A Computational Method for Non-standard Optimal Control Problems via Continuation Methods

Abstract

In this paper, we deal with non-standard optimal control problems, where the performance index and/or the right hand side of the state equation can be non-differentiable. Such non-standard problems are extremely difficult to solve numerically, because the solution of the state equation may escape to the infinity. Based on the continuation methods, we present two computational methods for obtaining the solutions of the non-standard optimal control problems. One is to approximate non-differentiable functions by differentiable ones, and the other is to adjust the control-time-interval so that the resulting control problems can be solvable. Moreover, we demonstrate the effectiveness of those two methods by numerical simulations.