Computational Method of Optimal Control Problem Using Mathematical Programming (2nd Report). Introduction of Block Diagonal Hessian Method.
Takeshi Tsuchiya, Shinji Suzuki · The Journal of the Japan Society of Aeronautical Engineering · 1998
This paper considers a numerical method to solve optimal control problems which are formulated by a mathematical programming. In this 2nd report, A new method named Block Diagonal Hessian (BDH) method is proposed. This proposed method transforms the optimal control problem into a new formulated nonlinear programming problem. Considering that the nonlinear programming problem is solved by using a sequential quadratic programming method, the diagonal form of the Hessian matrix for the Lagrange function is introduced in BDH method. The BDH method is applied to a simple optimization problem and its characteristics are compared with those of other methods. As a result, though the accuracy of the BDH method is lower than that of the other methods, the BDH converges quickly and has robust characteristics in the selection of the nominal solution. Through this study, the effectiveness of the BDH method was confirmed.