Accession Number : ADA019685

Title :   Lagrange Duality Theory for Convex Control Problems,


Personal Author(s) : Hager,William W. ; Mitter,Sanjoy K.

Report Date : 03 NOV 1975

Pagination or Media Count : 32

Abstract : The Lagrange dual of control problems with linear dynamics, convex cost, and convex inequality state and control constraints is analyzed. If an interior point assumption is satisfied, then the existence of a solution to the dual problem is proved and if there exists a solution to the primal problem, then a complementary slackness condition is satisfied. A necessary and sufficient condition for feasible solutions in the primal and dual problems to be optimal is also given. The dual variables p and v corresponding to the system dynamics and state constraints are proved to be of bounded variation while the multiplier corresponding to the control constraints is proved to lie in 1. Finally, a control and state minimum principle is proved. If the cost function is differentiable and the state constraints have too derivatives, then the state minimum principle implies that a linear combination of p and v satisfy the convential adjoint condition for state constrained control problems. (Author)

Descriptors :   *Control theory, Convex sets, Lagrangian functions, Dynamics, Inequalities, Linear systems, Optimization

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE