R. Gabasov, A.I. Kalinin, F.M. Kirillova, L.I. Lavrinovich. On asymptotic optimization methods for quasilinear control systems ... P. 62-72

Mathematical models of dynamical systems containing small parameters in nonlinearities are usually called quasilinear systems. We present a survey of results obtained for problems of optimization of quasilinear dynamical systems in the Minsk scientific school on optimal control. We consider time-optimal control problems, terminal control problems with variable right ends of trajectories, minimum force control problems, and problems of minimization of integral quadratic functionals. The research is based on the idea of a special finite-dimensional parameterization of optimal controls. The computation of asymptotic approximations to optimal controls in the quasilinear problems under consideration is reduced to solving some basic problems, which, unlike the original problems for quasilinear systems, are optimization problems for linear systems, to the integration of linear differential equations, and to finding roots of nonsingular linear algebraic systems.

Keywords: quasilinear systems, small parameter, asymptotic approximation, finite-dimensional parameterization, optimal control, feedback control

Received April 18, 2019

Revised May 6, 2019

Accepted May 13, 2019

Funding Agency: This work was supported by the National Program for Scientific Research of the Republic of Belarus “Convergence 2020.”

Rafail Gabasov, Dr. Phys.-Math. Sci., Prof., Belarusian State University, Minsk, 220030 Belarus, e-mail:kirillova.f@yandex.by

Anatoly Iosifovich Kalinin, Dr. Phys.-Math. Sci., Prof., Belarusian State University, Minsk, 220030 Belarus, e-mail: kalininai@bsu.by

Faina Mikhaylovna Kirillova, Dr. Phys.-Math. Sci., Prof., Corresponding Member of the Belarus National Academy of Sciences, Institute of Mathematics of Belarus National Academy of Sciences, Minsk, 220030 Belarus, e-mail: kirillova.f@yandex.by

Leonid Ivanovich Lavrinovich, Cand. Phys.-Mat.  Sci.,Assoc. Prof., Belarusian State University, Minsk, 220030 Belarus, e-mail: lavrinovich@bsu.by

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Cite this article as: R. Gabasov, A.I. Kalinin, F.M. Kirillova, L.I. Lavrinovich. On asymptotic optimization methods for quasilinear control systems., Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 62–72.