Nonconvex Optimization Problems for Maximum Hands-Off Control

Maximum hands-off control is the optimal solution to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L^{0}$</tex-math></inline-formula> optimal control problem. While convex approximation is typically used to relax this problem, it does not necessarily result in maximum hands-off control. Therefore, this study introduces a nonconvex approximation method and a class of nonconvex optimal control problems that are always equivalent to the maximum hands-off control problem. A computation method based on difference of convex functions optimization is then derived and numerically validated.