Decomposition is shown to provide a good approximation when the system dynamics involve nearly decomposable matrices or variables with strong and weak interactions. Aggregation provides a good approximation if each of the decomposed matrices has one or more dominant eigenvalues. It is shown how one can construct nearly-optimal controls for the given system from the optimal solutions of the simpler reduced problems. Am iterative procedure is proposed for both the linear and nonlinear cases.
Error estimates fbr approximate solutions are obtained.
The implementation of the method on parallel architectures is discussed. Numerical examples are presented to illustrate the present technique. In this method, an asymptotic approximation is incorporated into a finite-difference scheme to improve the numerical solution. Uniform error estimates are derived when implemented in known difference schemes. Numerical results are presented in support of the proposed method.