de Pinho, Maria do Rosário (Faculdade de Engenharia da Univ. do Porto), Rosenblueth, Javier F (National Autonomous Univ. of Mexico)

A Derivation of Second Order Conditions for Mixed Constrained Optimal Control Problems

Scheduled for presentation during the Mini-Symposium "Recent Developments in Optimal Control: Theory and Applications" (MoP11), Monday, July 24, 2006, 17:00−17:25, Room 104a

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 19, 2024

Abstract

This work deals with a fixed-endpoint control problem of Lagrange posed over piecewise continuous controls and involving mixed equality and inequality constraints. We establish second order necessary conditions for such a problem, yielding the introduction of a set of admissible variations where the second variation is nonnegative together with a corresponding notion of a normal extremal, and show how those conditions can be derived by means of a uniform implicit function theorem applied to the classical necessary conditions for a control problem without constraints.