Evaluation of alternative control strategies for the systems with asymptotically stable equilibrium positions
In some applied optimal control problems it is possible to construct a control function only with the help of the analysis of the system dynamics. Such controls are called alternative to the controls satisfying Pontryagin’s maximum principle. In this article we consider autonomous systems of ordinary differential equations with a terminal objective functional, which have the unique asymptotically stable equilibrium position for each fixed value of the control parameter. It is shown that in this case the task of the alternative controls’ construction can be reduced to some finite dimensional problems of mathematical programming. The evaluation of the constructed alternative control with respect to the objective functional is found. Sufficient conditions for the possibility of obtaining this evaluation are derived. A mathematical model of optimal leukemia therapy is considered as an example.