Assessing alternative control strategies for systems with asymptotically stable equilibrium positions

In a number of optimal control applications, it is possible to arrange control guided only by an analysis of a system’s dynamic properties. These controls are customarily referred to as alternatives to those that satisfy the Pontryagin maximum principle. This work considers autonomous systems of ordinary differential equations with a terminal objective functional that at each fixed value of the control parameter have unique and asymptotically stable equilibrium positions. It is shown that the problem of arranging alternative control can then be reduced to a finite-dimensional problem of mathematical programming. An estimate of the alternative control error in terms of the objective functional is obtained. Sufficient conditions for obtaining this estimate are given. A mathematical model of leukemia therapy is considered as an example.