Hybrid functions approach for nonlinear constrained optimal control problems

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 4, 2012, Pages 1831-1843

  Mashayekhi, S ^a   Ordokhani, Y ^a   Razzaghi, M ^b  

^a ALZAHRA UNIVERSITY   (Iran)

^b MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

Bernoulli polynomials; Block pulse; Constrained optimal control; Hybrid

Indexed keywords

NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS;

BERNOULLI POLYNOMIALS; BLOCK-PULSE; CONSTRAINED OPTIMAL CONTROL; CONSTRAINED OPTIMAL CONTROL PROBLEMS; FUNCTION APPROACHES; FUNCTIONS APPROXIMATIONS; HYBRID; HYBRID FUNCTIONS; PROPERTY; QUADRATIC PERFORMANCE INDICES;

NONLINEAR PROGRAMMING;

EID: 80054973762     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.09.008     Document Type: Article

References (37)

1. Kirk D.E. Optimal control theory 1970, Prentice Hall, Englewood Cliffs, NJ.
2. Kleiman D.L., Fortmann T., Athans M. On the design of linear systems with piecewise-constant feedback gains. IEEE Trans Automat Contr 1968, 13:354-361.
3. Drefus S.F. Variational problems with state variable inequality constraints. J Math Anal Appl 1962, 4:291-301.
4. Mehra R.K., Davis R.E. A generalized gradient method for optimal control problems with inequality constraints and singular arcs. IEEE Trans Automat Contr 1972, 17:69-72.
5. Pananisamy K.R., Rao G.P. Minimum energy control of time-delay systems via Walsh functions. Optim Contr Appl Methods 1983, 4:213-226.
6. Chang R.Y., Wang M.L. Shifted Legendre direct method for variational problems. J Optim Theory Appl 1983, 39:299-307.
7. Hwang C., Shih Y.P. Optimal control of delay systems via block-pulse functions. J Optim Theory Appl 1985, 45:101-112.
8. Horng I.R., Chou J.H. Shifted Chebyshev direct method for solving variational problems. Int J Syst Sci 1985, 16:855-861.
9. Vlassenbroeck J. A Chebyshev polynomial method for optimal control with constraints. Automatica 1988, 24:499-506.
10. Vlassenbroeck J., Van Dooren R. A Chebyshev technique for solving nonlinear optimal control problems. IEEE Trans Automat Contr 1988, 33:333-340.
11. Yen V., Nagurka M. Linear quadratic optimal control via Fourier-based state parameterization. J Dyn Syst Measure Contr 1991, 11:206-215.
12. Elnegar G.N., Kazemi M.A. Pseudospectral Chebyshev optimal control of constrained nonlinear dynamical systems. Comput Optim Applica 1998, 11:195-217.
13. Marzban H.R., Razzaghi M. Hybrid functions approach for linearly constrained quadratic optimal control problems. Appl Math Modell 2003, 27:471-485.
14. Ordokhani Y., Razzaghi M. Linear quadratic optimal control problems with inequality constraints via rationalized Haar functions. Dyn Contin Discrete Impul Syst Ser B 2005, 12:761-773.
15. Marzban H.R., Razzaghi M. Rationalized Haar approach for nonlinear constrined optimal control problems. Appl Math Modell 2010, 34:174-183.
16. Razzaghi M., Elnagar G. Linear quadratic optimal control problems via shifted Legendre state parametrization. Int J Syst Sci 1994, 25:393-399.
17. Razzaghi M., Razzaghi M. Instabilities in the solution of a heat conduction problem using Taylor series and alternative approaches. J Frank Instit 1989, 32:683-690.
18. Razzaghi M., Marzban H.R. Direct method for variational problems via hybrid of block-pulse and Chebyshev functions. Math Prob Eng 2000, 6:85-97.
19. Kajani M.T., Vencheh A.H. Solving second kind integral equations with hybrid Chebyshev and block-pulse functions. Appl Math Comput 2005, 163:71-77.
20. Wang X.T., Li Y.M. Numerical solutions of integro differential systems by hybrid of general block-pulse functions and the second Chebyshev polynomials. Appl Math Comput 2009, 209:266-272.
21. Marzban H.R., Razzaghi M. Optimal control of linear delay systems via hybrid of block-pulse and Legendre polynomials. J Frank Inst 2004, 341:279-293.
22. Hsiao C.H. Hybrid function method for solving Fredholm and Volterra integral equations of the second kind. J Comput Appl Math 2009, 230:59-68.
23. Singh V.K., Pandey R.K., Singh S. A stable algorithm for Hankel transforms using hybrid of block-pulse and Legendre polynomials. Comput Phys Commun 2010, 181:1-10.
24. Marzban H.R., Razzaghi M. Analysis of time-delay systems via hybrid of block-pulse functions and Taylor series. J Vibr Contr 2005, 11:1455-1468.
25. Marzban H.R., Razzaghi M. Solution of multi-delay systems using hybrid of block-pulse functions and Taylor series. J Sound Vibr 2006, 292:954-963.
26. Avrile M. Nonlinear programming. Analysis and Methods 1976, Prentice-Hall, Englewood Cliffs, NJ.
27. Belegundu A.D., Arora J.S. A study of mathematical programming methods for structural optimization. Part II. Int J Numer Methods Eng 1985, 21:1601-1623.
28. Gill P.E., Murray W. Linearly constrained problems including linear and quadratic programming. The State of the Art in Numerical Analysis 1977, Academic Press, London, New York, p. 313-63. D. Jacobs (Ed.).
29. Nelder J.A., Mead R.A. A simplex method for function minimization. Comput J 1965, 7:308-313.
30. Powell M.J.D. An efficient method for finding the minimum of a function of several variables without calculating the derivatives. Comput J 1964, 7:155-162.
31. Schittkowskki K. NLPQL: a FoRTRAN subroutine for solving constrained nonlinear programming problems. Ann Operat Res 1985, 5:485-500.
32. Costabile F., Dellaccio F., Gualtieri M.I. A new approach to Bernoulli polynomials. Rendiconti di Matemat 2006, 26:1-12. Serie VII.
33. Arfken G. Mathematical methods for physicists 1985, Academic press, San Diego. third ed.
34. Kreyszig E. Introductory functional analysis with applications 1978, John Wiley and Sons Press, New York.
35. Lancaster P. theory of matrixes 1969, Academic Press, New York.
36. Jaddu H. Direct solution of nonlinear optimal control problems using quasilinearization and Chebyshev polynomials. J Frank Inst 2002, 339:479-498.
37. Teo K.L., Wong K.H. Nonlinearly constrained optimal control problems. J Austral Math Soc Ser B 1992, 33:507-530.