Proportional-Integral Projected Gradient Method for Model Predictive Control

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 method, termed proportional-integral projected gradient MPC where underlying finite horizon optimal problem both state and input constraints. Instead of Lagrangian, iteration our method only computes single projection onto constraint set. Our ensures that, along sequence averaged iterates, distance to optimum violation converge zero rate O(1/k) if objective function is convex, k number. If strongly this can be improved O(1/k 2 ) xmlns:xlink="http://www.w3.org/1999/xlink">3 violation. compare against existing via trajectory-planning example with convexified keep-out-zone