关键词: 最优控制, 非线性规化, 直接转换法, 拟谱法, 常微分方程, 微分代数方程

Abstract: A novel numerical method for solving optimal control problems based on ordinary differential equations (ODE) and/or differentialalgebra equations (DAE) is proposed. This method is based on the direct transcription method that converts an optimal control problem into a nonlinear programming problem using LegendreGauss pseudospectral method via simultaneous state and control discretization. Compared with other standard direct transcription methods, the scheme has the advantages of higher precision and lower computational effort with a simpler structure which can also be used for the socalled optimal control multi-phase problems. Numerical results show the approach is a general purpose higher precision optimal control direct transcription method which can be used for solving ODE/DAE optimal control problems.

Key words: optimal control, nonlinear programming, direct transcription method, pseudospectral method, ordinary differential equation, differentialalgebra equation