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.

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