Spatiotemporal Control of Systems with Distributed Parameters in Linear-Quadratic Optimization Problems with Uniform Estimates of Target Sets

A constructive method is proposed for solving a linear-quadratic spatiotemporal control problem in systems with distributed parabolic parameters under the conditions of the given accuracy of uniform approximation of the final state of a plant to the required spatial distribution of the controlled variable. The developed approach is based on the previously developed alternance method for constructing parameterizable programmed control algorithms, which extends the results of the theory of nonlinear Chebyshev approximations to a wide range of optimization problems and uses the fundamental laws of the subject area. It is shown that the equations of optimal controllers with autonomous modal controls in the open domain of their definition and taking into account restrictions on the nature of the spatial distribution of the control actions specified by the conditions of technical implementation are reduced to linear feedback algorithms for the measured state of the plant with nonstationary transmission coefficients and the given dependence on the spatial arguments of the controlled value. The results obtained are extended to the problem of searching for time-invariant spatially distributed controls, considered as the desired design solutions for a plant.