A way of estimating adjoint variables of optimal control problems by a direct collocation method has been described. The method seems to be superior to previous approaches for estimating adjoint variables in terms of reliability and the ability to include discontinuities in adjoints at the junction points of state constraint subarcs. Furthermore, the estimates of the adjoint variables and the suboptimal controls have been improved by including the switching structure of active state constraints in the optimization procedure.
Acknowledgement. The author is indebted to Prof. Dr. P. E. Gill who supplied him with a version of the SQP-method NPSOL for this scientific research. The author is also indebted to the numerical analysis and optimal control group of Prof. Dr. R. Bulirsch for helpful discussions.