Optimal control of a concentrated system on the class of piecewise constant functions under uncertainty in the parameters and initial conditions

Abstract

The authors analyze optimal control problems for objects described by systems of ordinary differential equations on the class of piecewise constant control functions with uncertain initial information about the parameters of the initial conditions and about object parameters. Piecewise constant values of the controls and, what is most important, the boundaries of the intervals of constancy of the controls are optimized in the problem. Given the number of the intervals of constancy, the necessary optimality conditions and formulas for the gradient of the objective functional are obtained. These formulas allow using efficient first-order optimization methods. For the case where the number of intervals of constancy is not specified, an algorithm of its optimization is proposed.