The small parameter method in the optimisation of a quasi-linear dynamical system problem

We consider an optimisation problem for the transient process in a quasi-linear dynamical system (contains small parameter at non-linearities) with performance index that is linear combination of energy costs and duration process. An algorithm constructing asymptotic approximations given order to solution this proposed. The based on decomposition by integer powers initial values adjoint variables are finite-dimensional elements, according which easily restored. computational procedure includes solving optimising system, integrating systems differential equations, finding roots non-degenerate algebraic systems. also show how constructed can be used construct optimal control under consideration value parameter.