Wavelet Approach to Nonlinear Optimal Control Problem

We give the explicit time description of optimal dynamics for nonlinear diierential systems of equations (energy minimization in high power electromechanical system). We consider two cases of our general construction. In a particular case we have the solution as a series on shifted Legendre polynomials, which is parametrized by the solution of reduced algebraical system of equations. In the general case we have the solution as a multiresolution expansion from wavelet analysis. In this case the solution is parametrized by solutions of two reduced algebraic problems, one as in the rst case and the second is some linear problem, which is obtained from one of the next wavelet constructions: Fast Wavelet Transform, Stationary Subdivision Schemes, the method of Connection Coeecients.