AAS 98-163

NECESSARY AND SUFFICIENT CONDITIONS FOR OPTIMAL CONTROL PROBLEMS WITH SCALAR TERMINAL CONSTRAINT

Jang-Won Jo, J. E. Prussing - University of Illinois at Urbana-Champaign

Abstract

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.

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