Geodesic
The small parameter method in the optimisation of a quasi-linear dynamical system problem
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2022), pp. 23-33

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We consider an optimisation problem for the transient process in a quasi-linear dynamical system (contains a small parameter at non-linearities) with a performance index that is a linear combination of energy costs and the duration of the process. An algorithm for constructing asymptotic approximations of a given order to the solution of this problem is proposed. The algorithm is based on the asymptotic decomposition by integer powers of a small parameter of the initial values of adjoint variables and the duration of the process that are finite-dimensional elements, according to which the solution of the problem is easily restored. The computational procedure of the algorithm includes solving the problem of optimising the transient process in a linear dynamical system, integrating systems of linear differential equations, and finding the roots of non-degenerate linear algebraic systems. We also show how the constructed asymptotic approximations can be used to construct optimal control in the problem under consideration for a given value of a small parameter.
Keywords: Small parameter; quasi-linear system; optimal control; asymptotic approximations. 
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     title = {The small parameter method in the optimisation of a quasi-linear dynamical system problem},
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     pages = {23--33},
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A. I. Kalinin; L. I. Lavrinovich; D. Y. Prudnikova. The small parameter method in the optimisation of a quasi-linear dynamical system problem. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2022), pp. 23-33. http://geodesic.mathdoc.fr/item/BGUMI_2022_2_a2/