Guaranteed optimum control program on the set of operating states
This article deals with a parameter dependent optimization problem. The optimal control problem of ordinary differential equations with fixed end point and fixed time intervals is considered. It is supposed that the set of parameter values is finite and the parameter value does not change with time. An admissible controller is called a guaranteed program if it does not depend on parameter values and properties hold for any parameter values. To analyse the existence and synthesis problems of the guaranteed program, the authors introduce an extended object described by differential equations and a direct product structure corresponding to the different parameter values. In this way, the conditions of guaranteed program existence is established for the linear systems. These conditions coincide with the complete controllability criteria for the extended object. In conclusion, some examples of guaranteed optimum control construction are given. The article reviewed is intended for researchers interested in the problem of control by stochastic and variable structure objects.
scientific article; zbMATH DE number 561166