Infinite Horizon Optimal Control
Deterministic and Stochastic Systems
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Beschreibung
This monograph deals with various classes of deterministic and stochastic continuous time optimal control problems that are defined over unbounded time intervals. For these problems the performance criterion is described by an improper integral and it is possible that, when evaluated at a given admissible element, this criterion is unbounded. To cope with this divergence new optimality concepts, referred to here as overtaking optimality, weakly overtaking optimality, agreeable plans, etc. , have been proposed. The motivation for studying these problems arises primarily from the economic and biological sciences where models of this type arise naturally. Indeed, any bound placed on the time hori zon is artificial when one considers the evolution of the state of an economy or species. The responsibility for the introduction of this interesting class of problems rests with the economists who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey [152] who, in his seminal work on the theory of saving in 1928, considered a dynamic optimization model defined on an infinite time horizon. Briefly, this problem can be described as a Lagrange problem with unbounded time interval. The advent of modern control theory, particularly the formulation of the famous Maximum Principle of Pontryagin, has had a considerable impact on the treat ment of these models as well as optimization theory in general.
This work presents a systematic account of the development of infinite horizon optimal control. It is demonstrated that the usual concept of optimality is insufficient as it assumes, a priori, that the objective functional is finite. To avoid this difficulty a hierarchy of optimality concepts have been developed, which serves as a background for the treatment of the usual questions encountered in optimization. Namely, the book investigates necessary conditions for optimality, sufficient conditions for optimality, and the existence of optimal solutions.
Autor*in
Dean A. Carlson
Themen in »Infinite Horizon Optimal Control«
Infinite Horizon Kontrolltheorie Overtaking Optimality Stochastische Systeme Unbegrenzter Zeithorizont control control system control theory optimal control system