Widely used in open fishing and solving daily practical problems. However, although it solves the difficulties encountered by the classical variational method and gives the necessary conditions for the optimal control of the problem solution, it is by no means a sufficient condition and has certain limitations in application.
Limitations of the maximum principle
Although the maximum principle solves the difficulties encountered by the classical variational method, it only gives the necessary conditions for the solution of the optimal control problem, but not the sufficient conditions, so the control function obtained by the maximum principle is not necessarily the optimal control, because it is possible that the optimal control does not exist at all. If the solution of the optimal control problem exists, but there is more than one control function obtained by this method, it needs to be tested one by one to determine the optimal solution. If there is an optimal control in the actual physical background of the problem and there is only one solution from the maximum principle, then this solution must be the optimal control.