Quasicanonical structure of optimal control in constrained discrete systems.
type: Item
instance of: scholarly article
title: Quasicanonical structure of optimal control in constrained discrete systems.
zbMATH Open document ID: 1086.93005
DOI: 10.1016/S0034-4877(03)80027-7
author: Sumit K. Garg
published in: Reports on Mathematical Physics
publication date: 2004-08-06T00:00:00Z
review text: This paper considers discrete processes governed by difference rather than differential equations for the state transformation. The basic question asked is if and when Hamiltonian canonical structures are possible in optimal discrete systems. Considering constrained discrete control, general optimization algorithms are derived that constitute suitable theoretical and computational tools when evaluating extremum properties of constrained physical models. The mathematical basis of the general theory is the Bellman method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage criterion which allows a variation of the terminal state that is otherwise fixed in the Bellman's method. Two relatively unknown, powerful optimization algorithms are obtained: an unconventional discrete formalism of optimization based on a Hamiltonian for multistage systems with unconstrained intervals of holdup time, and the time interval constrained extension of the formalism. These results are general; namely, one arrives at: the discrete canonical Hamilton equations, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory along with all basic results of variational calculus. Vast spectrum of applications of the theory is briefly discussed.
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 2084218
zbMATH Keywords: Optimal control
zbMATH Keywords: discrete Hamiltonian systems
zbMATH Keywords: canonical equations
zbMATH Keywords: dynamic programming
MaRDI profile type: Publication
cites work: Q5734848
cites work: Q3241581
cites work: Q5519754
cites work: Q3903595
description: scientific article; zbMATH DE number 2084218