Continuous Hands-off Control by CLOT Norm Minimization

TL;DR

This paper introduces a novel control method using CLOT norm minimization to achieve continuous, sparse control signals that are more practical than traditional bang-off-bang controls, demonstrated through numerical simulations.

Contribution

The paper proposes using the CLOT norm for hands-off control to obtain continuous, sparse controls, improving practical applicability over existing methods.

Findings

CLOT control is continuous and sparser than EN control.

Numerical simulations demonstrate the effectiveness of CLOT norm minimization.

CLOT norm achieves longer zero-control durations while maintaining control performance.

Abstract

In this paper, we consider hands-off control via minimization of the CLOT (Combined L-One and Two) norm. The maximum hands-off control is the L0-optimal (or the sparsest) control among all feasible controls that are bounded by a specified value and transfer the state from a given initial state to the origin within a fixed time duration. In general, the maximum hands-off control is a bang-off-bang control taking values of +1, -1, and 0. For many real applications, such discontinuity in the control is not desirable. To obtain a continuous but still relatively sparse control, we propose to use the CLOT norm, a convex combination of L1 and L2 norms. We show by numerical simulation that the CLOT control is continuous and much sparser (i.e. has longer time duration on which the control takes 0) than the conventional EN (elastic net) control, which is a convex combination of L1 and squared L2 norms.