The Switch Point Algorithm

Abstract

The Switch Point Algorithm is a new approach for solving optimal control problems whose solutions are either singular or bang-bang or both, and which possess a finite number of jump discontinuities in an optimal control at the points in time where the solution structure changes. This class of problems can often be reduced to an optimization over the switching points. Formulas are derived for the derivative of the objective with respect to the switching points. Hence, gradient-based unconstrained optimization techniques including the conjugate gradient method or quasi-Newton methods can be used to solve the control problem. Three examples with known analytical solutions are used to illustrate the algorithm.