Active set solver for min‐max robust control with state and input constraints

Summary This paper proposes an online active set strategy for computing the dynamic programming solution to a min-max robust optimal control problem with quadratic stage cost for linear systems with linear state and input constraints in the presence of bounded disturbances. The solver determines the optimal active constraint set for a given plant state using an iterative procedure that computes the optimal sequence of feedback laws for a candidate active set and updates the active set by performing a line search in state space. The computational complexity of each iteration depends linearly on the length of the prediction horizon. The main contribution of the paper is its treatment of degeneracy caused by linearly dependent state and input constraints, and its efficient handling is a crucial step in formulating the active set algorithm. The proposed approach ensures the continuity of optimal control laws along the line-of-search, thus enabling an efficient solution method based on homotopy. Conditions for global optimality are given, and the convergence of the active set solver is established using the geometric properties of an associated multiparametric programming problem. A receding horizon control strategy is proposed, which ensures a specified l2-gain from the disturbance input to the state and control inputs in the presence of linearly dependent constraints. Copyright © 2016 John Wiley & Sons, Ltd.