Resource-aware time-optimal control with multiple sparsity measures

Abstract

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 L0 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 ℓ0 norm constraint. Since the L0/ℓ0 optimization problem is highly non-convex, we propose to solve a convex relaxation using L1 and ℓ1 norms. We give sufficient conditions for the equivalence between the original L0/ℓ0 problem and the relaxed L1/ℓ1 problem. Based on the relaxation, we also propose a numerical computation method for the L1/ℓ1 problem by sequential linear programming. We show numerical examples to illustrate the effectiveness of the proposed control method.