Optimal Control of Systems with Distributed Parameters Under the Interval Uncertainty of an Object’s Characteristics

A constructive method is proposed for solving a linear-quadratic problem of the robust optimization of spatiotemporal control actions in systems with distributed parabolic parameters under conditions of interval uncertainty of the time-invariant parametric characteristics of an object. In accordance with the control strategy according to the principle of the best guaranteed result, the assessment of achievable target sets of the controlled system is carried out according to the accuracy of uniform approximation to the required final state on an extended set of arguments, which includes, in addition to spatial variables, the entire admissible set of uncertain factors. The developed approach is based on the previously developed alternance method for constructing parameterizable program 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 proposed equations of optimal controllers, which are reduced to linear feedback laws on the measured state of the object with nonstationary transmission coefficients, lead to achievable values of the optimality criteria that do not exceed their upper bounds under the considered uncertainty conditions