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<title>AAS 98-163</title><body BGCOLOR="ffffff"> <h2>AAS 98-163</h2> <h2>NECESSARY AND SUFFICIENT CONDITIONS FOR OPTIMAL CONTROL PROBLEMS WITH SCALAR TERMINAL CONSTRAINT</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. This improved procedure provides routine testing of second-order conditions in optimal control problems. Two example problems are analyzed, including a spacecraft trajectory with a low-thrust power-limited rocket engine. A solution for a multi-objective performance index that depends on final orbit energy and propellant consumption is found. It satisfies the usual first-order necessary conditions, but is found to be non-optimal. <P><A HREF="http://www.space-flight.org/AAS_meetings/1998_winter/sessions.html">Back</A>