International Conference «Mathematical and Informational Technologies, MIT-2013»
(X Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, September, 5–8, 2013

Budva, Montenegro, September, 9-14, 2013

Buldaev A.S.  

An approach to parametric optimization of nonlinear dynamic systems

One class of parametric optimization of nonlinear systems described by differential equations is investigated. The proposed approach is an extension of the results for nonlinear optimal control problems, and is based on a modification of the adjoint  system to get a custom formula increment of the objective function in this class of extremal problems, which do not contain the residual terms of the expansions. On the basis of this formula is constructed task of the fixed point for a special projection operator, the solution of which leads to the construction of better (on the objective function) of the vector of parameters. The proposed design is much easier then a common operation of the gradient method and provides a new necessary optimality condition that is stronger the maximum principle which known in the class of optimization problems. Positive characteristics of the proposed approach are the  nonlocality (no operation of local variation of parameters, providing relaxation of the objective function) and basic opportunity to improve the parameters that satisfy the maximum principle. The illustrative examples are provided. Computation of sequence tasks of the fixed point with the help of iteration methods is used for the numerical optimization of the parameters. The iterative process is carried out to improve the parameters of the first, then building a new problem of the fixed-point and the process repeats. In comparison with the known approaches to numerical optimization of the parameters of the proposed procedure is original and has the prospects for effective implementation.

Abstracts file: abstact MIT 2013 Buldaev.doc

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