Neighbouring extremals of dynamic optimization problems with parameter variations

Neighbouring extremals of dynamic optimization problems with a known parameter vector θµ and an unknown parameter vector &phiµ are considered in this paper. The parameter vector &phiµ and the control are to be optimally determined to minimize a cost functional with a given θµ. With some simplifications, the neighbouring extremal problem is reduced to one of solving a linear, time-varying, two-point boundary value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Example problems are solved to illustrate the validity and usefulness of the solution technique.