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Uniqueness results for the value function via direct trajectory-construction methods

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1 Author(s)
H. J. Sussmann ; Dept. of Math., Rutgers State Univ. of New Jersey, Piscataway, NJ, USA

We present some new results, together with a number of particularly simple and user-friendly versions of results obtained in recent years by the author and M. Malisoff, on the uniqueness of solutions of the Hamilton-Jacobi-Bellman equation (HJBE) for deterministic finite-dimensional optimal control problems under non-standard hypotheses. Our approach is completely control-theoretic and totally self-contained, using the systematic construction of special trajectories of various kinds, and not involving any PDE methods. We donot assume that the Lagrangian is positive, or that the dynamics is Lipschitz-continuous.

Published in:

Decision and Control, 2003. Proceedings. 42nd IEEE Conference on  (Volume:4 )

Date of Conference:

9-12 Dec. 2003