A Unified Framework for Linear Control Problems with State Variable Inequality Constraints

Journal of Optimization Theory and Applications, Vol. 36, No. 1, pp. 93-109, January 1982

18 Pages Posted: 24 Jun 2009 Last revised: 9 May 2017

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

William P. Drews (deceased)

affiliation not provided to SSRN (deceased)

Richard G. Segers

Exxon Mobil Corporation

Date Written: January 1, 1982

Abstract

This paper briefly reviews the literature on necessary optimality conditions for optimal control problems with state-variable inequality constraints. Then, it attempts to unify the treatment of linear optimal control problems with state variable inequality constraints in the framework of continuous linear programming. The duality theory in this framework makes it possible to relate the adjoint variables arising in different formulations of a problem; these relationships are illustrated by the use of a simple example. This framework also allows more general problems and admits a simplex-like algorithm to solve these problems.

Keywords: Linear optimal control problems, inequality constraints, continuous linear programming, simplex like algorithm, Lagrangian construction, duality

JEL Classification: C61

Suggested Citation

Sethi, Suresh and Drews (deceased), William P. and Segers, Richard G., A Unified Framework for Linear Control Problems with State Variable Inequality Constraints (January 1, 1982). Journal of Optimization Theory and Applications, Vol. 36, No. 1, pp. 93-109, January 1982, Available at SSRN: https://ssrn.com/abstract=1421424

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

William P. Drews (deceased)

affiliation not provided to SSRN (deceased)

Richard G. Segers

Exxon Mobil Corporation ( email )

3225 Gallows Road
Vienna, VA 22037
United States

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