ISSN:
1573-2878
Keywords:
Optimal control
;
maximum principle
;
dynamic programming
;
viscosity solutions
;
superdifferential
;
subdifferential
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Two major tools for studying optimally controlled systems are Pontryagin's maximum principle and Bellman's dynamic programming, which involve 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 notions of superdifferential and subdifferential introduced by Crandall and Lions. Our results are essentially non-smooth 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01102352
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