Optimal control of linear time-delayed systems by linear Legendre multiwavelets

Journal of Optimization Theory and Applications

Volumn 143, Issue 1, 2009, Pages 107-121

  Khellat, F ^a  

^a SHAHID BEHESHTI UNIVERSITY   (Iran)

Author keywords

Linear Legendre multiwavelets; Optimal control; Time delayed system

Indexed keywords

TIME DELAY;

CONTROL SYNTHESIS; COST FUNCTIONALS; LINEAR LEGENDRE MULTI-WAVELETS; LINEAR TIME; OPERATIONAL MATRICES; OPTIMAL CONTROLS; PROPERTY; QUADRATIC COSTS; TIME-DELAYED SYSTEMS; USEFUL PROPERTIES;

LAGRANGE MULTIPLIERS;

EID: 70350297708     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-009-9548-x     Document Type: Article

References (21)

1. Jamshidi, M., Wang, C.M.: A computational algorithm for large-scale nonlinear time-delay systems. IEEE Trans. Syst. Man Cybern. 14, 2-9 (1984).
2. Kwakernaak, H., Sivan, R.: Linear Optimal Control Systems. Wiley-Interscience, New York (1972).
3. Malek-Zavarei, M., Jamshidi, M.: Time-Delay Systems: Analysis, Optimization and Applications. North-Holland, Amsterdam (1987).
4. Eller, D.H., Aggarwal, J.K., Banks, H.T.: Optimal control of linear time-delay systems. IEEE Trans. Automat. Control 14, 678-687 (1969).
5. Alekal, Y., Brunovsky, P., Chyung, D.H., Lee, E.B.: The quadratic problem for systems with time delays. IEEE Trans. Automat. Control 16, 673-687 (1971).
6. Delfour, M.C.: The linear quadratic control problem with delays in state and control variables: A state space approach. SIAM J. Control Optim. 24, 835-883 (1986).
7. Uchida, K., Shimemura, E., Kubo, T., Abe, N.: The linear-quadratic optimal control approach to feedback control design for systems with delay. Automatica 24, 773-780 (1988).
8. Pananisamy, K.R., Rao, G.P.: Optimal control of linear systems with delays in state and control via Wash functions. IEEE Proc. 130, 300-312 (1983).
9. Hwang, C., Shih, Y.P.: Optimal control of delay systems via block pulse functions. J. Optim. Theory Appl. 45, 101-112 (1985).
10. Perng, M.H.: Direct approach for the optimal control of linear time-delay systems via shifted Legendre polynomials. Int. J. Control 43, 1897-1904 (1986).
11. Horng, I.R., Chou, J.H.: Analysis, parameter estimation and optimal control of time-delay systems via Chebyshev series. Int. J. Control 41, 1221-1234 (1985).
12. Marzban, H.R., Razzaghi, M.: Optimal control of linear delay systems via Hybrid of block-pulse and Legendre polynomials. J. Franklin I. 341, 279-293 (2004).
13. Khellat, F.: Yousefi S.A., The linear Legendre mother wavelets operational matrix of integral and its application. J. Franklin I. 343, 181-190 (2006).
14. Hosseiniun, S.A.R., Khellat, F., Radjabalipour, M.: Analysis of time-delay dynamical systems using the linear Legendre mother wavelets. J. Franklin I. (2007, submitted).
15. Daubechies, I.: Ten Lectures on Wavelets. SIAM, Philadelphia (1992).
16. Strela, V.: Multiwavelets: Theory and application. Ph.D. Thesis, MIT University (1996).
17. Felippa, C.A.: Introduction to finite element methods. University of Colorado Boulder, Colorado 80309-0429, USA.
18. Banks, H.T., Burns, J.A.: Hereditary control problem: numerical methods based on averaging approximations. SIAM J. Control Optim. 16, 169-208 (1978).
19. Teo, K.L., Wong, K.H., Clements, D.J.: Optimal control computation for linear time-lag systems with linear terminal constrains. J. Optim. Theory Appl. 44, 509-526 (1984).
20. Lee, A.Y.: Numerical solution of time-delayed optimal control problems with terminal inequality constraints. Optim. Control Appl. Methods 14, 203-210 (1993).
21. Wang, X.T.: Numerical solutions of optimal control for time delay systems by hybrid of block-pulse functions and Legendre polynomials. Appl. Math. Comput. 184, 849-856 (2007).