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IMA Journal of Mathematical Control and Information 1985 2(3):241-250; doi:10.1093/imamci/2.3.241
© 1985 by Institute of Mathematics and its Applications
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Global Optimality Conditions for Nonnormal Control Problems

R. B. VINTER and L. A. MENDOZA

Department of Electrical Engineering, Imperial College London, SW7 2BT UK
CIMAT, A C Apdo Postal 402 Valenciana Guanajhato GTA Mexico

A sufficient condition for optimality, involving a solution to the Hamilton—Jacobi equation, is well known. We provide here a modification of such a condition. This is expressed in terms of a sequence of locally Lipschitz-continuous functions which are extended solutions of the Hamilton-Jacobi equation. The condition is necessary as well as sufficient for optimality for a large class of problems, including nonnormal ones. The optimality condition admits simple constructive proofs in contrast to earlier, related conditions.


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