Method of Uniform Optimization for Controlled Systems with Distributed Parameters

The constructive method is proposed for solving a wide range of optimal control problems for technical systems with distributed parameters described by partial differential equations of parabolic type, under the condition of achieving a specified accuracy of the uniform approximation of the final system’s state to the desired spatial distribution of the controlled variable. The developed approach consists of a set of procedures: sequential parameterization of control actions determined by analytical optimality conditions, reduction to a semi-infinite optimization problem concerning the sought-after parameter vector, and solution using the alternance method to construct parameterized control algorithms. This approach extends the results of the theory of nonlinear Chebyshev approximations to the considered problems and makes substantial use of the fundamental regularities of the subject area. The obtained results are generalized to problems with vector-valued performance criteria, constraints on the final state of the system, and control actions. An analytical method is proposed for constructing optimal controllers in situations where the classical transversality conditions are not applicable due to the non-smooth boundaries of the target set. Instead, finite values of the conjugate variables and modal components of the controlled variable in the optimal process are used, which are determined through the solution of the programming problem.