Optimal Control of Neutral Functional-Differential Inclusions Linear in Velocities
DOI:
https://doi.org/10.5540/tema.2004.05.01.0001Abstract
This paper studies optimal control problems for dynamical systems governed by neutral functional-differential inclusions that linearly depend on delayed velocity variables. Developing the method of discrete approximations, we derive new necessary optimality conditions for such problems in both Euler- Lagrange and Hamiltonian forms. The results obtained are expressed in terms of advanced generalized differential constructions in variational analysis.References
[1] J.-P. Aubin and A. Cellina, “Differential Inclusions”, Springer, 1984.
F.H. Clarke and G.G. Watkins, Necessary conditions, controllability and the value function for diffferential–difference inclusions, Nonlinear Anal., 10 (1986), 1155–1179.
F.H. Clarke and P.R. Wolenski, Necessary conditions for functional differential inclusions, Appl. Math. Optim., 34 (1996), 34–51.
A.L. Dontchev and E.M. Farkhi, Error estimates for discretized differential inclusions, Computing, 41 (1989), 349–358.
J. Hale, “Theory of Functional Differential Equations”, Springer-Verlag, New York, 1977.
M. Kisielewicz, “Differential Inclusions and Optimal Control”, Kluwer, Dordrecht, The Netherlands, 1991.
L.I. Minchenko, Necessary optimality conditions for differential–difference inclusions, Nonlinear Anal., 35 (1999), 307–322.
B.S. Mordukhovich, “Approximation Methods in Problems of Optimization and Control”, Nauka, Moscow, 1988.
B.S. Mordukhovich, Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions, Trans. Amer. Math. Soc., 340 (1993), 1–35.
B.S. Mordukhovich, Discrete approximations and refined Euler–Lagrange conditions for nonconvex differential inclusions, SIAM J. Control Optim., 33 (1995), 882–915.
B.S. Mordukhovich, J.S. Treiman and Q.J. Zhu, An extended extremal principle with applications to multiobjective optimization, SIAM J. Optim., 14 (2003), 359–379.
B.S. Mordukhovich and R. Trubnik, Stability of discrete approximation and necessary optimality conditions for delay-differential inclusions, Ann. Oper. Res., 101 (2001), 149–170.
B.S. Mordukhovich and L. Wang, Optimal control of constrained delay-differential inclusions with multivalued initial conditions, Control and Cybernetics, 28 (2003), 585-609.
B.S. Mordukhovich and L.Wang, Optimal control of hereditary differential inclusions, in “Proc 41st IEEE Conference on Decision and Control”, Las Vegas, NV, Dec. 2002, pp. 1107–1112.
B.S. Mordukhovich and L. Wang, Optimal control of neutral functional-differential inclusions, SIAM J. Control Optim., 43 (2004), 111-136.
R.T. Rockafellar, Equivalent subgradient versions of Hamiltonian and Euler–Lagrange conditions in variational analysis, SIAM J. Control Optim., 34 (1996), 1300–1314.
R.T. Rockafellar and R.J.-B. Wets, “Variational Analysis”, Springer-Verlag, Berlin, 1998.
R.B. Vinter, “Optimal Control”, Birkh¨auser, Boston, 2000.
L. Wang, Discrete approximations of neutral functional-differential inclusions, preprint, 2004.
J. Warga, “Optimal Control of Differential and Functional Equations”, Academic Press, Newc York, 1972.
Downloads
Published
How to Cite
Issue
Section
License
Copyright
Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.
Intellectual Property and Terms of Use
The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.
The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.
