Hamiltonian (control theory)

The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of the Lagrangian expression of the problem that is to be optimized over a certain time period.[1] Inspired by—but distinct from—the Hamiltonian of classical mechanics, the Hamiltonian of optimal control theory was developed by Lev Pontryagin as part of his maximum principle.[2] Pontryagin proved that a necessary condition for solving the optimal control problem is that the control should be chosen so as to optimize the Hamiltonian.[3]

  1. ^ Ferguson, Brian S.; Lim, G. C. (1998). Introduction to Dynamic Economic Problems. Manchester: Manchester University Press. pp. 166–167. ISBN 0-7190-4996-2.
  2. ^ Dixit, Avinash K. (1990). Optimization in Economic Theory. New York: Oxford University Press. pp. 145–161. ISBN 978-0-19-877210-1.
  3. ^ Kirk, Donald E. (1970). Optimal Control Theory : An Introduction. Englewood Cliffs: Prentice Hall. p. 232. ISBN 0-13-638098-0.