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A unified parameter identification method for nonlinear time-delay systems
1. | School of Information Science & Engineering, Central South University, Changsha, China |
2. | Department of Mathematics and Statistics, Curtin University, Perth 6845 |
3. | Department of Mathematics and Statistics, Curtin University, Perth, W.A. 6845 |
4. | School of Information Science and Engineering, Central South University, Changsha, 410083 |
References:
[1] |
N. U. Ahmed, "Dynamic Systems and Control with Applications,", World Scientific Publishing Co. Pte. Ltd., (2006).
|
[2] |
L. Belkoura, J.-P. Richard and M. Fliess, Parameters estimation of systems with delayed and structured entries,, Automatica J. IFAC, 45 (2009), 1117.
doi: 10.1016/j.automatica.2008.12.026. |
[3] |
Q. Q. Chai, C. H. Yang, K. L. Teo and W. H. Gui, Time-delayed optimal control of an industrial-scale evaporation process sodium aluminate solution,, Control Engineering Practice, 20 (2012), 618. Google Scholar |
[4] |
R. Datko, Two examples of ill-posedness with respect to time delays revisited,, IEEE Transactions on Automatic Control, 42 (1997), 511.
doi: 10.1109/9.566660. |
[5] |
L. Denis-Vidal, C. Jauberthie and G. Joly-Blanchard, Identifiability of a nonlinear delayed-differential aerospace model,, IEEE Transactions on Automatic Control, 51 (2006), 154.
doi: 10.1109/TAC.2005.861700. |
[6] |
S. Diop, I. Kolmanovsky, P. E. Moraal and M. V. Nieuwstadt, Preserving stability/performance when facing an unknown time-delay,, Control Engineering Practice, 9 (2001), 1319. Google Scholar |
[7] |
S. V. Drakunov, W. Perruquetti, J. P. Richard and L. Belkoura, Delay identification in time-delay systems using variable structure observers,, Annual Reviews in Control, 30 (2006), 143. Google Scholar |
[8] |
P. J. Gawthrop and M. T. Nihtilä, Identification of time delays using a polynomial identification method,, Systems and Control Letters, 5 (1985), 267.
doi: 10.1016/0167-6911(85)90020-9. |
[9] |
L. Göllmann, D. Kern and H. Maurer, Optimal control problems with delays in state and control variables subject to mixed control-state constraints,, Optimal Control Applications and Methods, 30 (2009), 341.
doi: 10.1002/oca.843. |
[10] |
Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, A new computational method for optimizing nonlinear impulsive systems,, Dynamics of Continuous, 18 (2011), 59.
|
[11] |
Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, A new computational method for a class of free terminal time optimal control problems,, Pacific Journal of Optimization, 7 (2011), 63.
|
[12] |
X. Liu, Constrained control of positive systems with delays,, IEEE Transactions on Automatic Control, 54 (2009), 1596.
doi: 10.1109/TAC.2009.2017961. |
[13] |
R. C. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints,, Automatica, 44 (2008), 2923.
doi: 10.1016/j.automatica.2008.04.011. |
[14] |
R. Loxton, K. L. Teo and V. Rehbock, An optimization approach to state-delay identification,, IEEE Transactions on Automatic Control, 55 (2010), 2113.
doi: 10.1109/TAC.2010.2050710. |
[15] |
R. Loxton, K. L. Teo and V. Rehbock, Robust suboptimal control of nonlinear systems,, Applied Mathematics and Computation, 217 (2011), 6566.
doi: 10.1016/j.amc.2011.01.039. |
[16] |
D. G. Luenberger and Y. Ye, "Linear and Nonlinear Programming,", $3^{rd}$ edition, 116 (2008).
|
[17] |
R. B. Martin, Optimal control drug scheduling of cancer chemotherapy,, Automatica J. IFAC, 28 (1992), 1113.
doi: 10.1016/0005-1098(92)90054-J. |
[18] |
F. Pan, R. C. Han and D. M. Feng, "An identification method of time-varying delay based on genetic algorithm,", in Proceedings of the 2003 International Conference on Machine Learning and Cybernetics, (2003), 781. Google Scholar |
[19] |
C. Pignotti, A note on stabilization of locally damped wave equations with time delay,, Systems and Control Letters, 61 (2012), 92.
doi: 10.1016/j.sysconle.2011.09.016. |
[20] |
J.-P. Richard, Time-delay systems: An overview of some recent advances and open problems,, Automatica J. IFAC, 39 (2003), 1667.
doi: 10.1016/S0005-1098(03)00167-5. |
[21] |
R. F. Stengel, R. Ghigliazza, N. Kulkarni and O. Laplace, Optimal control of innate immune response,, Optimal Control Applications and Methods, 23 (2002), 91.
doi: 10.1002/oca.704. |
[22] |
L. Wang, W. Gui, K. L. Teo, R. Loxton and C. Yang, Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications,, Journal of Industrial and Management Optimization, 5 (2009), 705.
doi: 10.3934/jimo.2009.5.705. |
[23] |
L. Y. Wang, W. H. Gui, K. L. Teo, R. Loxton and C. H. Yang, Optimal control problems arising in the zinc sulphate electrolyte purification process,, Journal of Global Optimization, 54 (2012), 307.
doi: 10.1007/s10898-012-9863-x. |
[24] |
F. Y. Wang and Q. Yu, Optimal protein separations with time lags in control functions,, Journal of Process Control, 4 (1994), 135. Google Scholar |
[25] |
K. H. Wong, L. S. Jennings and F. Benyah, The control parametrization enhancing transform for constrained time-delayed optimal control problems,, ANZIAM Journal, 43 ().
|
[26] |
L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso and C. R. Mirasso, Permutation-information-theory approach to unveil delay dynamics from time-series analysis,, Physical Review E, 82 (2010).
doi: 10.1103/PhysRevE.82.046212. |
show all references
References:
[1] |
N. U. Ahmed, "Dynamic Systems and Control with Applications,", World Scientific Publishing Co. Pte. Ltd., (2006).
|
[2] |
L. Belkoura, J.-P. Richard and M. Fliess, Parameters estimation of systems with delayed and structured entries,, Automatica J. IFAC, 45 (2009), 1117.
doi: 10.1016/j.automatica.2008.12.026. |
[3] |
Q. Q. Chai, C. H. Yang, K. L. Teo and W. H. Gui, Time-delayed optimal control of an industrial-scale evaporation process sodium aluminate solution,, Control Engineering Practice, 20 (2012), 618. Google Scholar |
[4] |
R. Datko, Two examples of ill-posedness with respect to time delays revisited,, IEEE Transactions on Automatic Control, 42 (1997), 511.
doi: 10.1109/9.566660. |
[5] |
L. Denis-Vidal, C. Jauberthie and G. Joly-Blanchard, Identifiability of a nonlinear delayed-differential aerospace model,, IEEE Transactions on Automatic Control, 51 (2006), 154.
doi: 10.1109/TAC.2005.861700. |
[6] |
S. Diop, I. Kolmanovsky, P. E. Moraal and M. V. Nieuwstadt, Preserving stability/performance when facing an unknown time-delay,, Control Engineering Practice, 9 (2001), 1319. Google Scholar |
[7] |
S. V. Drakunov, W. Perruquetti, J. P. Richard and L. Belkoura, Delay identification in time-delay systems using variable structure observers,, Annual Reviews in Control, 30 (2006), 143. Google Scholar |
[8] |
P. J. Gawthrop and M. T. Nihtilä, Identification of time delays using a polynomial identification method,, Systems and Control Letters, 5 (1985), 267.
doi: 10.1016/0167-6911(85)90020-9. |
[9] |
L. Göllmann, D. Kern and H. Maurer, Optimal control problems with delays in state and control variables subject to mixed control-state constraints,, Optimal Control Applications and Methods, 30 (2009), 341.
doi: 10.1002/oca.843. |
[10] |
Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, A new computational method for optimizing nonlinear impulsive systems,, Dynamics of Continuous, 18 (2011), 59.
|
[11] |
Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, A new computational method for a class of free terminal time optimal control problems,, Pacific Journal of Optimization, 7 (2011), 63.
|
[12] |
X. Liu, Constrained control of positive systems with delays,, IEEE Transactions on Automatic Control, 54 (2009), 1596.
doi: 10.1109/TAC.2009.2017961. |
[13] |
R. C. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints,, Automatica, 44 (2008), 2923.
doi: 10.1016/j.automatica.2008.04.011. |
[14] |
R. Loxton, K. L. Teo and V. Rehbock, An optimization approach to state-delay identification,, IEEE Transactions on Automatic Control, 55 (2010), 2113.
doi: 10.1109/TAC.2010.2050710. |
[15] |
R. Loxton, K. L. Teo and V. Rehbock, Robust suboptimal control of nonlinear systems,, Applied Mathematics and Computation, 217 (2011), 6566.
doi: 10.1016/j.amc.2011.01.039. |
[16] |
D. G. Luenberger and Y. Ye, "Linear and Nonlinear Programming,", $3^{rd}$ edition, 116 (2008).
|
[17] |
R. B. Martin, Optimal control drug scheduling of cancer chemotherapy,, Automatica J. IFAC, 28 (1992), 1113.
doi: 10.1016/0005-1098(92)90054-J. |
[18] |
F. Pan, R. C. Han and D. M. Feng, "An identification method of time-varying delay based on genetic algorithm,", in Proceedings of the 2003 International Conference on Machine Learning and Cybernetics, (2003), 781. Google Scholar |
[19] |
C. Pignotti, A note on stabilization of locally damped wave equations with time delay,, Systems and Control Letters, 61 (2012), 92.
doi: 10.1016/j.sysconle.2011.09.016. |
[20] |
J.-P. Richard, Time-delay systems: An overview of some recent advances and open problems,, Automatica J. IFAC, 39 (2003), 1667.
doi: 10.1016/S0005-1098(03)00167-5. |
[21] |
R. F. Stengel, R. Ghigliazza, N. Kulkarni and O. Laplace, Optimal control of innate immune response,, Optimal Control Applications and Methods, 23 (2002), 91.
doi: 10.1002/oca.704. |
[22] |
L. Wang, W. Gui, K. L. Teo, R. Loxton and C. Yang, Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications,, Journal of Industrial and Management Optimization, 5 (2009), 705.
doi: 10.3934/jimo.2009.5.705. |
[23] |
L. Y. Wang, W. H. Gui, K. L. Teo, R. Loxton and C. H. Yang, Optimal control problems arising in the zinc sulphate electrolyte purification process,, Journal of Global Optimization, 54 (2012), 307.
doi: 10.1007/s10898-012-9863-x. |
[24] |
F. Y. Wang and Q. Yu, Optimal protein separations with time lags in control functions,, Journal of Process Control, 4 (1994), 135. Google Scholar |
[25] |
K. H. Wong, L. S. Jennings and F. Benyah, The control parametrization enhancing transform for constrained time-delayed optimal control problems,, ANZIAM Journal, 43 ().
|
[26] |
L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso and C. R. Mirasso, Permutation-information-theory approach to unveil delay dynamics from time-series analysis,, Physical Review E, 82 (2010).
doi: 10.1103/PhysRevE.82.046212. |
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