A New Zero-Order Algorithm to Solve the Maximum Hands-Off Control

A new zero-order algorithm to solve the maximum hands-off control is proposed. Maximum hands-off control is discretized into a convex linear programming problem by zero-order-hold discretization. The first-order necessary conditions for linear programming problems are presented. To ensure that the switching points meet the allowable error, the jump function is used to preliminarily determine the switching points of the control variable. The finite switch number lemma for the maximum hands-off control is used as the initial estimate of the number of switching points. Numerical example results show that the zero-order algorithm is more effective than the alternating direction method of multipliers in solving the maximum hands-off control.