Linear Optimal Control Problems and Generalized Linear Programs

The Journal of the Operational Research Society, Vol. 32, No. 6, pp. 467-476, June 1981

10 Pages Posted: 4 Jul 2009 Last revised: 21 Apr 2015

See all articles by George B. Dantzig (deceased)

George B. Dantzig (deceased)

affiliation not provided to SSRN (deceased)

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: 1981

Abstract

Linear optimal control problems with state inequality constraints is an important class of large systems. This paper shows that a generalized programming formulation of these problems does not result in a decomposition over time or a maximum principle as it does for problems without the state constraints. A semi-infinite generalized programming formulation, however, can be used to formally produce the maximum principle, i.e. the necessary optimality conditions, for problems under consideration.

Keywords: Linear Programming, generalized programming, maximum principle, semi-infinite programming, linear optimal control problems, optimal control, state constraints, necessary optimality conditions, Hamiltoinian, mathematical programming

JEL Classification: C61

Suggested Citation

Dantzig (deceased), George B. and Sethi, Suresh, Linear Optimal Control Problems and Generalized Linear Programs (1981). The Journal of the Operational Research Society, Vol. 32, No. 6, pp. 467-476, June 1981, Available at SSRN: https://ssrn.com/abstract=1429505

George B. Dantzig (deceased)

affiliation not provided to SSRN (deceased)

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

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