On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions
ESAIM: Control, Optimisation and Calculus of Variations (2007)
- Volume: 14, Issue: 3, page 590-603
- ISSN: 1292-8119
Access Full Article
topAbstract
topHow to cite
topReferences
top- J.-P. Aubin, Optima and Equilibria: an introduction to Nonlinear Analysis. Springer, 2nd Edn. (1988).
- A.S. Besicovitch, Almost Periodic Functions. Cambridge University Press, Cambridge (1932) (and Dover, 1954).
- J. Blot, Le théorème de Markov-Kakutani et la presque-périodicité, Fixed Point Theory and Applications, M. Théra and J.B. Baillon Eds., Pitman Research Notes in Mathematical Series252, Longman, London (1991) 45–56.
- J. Blot, Oscillations presque-périodiques forcées d'équations d'Euler-Lagrange. Bull. Soc. Math. France122 (1994) 285–304.
- J. Blot, Variational Methods for the Almost Periodic Lagrangian Oscillations. Preprint, Cahiers Eco et Maths No. 96.44 (1996).
- J. Blot and D. Pennequin, Spaces of quasi-periodic functions and oscillations in dynamical systems. Acta Appl. Math.65 (2001) 83–113.
- J. Blot and D. Pennequin, Existence and structure results on Almost Periodic solutions of Difference Equations. J. Diff. Equa. Appl.7 (2001) 383–402.
- H. Bohr, Almost Periodic Functions. Julius Springer, Berlin (1933) (Chelsea Publishing Company, N.Y., 1947).
- F. Colonius, Optimal Periodic Control, in Lect. Notes Math.1313, Springer, Berlin (1988).
- C. Corduneanu, Almost Periodic Functions. Chelsea (1989).
- G. Da Prato and A. Ichikawa, Optimal control of linear systems with a.p. inputs. SIAM J. Control Optim.25 (1987) 1007–1019.
- D.G. De Figueiredo, Lectures on the Ekeland Variational Principle with Applications and Detours. Tata Institute of Fundamental Research, Bombay (1989).
- J. Favard, Leçons sur les fonctions presque-périodiques. Gauthiers-Villars, Paris (1933).
- A. Halanay, Optimal Control of Periodic solutions. Rev. Rouman. Mat. Pure Appl.19 (1974) 3–16.
- V.P. Havin and N.K. Nikolski Eds., Commutative Harmonic Analysis II. Springer, Berlin (1991).
- E. Hewitt, K.A. Ross, Abstract Harmonic Analysis I & II. Springer, Berlin, 2nd Edn. (1979) (and 1970).
- F.J.M. Horn and J.E. Bailey, An application of the theorem of relaxed control to the problem of increasing catalyst selectivity. J. Opt. Theory Appl.2 (1968) 441–449.
- A. Kovaleva, Optimal Control of Mechanical Oscillations. Springer, Berlin (1999).
- J.L. Mauclaire, Intégration et Théorie des Nombres. Travaux en Cours, Hermann, Paris (1986).
- G.M. N'Guérékata, Almost automorphic and almost periodic functions in abstract spaces. Kluwer Academic Publishers (2001)
- P. Nistri, Periodic Control Problems for a class of nonlinear periodic differential systems. Nonlinear Anal. Theor. Meth. Appl.7 (1983) 79–90.
- D. Pennequin, Existence results on almost periodic solutions of discrete time equations. Discrete Cont. Dynam. Syst.7 (2001) 51–60.
- I.C. Percival, Variational principles for the invariant toroids of classical dynamics. J. Phys. A: Math. Nucl. Gen.7 (1974) 794–802.
- I.C. Percival, Variational principles for invariant tori and cantori. A.I.P. Conf. Proc.57 (1979) 302–310.
- L. Pontryagin, Topological Groups. N.Y. Gordon and Breach (1966).
- J.L. Speyer, Periodic optimal flight. J. Guid. Control Dynam.61 (1996) 745–754.
- W. Rudin, Fourier Analysis on Groups. Interscience Publishers, N.Y. (1962).
- A. Weil, L'intégration dans les Groupes Topologiques. Hermann, Paris (1940).