An Approach to Minimum Attention Control by Sparse Derivative
Minimum attention control proposed by Brockett is an important formulation for resource-aware control, while his problem formulation and the underlying optimization problem that he proposed is in general very hard. In this paper, we propose a computationally tractable design method of minimum attention control based on promoting sparsity of the derivative of control. The optimal control problem is formulated as L0 norm minimization of the time derivative of control under the constraint that the derivative is bounded by a fixed value. This is a non-convex problem, and we propose L1 relaxation for linear systems to obtain optimal control by efficient numerical computation. We then show equivalence theorems between the L0 and L1 optimal controls. Also, we present an example of feedback control for the first-order integrator, that illustrates the proposed methodology.