Closable feedback for guaranteed optimimization of undeterminate systems of control
The paper deals with the construction of an optimal control for a linear uncertain system. The uncertainty is represented by an unknown additive piecewise continuous perturbation parameter. The state is assumed to be available for feedback at any current instant of time \(\tau \). Essentially, the ``best control in the worst case'' is considered, and the current value of the optimal control is used defining in this manner a feedback. The main idea of the proposed method is to refine the optimization procedure by dividing the future time interval into two parts and performing a ``closing'' at the joint time instant. This leads to the notions of ``openable optimal feedback'' and ``optimal regulator''. To reduce the computational complexity, certain approximations are considered so that the proposed control is completely determined by a finite number of parameters. These parameters can be found from the so-called determining equations. To improve the quality of the feedback a generalized version of the method is proposed: the future time interval has to be divided into several parts with multiple ``closing'' at the joint time instants.
scientific article; zbMATH DE number 1113088