Linear Direct Transcription for Nonlinear Constrained Optimal Control Problems

Abstract

Nonlinear optimal control problems are frequently transformed into nonlinear programming problems for which the solving process is generally time-consuming. In this paper, a linear direct transcription method is proposed for nonlinear optimal control problems. Taking advantage of the state-dependent coefficient parameterization method and the spectral discretization method, the nonlinear optimal control problem is successively linearized and turned into a sequence of efficiently solvable mixed linear complementarity problems. The proposed direct transcription method is linear in two ways: the nonlinear system is linearized using state-dependent coefficient parameterization; the resulting quadratic programming problem is converted into a mixed linear complementarity problem. Simulations are implemented, and numerical results verify the effectiveness and efficiency of the proposed method.