The Pontryagin maximum principle and transversality conditions for a class optimal control problems with infinite horizons
Authors: Aseev SM, Kryazhimskiy AV
Publication Year: 2004
Reference: SIAM Journal on Control and Optimization, 43(3): 1094-1119 [2004]
Also reprinted as IIASA RP-05-003
Abstract
This paper suggests some further developments in the theory of first-order necessary optimality conditions for problems of optimal control with infinite time horizons. We describe an approximation technique involving auxiliary finite-horizon optimal control problems and use it to prove new versions of the Pontryagin maximum principle. Special attention is paid to the behavior of the adjoint variables and the Hamiltonian. Typical cases, in which standard transversality conditions hold at infinity, are described. Several significant earlier results are generalized.