Higher Order Methods for Determining Optimal Controls and Their Sensitivities
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In this paper, the Hamilton-Jacobi-Bellman (HJB) equation is utilized to solve a class of weakly nonlinear optimal control problems. Through successive higher-order differentiations of the HJB equation, optimal controls and their sensitivities to changes in initial conditions are approximated without iteration. For highly nonlinear problems, the approximation scheme is modified to provide only sensitivities of the nominal control, with respect to initial conditions and system parameters, which can be used to quickly generate a family of neighboring optimal solutions. Three numerical examples are presented to demonstrate the utility of this approximation scheme. Copyright © 2010 by Chris McCrate.
author list (cited authors)
McCrate, C., Vadali, S., & Bhattacharya, R.