Control studies of time-delayed dynamical systems with the method of continuous time approximation

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 11, 2009, Pages 3933-3944

  Sun, Jian Qiao ^a   Song, Bo ^a  

^a University of California   (United States)

Author keywords

Finite dimensional state space approximation; Optimal control; Optimal feedback gains via mapping; Output feedback; Time delay

Indexed keywords

CONTINUOUS TIME SYSTEMS; DELAY CONTROL SYSTEMS; DYNAMICAL SYSTEMS; FEEDBACK CONTROL; FREQUENCY DOMAIN ANALYSIS; NUMERICAL METHODS; POLES; STATE SPACE METHODS; TIME DOMAIN ANALYSIS; TIMING CIRCUITS;

CONTINOUS TIME; CONTROL STUDIES; FINITE DIMENSIONAL; FINITE DIMENSIONAL STATE SPACE APPROXIMATION; OPTIMAL CONTROLS; OPTIMAL FEEDBACK GAIN VIA MAPPING; OPTIMAL FEEDBACK GAINS; OUTPUT-FEEDBACK; STATE-SPACE; TIME-DELAYS;

TIME DELAY;

EID: 67349094951     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.02.011     Document Type: Article

References (24)

1. Sun JQ. A method of continuous time approximation of delayed dynamical systems. Communications in nonlinear science and numerical simulation doi:10.1016/j.cnsns.2008.02.008.
2. Pinto O.C., and Goncalves P.B. Control of structures with cubic and quadratic non-linearities with time delay consideration. Revista Brasileira de Ciencias Mecanicas/J Brazil Soc Mech Sci 24 2 (2002) 99-104
3. Klein E.J., and Ramirez W.F. State controllability and optimal regulator control of time-delayed systems. Int J Control 74 3 (2001) 281-289
4. Yang B., and Wu X. Modal expansion of structural systems with time delays. AIAA J 36 12 (1998) 2218-2224
5. Stepan G. Delay-differential equation models for machine tool chatter. In: Moon F.C. (Ed). Dynamics and chaos in manufacturing processes (1998), Wiley, New York 165-192
6. Ali M.S., Hou Z.K., and Noori M.N. Stability and performance of feedback control systems with time delays. Comput Struct 66 2-3 (1998) 241-248
7. Deshmukh V, Butcher EA, Bueler E. Dimensional reduction of nonlinear delay differential equations with periodic coefficients using Chebyshev spectral collocation. Nonlinear dynamics 52 (1-2).
8. Deshmukh V., Ma H., and Butchern E.A. Optimal control of parametrically excited linear delay differential systems via Chebyshev polynomials. Optim Control Appl Meth 27 (2006) 1231́C136.
9. Ma H., Deshmukh V., Butcher E.A., and Averina V. Delayed state feedback and chaos control for time periodic systems via a symbolic approach. Commun Nonlinear Sci Num Simul 10 5 (2005) 479-497
10. Ma H., Butcher E.A., and Bueler E. Chebyshev expansion of linear and piecewise linear dynamic systems with time delay and periodic coefficients under control excitations. J Dyn Syst Measur Control 125 (2003) 236-243
11. Garg N.K., Mann B.P., Kim N.H., and Kurdi M.H. Stability of a time-delayed system with parametric excitation. J Dyn Syst Measur Control 129 2 (2007) 125-135
12. Kalmar-Nagy T. A novel method for efficient numerical stability analysis of delay-differential equations. In: Proceedings of American control conference. Portland: Oregon; 2005. p. 2823-26.
13. Niculescu SI, Verriest EI, Dugard L, Dion JM. Stability of linear systems with delayed state: a guided tour. In: Proceedings of the IFAC workshop: linear time delay systems. Grenoble, France; 1998. p. 31-8.
14. Gu K., and Niculescu S.l. Survey on recent results in the stability and control of time-delay systems. J Dyn Syst Measur Control 125 (2003) 158-165
15. Insperger T, Stepan G. Semi-discretization of delayed dynamical systems. In: Proceedings of ASME 2001 design engineering technical conferences and computers and information in engineering conference, Pittsburgh, Pennsylvania; 2001.
16. Insperger T., and Stepan G. Semi-discretization method for delayed systems. Int J Num Meth Eng 55 5 (2002) 503-518
17. Sheng J., Elbeyli O., and Sun J.Q. Stability and optimal feedback controls for time-delayed linear periodic systems. AIAA J 42 5 (2004) 908-911
18. Sheng J., and Sun J.Q. Feedback controls and optimal gain design of delayed periodic linear systems. J Vibrat Control 11 2 (2005) 277-294
19. Elbeyli O., and Sun J.Q. On the semi-discretization method for feedback control design of linear systems with time delay. J Sound Vibrat 273 (2004) 429-440
20. Lewis F.L., and Syrmos V.L. Optimal control (1995), John Wiley and Sons, New York
21. Slotine J.-J.E., and Li W. Applied nonlinear control (1991), Prentice Hall
22. Carnahan B., Luther H.A., and Wilkes J.O. Appl Num Meth (1969), John Wiley and Sons, New York
23. Franklin G.F., Powell J.D., and Emami-Naeini A. Feedback Control Dyn Syst (1986), Addison-Wesley, Reading, Massachusetts
24. Vijta M. Some remarks on the Padé-approximations. In: Proceedings of the 3rd TEMPUS-INTCOM symposium, Veszpré, Hungary; 2000, p. 1-6.