Method for solving bang-bang and singular optimal control problems using adaptive Radau collocation

A method is developed for solving bang-bang and singular optimal control problems using adaptive Legendre–Gauss–Radau collocation. The divided into several parts. First, a structure detection that identifies switch times in the analyzes corresponding switching function segments where solution either or singular. Second, after has been detected, domain decomposed multiple domains such multiple-domain formulation includes additional decision variables represent control. In classified as bang-bang, set to its upper lower limit. identified singular, objective augmented with regularization term avoid arc. An iterative procedure then obtain lies close proximity demonstrated on four examples, three of which have and/or while fourth smooth nonsingular results demonstrate this paper provides accurate solutions whose are when compared against previously mesh refinement methods not tailored nonsmooth problems, produces equivalent those obtained smooth.