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Second-order weak composed epiderivatives and applications to optimality conditions
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., Hackensack, NJ, 2006. |
[2] |
L. Belkoura, J.-P. Richard and M. Fliess, Parameters estimation of systems with delayed and structured entries, Automatica J. IFAC, 45 (2009), 1117-1125.
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), 618-628. |
[4] |
R. Datko, Two examples of ill-posedness with respect to time delays revisited, IEEE Transactions on Automatic Control, 42 (1997), 511-515.
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), 154-158.
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), 1319-1325. |
[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), 143-158. |
[8] |
P. J. Gawthrop and M. T. Nihtilä, Identification of time delays using a polynomial identification method, Systems and Control Letters, 5 (1985), 267-271.
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), 341-365.
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, Discrete and Impulsive Systems Series B: Applications and Algorithms, 18 (2011), 59-76. |
[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), 63-81. |
[12] |
X. Liu, Constrained control of positive systems with delays, IEEE Transactions on Automatic Control, 54 (2009), 1596-1600.
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), 2923-2929.
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), 2113-2119.
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), 6566-6576.
doi: 10.1016/j.amc.2011.01.039. |
[16] |
D. G. Luenberger and Y. Ye, "Linear and Nonlinear Programming," $3^{rd}$ edition, International Series in Operations Research & Management Science, 116, Springer, New York, 2008. |
[17] |
R. B. Martin, Optimal control drug scheduling of cancer chemotherapy, Automatica J. IFAC, 28 (1992), 1113-1123.
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, Xi'an, China, (2003), 781-783. |
[19] |
C. Pignotti, A note on stabilization of locally damped wave equations with time delay, Systems and Control Letters, 61 (2012), 92-97.
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), 1667-1694.
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), 91-104.
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), 705-718.
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), 307-323.
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), 135-142. |
[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), 046212, 9 pp.
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., Hackensack, NJ, 2006. |
[2] |
L. Belkoura, J.-P. Richard and M. Fliess, Parameters estimation of systems with delayed and structured entries, Automatica J. IFAC, 45 (2009), 1117-1125.
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), 618-628. |
[4] |
R. Datko, Two examples of ill-posedness with respect to time delays revisited, IEEE Transactions on Automatic Control, 42 (1997), 511-515.
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), 154-158.
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), 1319-1325. |
[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), 143-158. |
[8] |
P. J. Gawthrop and M. T. Nihtilä, Identification of time delays using a polynomial identification method, Systems and Control Letters, 5 (1985), 267-271.
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), 341-365.
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, Discrete and Impulsive Systems Series B: Applications and Algorithms, 18 (2011), 59-76. |
[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), 63-81. |
[12] |
X. Liu, Constrained control of positive systems with delays, IEEE Transactions on Automatic Control, 54 (2009), 1596-1600.
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), 2923-2929.
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), 2113-2119.
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), 6566-6576.
doi: 10.1016/j.amc.2011.01.039. |
[16] |
D. G. Luenberger and Y. Ye, "Linear and Nonlinear Programming," $3^{rd}$ edition, International Series in Operations Research & Management Science, 116, Springer, New York, 2008. |
[17] |
R. B. Martin, Optimal control drug scheduling of cancer chemotherapy, Automatica J. IFAC, 28 (1992), 1113-1123.
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, Xi'an, China, (2003), 781-783. |
[19] |
C. Pignotti, A note on stabilization of locally damped wave equations with time delay, Systems and Control Letters, 61 (2012), 92-97.
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), 1667-1694.
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), 91-104.
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), 705-718.
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), 307-323.
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), 135-142. |
[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), 046212, 9 pp.
doi: 10.1103/PhysRevE.82.046212. |
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