線形モデルベースの非線形系表現法とその最適制御問題への応用

抄録

The result of optimal control is sometimes unsatisfactory on the linear model obtained in the linearized version of a nonlinear system. In this case, the optimal control must be calculated once again on the nonlinear model with a revived nonlinearity. The nonlinear model description becomes complicated, however, to express the nonlinear information in a material form, and the numerical processing of the solutions of optimal control problems becomes difficult.
In this paper, the nonlinearity is considered as a kind of disturbance to the linear model, so it can be reproduced by adding the equivalent input for the disturbance to the linear model. From this thinking, the equivalent mathematical nonlinear model (NBL model) is proposed, which is based on the linear model. The procedure of transient response calculation for the NBL model is given, and the numerical stability of this method based on the Padé approximate method is inquired. In addition, an optimal control problem is formulated under the NBL model, and the optimal control is calculated actually by the optimization algorithm used the steepest descent method. As a result, its numerical solutions were obtained stably.