Numerical Schemes of Higher Order for a Class of Nonlinear Control Systems

摘要

We extend a systematic method for the derivation of high order schemes for affinely controlled nonlinear systems to a larger class of systems in which the control variables are allowed to appear nonlinearly in multiplicative terms. Using an adaptation of the Stochastic Taylor expansion to control systems we construct Taylor schemes of arbitrary high order and indicate how derivative free Runge-Kutta type schemes can be obtained.