Abstract:

To obtain the control law of finite\|horizon optimal tracking problems, the Riccati differential equation and the differential equation of the external driving function must be solved at first. The former is a nonlinear matrix differential equation and the latter is a linear time varying one. The precise integration method, which is based on the theory of analogy between structural mechanics and optimal control, can be employed to solve these differential equations precisely and efficiently. This method borrows ideas from the algorithm of computational structural mechanics. One distinguishing feature of the method is that great change of step\|size almost does not affect the precision of the numerical solution of Riccati differential equation. Another feature is that the linear time varying differential equation of the external driving function can also be solved by this method instead of the usual finite difference method. Both the process of implementing the precise integration and the numerical example are presented in this paper.

Key words: optimal control, tracking, Riccati equation, numerical method, structural mechanics