Double generating function approach to discrete-time nonlinear optimal control problems

Abstract

This paper develops the double generating function approach to the discrete-time nonlinear optimal control problems. This approach gives the optimal solutions as algebraic expressions only in terms of the pre-computed coefficients and boundary conditions such that it is useful for the on-line repetitive computation for different boundary conditions. Moreover, a Taylor series expansion based numerical implementation is also presented for solving the Hamilton-Jacobi equations and generating optimal solutions for the nonlinear problems in this paper. Examples demonstrate the effectiveness of the developed method.