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Meeting	ACGS Committee Meeting 113 - Englewood, Colorado - March 2014
Agenda Location	7 SUBCOMMITTEE C – AVIONICS AND SYSTEM INTEGRATION 7.4 Duality theory as a tool of Convexification: From Theory to Applications
Title	Duality theory as a tool of Convexification: From Theory to Applications
Presenter	Behcet Acikmese
Affiliation	University of Texas
Available Downloads*	presentation
	Downloads are available to members who are logged in and either Active* or attended this meeting.
Abstract	Duality theory of optimization is useful both in analysis of control problems and in developing numerical solution methods. Here we will first show that the duality theory of optimal control, Pontryagin’s Maximum Principle, can be used to convexify some important motion planning problem. The main motivating application is the powered descent landing on planets by vehicle propelled by rockets. In this and other aerospace applications, we have motion planning problems with non-convex constraints, which are convexified by using the Maximum Principle. We also develop custom Interior Point Method (IPM) algorithms to solve these problems on real-time processors, which was flight tested on NASA test rocket named “Xombie”. Then we present new results on the use of duality theory of convex optimization to convexify deign problems in Markov chain theory. The Markov matrix design problem with ergodicity, motion, and safety constraints are convexified by using the dual problem, and optimal design solutions are obtained. These results are then used for guiding large number of autonomous agents, swarm of agents, into desired distributions safely.