Maximum Hands-Off Control: A Paradigm of Control Effort Minimization
For control engineers, this provides a new paradigm for minimizing control effort, with theoretical justification and practical algorithms for sparse control.
This paper introduces the concept of maximum hands-off control, which minimizes the support of the control signal per unit time, and demonstrates its equivalence to L1-optimal control under normality. It also proposes an L1/L2-optimal control for smoothness and a self-triggered feedback algorithm achieving a given sparsity rate with practical stability.
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.