An Indirect Method for Inequality Constrained Optimal Control Problems

Abstract

The inequality constrained nonlinear optimal control problem is difficult to handle using indirect numerical methods, since solving the resulting two-point boundary value problem (TPBVP) usually requires a priori information about the structure of the solution. In this paper, a fast and accurate indirect method is proposed for a class of inequality constrained optimal control problems. Firstly, the analytic form of the optimal control is proved for the problem subject to input saturations. Secondly, trigonometric regularization function is designed and incorporated in the cost function to implement the state constraints. Then the state and input constrained optimal control problem is directly converted into a standard TPBVP without constraints. Comparisons with the pseudospectral method are conducted to verify the effectiveness and efficiency of the proposed method. In the input constrained case, the proposed indirect method gives more accurate solution with much faster convergence speed. While for the problem with both input and state constraints, the proposed method sacrifices a little accuracy for a faster speed.