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<title>AAS 98-164</title><body BGCOLOR="ffffff"> <h2>AAS 98-164</h2> <h2>NECESSARY AND SUFFICIENT CONDITIONS FOR OPTIMAL CONTROL PROBLEMS WITH MULTIPLE TERMINAL CONSTRAINTS</h2> <h4>Jang-Won Jo, J. E. Prussing - University of Illinois at Urbana-Champaign</h4> <h2> Abstract </h2> A recent advance in sufficient conditions for a weak local minimum in the Bolza optimal control problem is used to develop a procedure for applying second-order necessary and sufficient conditions to problems with multiple terminal constraints. Three example problems are analyzed: a minimum-time problem, the shortest path between two points on a sphere, and an application of Hamilton's Principle to a circular orbit in an inverse-square gravitational field. When the circular orbit violates the second-order conditions, a genetic algorithm is used to determine an alternate path of lower cost. <P><A HREF="http://www.space-flight.org/AAS_meetings/1998_winter/sessions.html">Back</A>