Asymptotic Approximations of a Regulator and a Convergent Iteration Process for a Singularly Perturbed Problem

The paper considers the construction of asymptotic expansions in a singularly perturbed weakly nonlinear control problem to design an approximate controller. The asymptotic expansions are used to construct interpolation and extrapolation procedures and are obtained by applying the SDRE technique and analyzing a convergent iterative process. The experiments performed showed the efficiency of the proposed approach.