Exact solution of Pontryagin's equations of optimal control—Part 1

In the treatment of constrained optimal control processes, it is customary to employ the Pontryagin maximum principle, which requires the solution of a two-point boundary-value problem. Various economic, mechanical, and biological control processes are of this type, including optimization of hemodialysis. Generally speaking, two-point boundary-value problems are more difficult to treat computationally than initial-value or Cauchy problems. In this paper, a Cauchy system is derived for a class of optimal control processes, and it is then shown that the solution of the Cauchy problem satisfies the Pontryagin equations.This research was supported by the National Science Foundation, Grant No. GF-294, and the National Institutes of Health, Grants Nos. GM-16197-01 and GM-16437-01.