Envelope representations in Hamilton-Jacobi theory for fully convex problems of control

R.T. Rockafellar, P.R. Wolenski
Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)  
This paper is a sequel to the one in this same session which surveys recent results on the role of convexity in Hamilton-Jacobi theory. We describe here how value functions in optimal control can be represented as upper and lower envelopes involving so-called kernel functions. Particularly noteworthy is a lower envelope formula given in terms of the dualizing kernel, which is a value function in its own right with many surprising and attractive properties.
doi:10.1109/cdc.2001.980692 fatcat:xji6fv7sbnb6jlqdmwg36visva