Maximum Hands-Off Control: A Paradigm of Control Effort Minimization

TL;DR

This paper introduces the maximum hands-off control paradigm, emphasizing minimal control activity over time, and demonstrates its equivalence to L1-optimal control under certain conditions, with practical algorithms for linear systems.

Contribution

It establishes the equivalence between maximum hands-off control and L1-optimal control, and proposes new control algorithms for sparse and smooth control in linear systems.

Findings

Maximum hands-off control is equivalent to L1-optimal control under normality.

Proposed L1/L2-optimal control yields smooth, sparse control signals.

Self-triggered feedback control achieves sparsity and stability in linear systems.

Abstract

In this paper, we propose a new paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a short support per unit time. The maximum hands-off control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon control, we show the equivalence between the maximum hands-off control and L1-optimal control under a uniqueness assumption called normality. This result rationalizes the use of L1 optimality in computing a maximum hands-off control. We also propose an L1/L2-optimal control to obtain a smooth hands-off control. Furthermore, we give a self-triggered feedback control algorithm for linear time-invariant systems, which achieves a given sparsity rate and practical stability in the case of plant disturbances. An example is included to illustrate the effectiveness of the proposed control.