Minimization of an Integral Quadratic Estimate of the Controlled Variable in Systems with Distributed Parameters

Abstract

A constructive method for solving the linear-quadratic problem of the optimal control of a parabolic-type system with distributed parameters is proposed under the condition of the uniform estimation of the target sets. The optimality criterion takes the form of an integral quadratic estimate of the controlled state function in the spatiotemporal domain of its definition. A parameterized representation of the control inputs is given with the required accuracy within special intervals of the optimal process, where the control inputs cannot be determined using first-order analytical optimality conditions. The proposed approach is based on the previously developed alternance method for constructing parameterized algorithms of programmed control, which heavily relies on the fundamental regularities of the subject area. It is demonstrated that the equations of the optimal regulators within the special intervals are reduced to the linear feedback algorithms based on the measured states of the objects. These algorithms are supplemented with switches at the boundary points to apply the admissible control inputs corresponding to the calculated values of the controlled variable.