Title: Direct scheme in optimal control problems with fast and slow motions
Authors: S. V. Belokopytov, M. G. Dmitriev
Journal title: Systems and Control Letters
The nonlinear optimal control problems described by singularly perturbed models are studied in order to obtain the ways of decomposition and to construct the suboptimal control sequences. A new scheme, the so-called direct scheme, applying the Vasil'eva boundary layer functions method in control theory is introduced. It consists in directly expanding the problem's conditions into postulated asymptotic series and then in successively solving lower-dimensional approximate decomposition problems of optimal control. By means of the direct scheme a new property of an asymptotic expansion — the relaxation — is obtained, i.e. the decrease of the performance index with each new control approximation. Illustrating examples are given.