留区约束进行比较。
Recently there has been an increasing interest in primal-dual methods for model predictive control (MPC), which require minimizing the (augmented) Lagrangian at each iteration. We propose a novel first order primal-dual method, termed \emph{proportional-integral projected gradient method}, for MPC where the underlying finite horizon optimal control problem has both state and input constraints. Instead of minimizing the (augmented) Lagrangian, each iteration of our method only computes a single projection onto the state and input constraint set. Our method ensures that, along a sequence of averaged iterates, both the distance to optimum and the constraint violation converge to zero at a rate of \(O(1/k)\) if the objective function is convex, where \(k\) is the iteration number. If the objective function is strongly convex, this rate can be improved to \(O(1/k^2)\) for the distance to optimum and \(O(1/k^3)\) for the constraint violation. We compare our method against existing methods via a trajectory-planning example with convexified keep-out-zone constraints.
