Direct scheme in optimal control problems with fast and slow motions
The authors consider the problem \[ \min \{G(x(T),y(T))+\int^{T}_{0}F(x,y,u,t)dt\} \] subject to \[ \dot x=f(x,y,u,t),\quad \epsilon \dot y=g(x,y,u,t) \] where \(\epsilon\) is a small parameter. The unknown functions x, y and u are sought as asymptotic series, according to the method of the boundary layer functions. It is shown, that each order term can be found by solving three lower dimensional optimal control problems, corresponding to the regular and to the boundary layer components. Results concerning the convergence of the above scheme are also presented.
control problems with fast and slow motions
scientific article; zbMATH DE number 3986042