Approximation and interpolation of optimal nonlinear regulators

An optimal steady state regular for a class of nonlinear dynamical systems and nonquadratic performance indices is constructed, as a series of homogeneous polynomials in the state. Each term is iteratively obtained in closed form from the preceding terms. Local asymptotic stability and the preservation thereof after truncation are determined, and bounds are found for the radius of convergence. Finally, an interpolating spline is constructed in closed form, so that the accurate computation of the optimal control is required only at selected states.