Hamilton–Jacobi–Bellman equation (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Hamilton–Jacobi–Bellman equation" in English language version.

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arxiv.org

Jones, Morgan; Peet, Matthew (2020). "Polynomial Approximation of Value Functions and Nonlinear Controller Design with Performance Bounds". arXiv:2010.06828 [math.OC].

Kirk, Donald E. (1970). Optimal Control Theory: An Introduction. Englewood Cliffs, NJ: Prentice-Hall. pp. 86–90. ISBN 0-13-638098-0.
Yong, Jiongmin; Zhou, Xun Yu (1999). "Dynamic Programming and HJB Equations". Stochastic Controls : Hamiltonian Systems and HJB Equations. Springer. pp. 157–215 [p. 163]. ISBN 0-387-98723-1.
Naidu, Desineni S. (2003). "The Hamilton–Jacobi–Bellman Equation". Optimal Control Systems. Boca Raton: CRC Press. pp. 277–283 [p. 280]. ISBN 0-8493-0892-5.
Chang, Fwu-Ranq (2004). Stochastic Optimization in Continuous Time. Cambridge, UK: Cambridge University Press. pp. 113–168. ISBN 0-521-83406-6.

Bellman, R. E. (1954). "Dynamic Programming and a new formalism in the calculus of variations". Proc. Natl. Acad. Sci. 40 (4): 231–235. Bibcode:1954PNAS...40..231B. doi:10.1073/pnas.40.4.231. PMC 527981. PMID 16589462.
Kemajou-Brown, Isabelle (2016). "Brief History of Optimal Control Theory and Some Recent Developments". In Budzban, Gregory; Hughes, Harry Randolph; Schurz, Henri (eds.). Probability on Algebraic and Geometric Structures. Contemporary Mathematics. Vol. 668. pp. 119–130. doi:10.1090/conm/668/13400. ISBN 9781470419455.
Abu-Khalaf, Murad; Lewis, Frank L. (2005). "Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach". Automatica. 41 (5): 779–791. doi:10.1016/j.automatica.2004.11.034. S2CID 14757582.
Al-Tamimi, Asma; Lewis, Frank L.; Abu-Khalaf, Murad (2008). "Discrete-Time Nonlinear HJB Solution Using Approximate Dynamic Programming: Convergence Proof". IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics. 38 (4): 943–949. doi:10.1109/TSMCB.2008.926614. PMID 18632382. S2CID 14202785.

Bellman, R. E. (1954). "Dynamic Programming and a new formalism in the calculus of variations". Proc. Natl. Acad. Sci. 40 (4): 231–235. Bibcode:1954PNAS...40..231B. doi:10.1073/pnas.40.4.231. PMC 527981. PMID 16589462.
Al-Tamimi, Asma; Lewis, Frank L.; Abu-Khalaf, Murad (2008). "Discrete-Time Nonlinear HJB Solution Using Approximate Dynamic Programming: Convergence Proof". IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics. 38 (4): 943–949. doi:10.1109/TSMCB.2008.926614. PMID 18632382. S2CID 14202785.

Abu-Khalaf, Murad; Lewis, Frank L. (2005). "Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach". Automatica. 41 (5): 779–791. doi:10.1016/j.automatica.2004.11.034. S2CID 14757582.
Al-Tamimi, Asma; Lewis, Frank L.; Abu-Khalaf, Murad (2008). "Discrete-Time Nonlinear HJB Solution Using Approximate Dynamic Programming: Convergence Proof". IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics. 38 (4): 943–949. doi:10.1109/TSMCB.2008.926614. PMID 18632382. S2CID 14202785.

Kálmán, Rudolf E. (1963). "The Theory of Optimal Control and the Calculus of Variations". In Bellman, Richard (ed.). Mathematical Optimization Techniques. Berkeley: University of California Press. pp. 309–331. OCLC 1033974.