Resource-aware time-optimal control with multiple sparsity measures

The paper proposes a novel time-optimal control that is also sparse in both time and space domain to take account of resource constraints in networked control systems. The control problem is described as minimization of a weighted sum of the terminal time and the L-0 norm of multi-input control for a linear time-invariant dynamical system, with state and control constraints. In particular, we treat the constraint on the number of actuations at each time, which is described as an l(0) norm constraint. Since the L-0/l(0) optimization problem is highly non-convex, we propose to solve a convex relaxation using L-1 and l(1) norms. We give sufficient conditions for the equivalence between the original L-0/l(0) problem and the relaxed L-1/l(1) problem. Based on the relaxation, we also propose a numerical computation method for the L-1/l(1) problem by sequential linear programming. We show numerical examples to illustrate the effectiveness of the proposed control method. (C) 2021 Elsevier Ltd. All rights reserved.