Abstract
A necessary and sufficient condition for an optimal solution of the constrained optimal control problem in Banach space has been derived by means of an exterior penalty by the authors.
The purpose of this paper is to derive the similar condition by means of an interior penalty method.
It is shown that a series of the approximate solutions converges to the optimal one weakly and a series of the values of the cost functional generated from those approximate solutions converges to the optimal value. Using those results, the necessary and sufficient condition is derived by considering the minimization problem of a new functional.
In the main problem considered here, the control and state variables are defined in Lp (1<p≤∞) or Euclidean space. The constraints are described by equalities and inequalities, where the equality constraints are defined in Lp or Euclidean space and the inequality constraints are defined in L∞ or Euclidean space.
