Minimization of integral quadratic estimate of controlled variable in systems with distributed parameters

A constructive method for solving the linear-quadratic problem of optimal control of a parabolic-type system with distributed parameters is proposed under the condition of uniform estimation of target sets. The optimality criterion takes the form of an integral quadratic estimate of the controlled state function in the spatio-temporal domain of its definition. A parameterized representation of control inputs is given with the required accuracy within special intervals of the optimal process, where control inputs cannot be determined using first-order analytical optimality conditions. The suggested approach is based on a previously developed alternance method for constructing parameterized algorithms of programmed control, which heavily relies on 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 boundary points to apply admissible control inputs corresponding to the calculated values of the controlled variable.