Abstract
We suggest to apply the Bubnov–Galerkin procedure to solve scanning control problems for systems with distributed parameters. The algorithm is described in details for three-dimensional linear heat equation It allows to reduce the solution of control problem to finite-dimensional nonlinear moments problem. The procedure of derivation of moments problem is illustrated in details on the example of one-dimensional equation of thermal conductivity. The solution of obtained moments problem is found in a particular case. Based on obtained results a computer simulation is done using COMSOL Multiphysics platform in one-dimensional case for a rod. The main dependences of control function against input data of the problem are revealed. The state of the rod for several (constant) values of the source intensity is expressed in terms of graphs and illustrations. Corresponding illustrations are brought in case of control absence (null-power source) for comparison. An effective numerical scheme for solving the obtained system of nonlinear constraints is suggested in the case of extended class of admissible controls. Calculation of control parameters is reduced to the simplest problem of nonlinear programming.
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