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Problems of optimal indirect control are considered. It is assumed that information on the behavior of a controllable object first arrives at a control element that generates control signals for a dynamic controller. Using the external energy, the dynamic controller produces control actions of required power that enter the input of the controllable object. Control signals and actions are bounded by geometric constraints. The aim of control is to transfer an object to a prescribed terminal set with the security of a maximum value of the terminal quality criterion. The problems under consideration, which contain phase constraints, are solved by means of the earlier developed methods of solving the problems of optimal control of dynamic objects with simpler intermediate phase constraints. In this case, the main attention is given to the use of these methods for the effective implementation in real time of positional solutions (optimal controls of the feedback type). Examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

The problem of forcing a dynamic system to execute a predefined motion is studied. Optimal control methods are applied to design a controller algorithm, which in real time generates the current values of bounded feedback used by a closed-loop system to execute a given stable motion. Results are illustrated by an example on the design of dynamic systems executing limiting cycles, and an example on tracking. [ABSTRACT FROM AUTHOR]