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We propose a method for synthesizing energy-optimal controllers in open and closed domains of space-time control actions for linear multidimensional objects with distributed parabolic parameters under the conditions of a given accuracy of uniform approximation of the final state of the system to the desired spatial distribution of the controlled variable. The approach is based on the previously developed alternance method for constructing parameterizable algorithms of optimal program control, which uses the fundamental laws of the subject area. It is shown that the desired equations of the controllers are reduced to linear feedback laws with restrictions on incomplete observation of the state of the object with nonstationary transmission coefficients, which are determined by preliminary calculation of the program control action. [ABSTRACT FROM AUTHOR]

A constructive method is proposed for solving the problem of time-optimal two-channel boundary control of two physically inhomogeneous objects with distributed parameters described by linear heat conduction equations under conditions of a perfect thermal contact of interacting media with estimates of the target sets of controlled temperature fields in a uniform metric that are typical for engineering applications. The developed technique uses a special method for describing the studied temperature fields in a form containing uniformly converging series. The approach under development is based on the parameterization procedure for the desired control actions and the subsequent reduction to the problem of semi-infinite optimization, which is solved by the scheme of the alternance method under the additional restriction on the same duration of the control process for both control actions. [ABSTRACT FROM AUTHOR]

We consider the problem of optimal control of movable objects with distributed parameters according to standard performance criteria, as applied to the actual optimization problem of the operational temperature modes for continuous process units for preheating semifinished products before subsequent pressure treatment. The energy-optimal distributions of the heat release power along the length of the heater in stationary modes of its operation, which serve as the desired design solutions for the plant, are determined. Algorithms for automatic programmed and positional control of operational transient modes of a heating unit are proposed that are optimal in terms of a standard quadratic quality criterion for a given accuracy of the uniform approximation of the final spatial temperature distribution to the required one. It is shown that the procedure for synthesizing an optimal controller is reduced to constructing a control system with linear feedback based on an incomplete measurement of the state of the plant with nonstationary transmission coefficients determined by a preliminary calculation of the programmed control. [ABSTRACT FROM AUTHOR]

A method for analytical construction of optimal regulators in problems of energy-efficient control of linear distributed parameters systems under conditions of a given accuracy of the uniform approximation of the terminal state of the object to the required spatial distribution of the controlled quantity is proposed. The developed approach is based on the previously designed alternance method of constructing parameterized algorithms of optimal programmed control. It is shown that the sought procedure of optimal regulator design is reduced to constructing a linear feedback control system by incomplete measurement of the state. The feedback transfer coefficients are known functions of time and finite values of the controlled quantity which are determined by preliminary calculation of the programmed control action. [ABSTRACT FROM AUTHOR]

The previously developed technology of multi-objective optimization of deterministic systems with distributed parabolic parameters can be applied in typical situations with interval uncertainties of parametric characteristics of controlled plants. Minimax problems of mathematical programming are formed in accordance with a control strategy based on the principle of the best guaranteed result of a expanded set of arguments, which includes all permissible realizations of uncertain factors, in the case of estimating a given accuracy of approximation to a required finite system state in uniform metric. These problems are solved by an alternance method that uses the Chebyshev properties of desired extermals and fundamental laws of the problem domain. This paper also presents an example of multi-objective optimization of temperature modes of induction heating of metallic semifinished products before plastic deformation operations in technological complexes for pressure treatment of metal, which is of independent interest. [ABSTRACT FROM AUTHOR]

A constructive technology of multi-objective optimization of control of distributed parameter plants is proposed. The technology is based on a single-criterion version in the form of the minimax convolution of normalized performance criteria. The approach under development is based on the transition to an equivalent form of the variational problem with constraints, with the problem solution being a priori Pareto-effective. Further procedures of preliminary parameterization of control actions and subsequent reduction to a special problem of semi-infinite programming make it possible to find the sought extremals with the use of their Chebyshev properties and fundamental laws of the subject domain. An example of multi-objective optimization of operation modes of an engineering thermophysics object is presented, which is of independent interest. [ABSTRACT FROM AUTHOR]

This work is devoted to a possible way to construct time-optimal closed systems for incompletely determined linear models of distributed-parameter control plants of parabolic type, which provides real-time identification of their parametric characteristics according to the results of monitoring the state of the plants. The structural-parametric synthesis of the proposed controllers is based on the alternance method of designing optimal software controls. The paper gives an example (of independent interest) of constructing a time-optimal system for the control of the process of induction heating under typical conditions of interval uncertainty of the initial temperature and heat losses. [ABSTRACT FROM AUTHOR]

A method is proposed to solve the joint optimization problem based on system quality criteria for the thermophysical processes of preheating and subsequent plastic deformation of metal semi-finished products in industrial metal working systems with a free choice of the admissible initial temperature states before plastic deformation that integrate these processes in a single process system. Potentials for practical applications of the method is illustrated by the example of a process system for forming pressed articles from aluminum alloys. [ABSTRACT FROM AUTHOR]

The piecewise continuous (relay) nature of lumped control actions in problems of timeand energy-optimal control of a wide range of distributed-parameter nonlinear objects of engineering thermophysics is established. On this basis, the required programmed controls in a number of practical situations can be found by the proposed algorithmically precise (alternance) method. As an example, which is of independent interest, the problem of optimal control of nonlinear models of induction heating of metal semi-products before subsequent pressure treatment is considered. [ABSTRACT FROM AUTHOR]

A precise method based on a special procedure of successive parametrization of control actions is proposed to solve boundary-value optimal control problems for distributed-parameter systems with the tolerances for deviations from the required final state of the controlled object specified in the uniform metric. The method is used to solve the time optimal control problem for an innovative technology of induction heating of massive bodies rotating in a direct current magnetic field. [ABSTRACT FROM AUTHOR]