Consider finding an admissible control u0pt which causes the system
to follow an admissible trajectory, x*, that minimizes the criteria function
so that u0Vt is called the optimal control. In (18), the term k is a weighting factor which is determined in search of the minimum J.
Let criteria function be formulated as follows:
J = J L dt where the scalar function L is written as
In the calculus of variations, it is well known that a necessary condition for x* to be an optimal of the functional given by (19) is (Naidu, 2003)
This equation is called Euler equation. Application of Euler equation to (19) yields the optimal control law:
3kXuuu | u | 3Kppplpl 2T
Was this article helpful?