A hybrid approach to optimal control

Abstract

A hybrid approach to optimal control is presented which takes advantage of the best features of the direct and indirect approaches to optimal control. The original infinite-dimensional problem is first converted to a mathematical programming problem via the direct approach of transcription. Utilizing the fact that the necessary conditions of the resulting mathematical programming problem represent a discrete nonlinear two-point boundary-value problem, a solution can be obtained by embedding backward-forward integration sweeps within an iterative algorithm, a characteristic of the indirect approach. The hybrid approach not only allows for the preconditioning of ill-conditioned problems through knowledge of the Hessian, but also reduces the dimension of the search space through the solution of the discrete two-point boundary value problem. The reduction in the dimension of the search space is achieved by having to search only over the discrete control variables rather than both the discrete state and control variables and can lead to significant improvements in algorithm convergence.<>