Alternance method in vector problems of parametric optimization of systems with distributed parameters

Constructive methods are proposed for solving a wide range of vector problems of optimal control of systems with distributed parameters (DPS) under the conditions when an accuracy of uniform approximation to the required final state of an object is prescribed on a set of spatial arguments of a controlled quantity. After the transition to the relative equivalent estimates of particular efficiency criteria the problems of vector (multi-criteria) optimization are reduced to a single-criterion version in the form of a variational problem with an integral quality criterion and with the new restrictions on the final values of the additional phase variables of the extended DPS' model. Vector (combined) constraints on the final state of the DPS are replaced by one constraint on their linear combination, which is presented in the uniform metric on the extended set of arguments, including (besides the spatial variables) the weight factors of the summable components that vary within the standard simplex. The problems of vector (multichannel) control by one or by a system of interconnected distributed objects are considered under the conditions of a specific requirement of the same duration of the control process for all control actions. Further procedures of preliminary parameterization of control actions carried out using well-known analytical conditions of optimality provide accurate reduction of the initial statements to complicated modifications of semi-infinite programming problems, which are applied to computational algorithms developed earlier by the authors for the scalar version of the alternance method of searching for the desired extremals based on their Chebyshev properties. An example of independent solution of a vector problem of optimal control of an object of technological thermophysics is given.