AbstractNeighbouring extremals of dynamic optimization problems with a known parameter vector θ and an unknown parameter vector π are considered in this paper. The parameter vector π and the control are to be optimally determined to minimize a cost functional with a given θ. 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 te