Maximum principle, dynamic programming and their connection in deterministic control
Two major tools for studying optimally controlled systems are Pontryagin's maximum principle and Bellman's dynamic programming, involving the adjoint function, the Hamiltonian function, and the value function. The relationships among these functions are investigated in this work, in the case of deterministic, finite-dimensional systems, by employing the notion of superdifferential and subdifferential introduced by \textit{M. G. Crandall} and \textit{P.-L. Lions} [Trans. Am. Math. Soc. 277, 1-42 (1983; Zbl 0599.35024)]. Our results are essentially nonsmooth versions of the classical ones. The connection between the maximum principle and the Hamilton-Jacobi-Bellman equation (in the viscosity sense) is thereby explained by virtue of the above relationship.
scientific article; zbMATH DE number 4107551
scientific article