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Maximum principle, dynamic programming, and their connection in deterministic control (1990)

Zhou, X. Y.

Springer

Journal of optimization theory and applications 65 (1990), S. 363-373

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ISSN: 1573-2878

Schlagwort(e): Optimal control ; maximum principle ; dynamic programming ; viscosity solutions ; superdifferential ; subdifferential

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01102352

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