Necessary optimality conditions for optimal control problems with infinite horizon

Abstract

This article concerns the derivation of necessary conditions of optimality for infinitehorizon control problems whose cost functional depend on the state at the finaltime which is subject to constraints. Moreover, the optimization is conducted overtrajectories which converge asymptotically to an equilibrium point in the givencompact set C. This includes the case in which it is not possible to steer thestate to the equilibrium point in finite time. This feature distinguishes the problemaddressed in this article from the usual finite time control problem.