Second order sufficient optimality conditions for hybridcontrol problems with state jump

Lihua Li; Yan Gao; Hongjie Wang

doi:10.3934/jimo.2015.11.329

Article Contents

2015, Volume 11, Issue 1: 329-343. Doi: 10.3934/jimo.2015.11.329

This issue Previous Article A QP-free algorithm of quasi-strongly sub-feasible directions for inequality constrained optimization Next Article

Second order sufficient optimality conditions for hybrid control problems with state jump

1.
School of Management, University of Shanghai for Science and Technology, Shanghai 200093
2.
Business School, University of Shanghai for Science and Technology, Shanghai, 200093

Received: April 30, 2013

Revised: January 31, 2014

Published: December 2014

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Abstract

In this paper, an optimal control problem for a class of hybrid systems is considered. By introducing a new time variable and transforming the hybrid optimal control problem into an equivalent problem, second order sufficient optimality conditions for this hybrid problem are derived. It is shown that sufficient optimality conditions can be verified by checking the Legendre-Clebsch condition and solving some Riccati equations with certain boundary and jump conditions. An example is given to show the effectiveness of the main results.

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Mathematics Subject Classification: Primary: 93C30, 49K15; Secondary: 49J15.

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