March  2021, 11(1): 1-12. doi: 10.3934/naco.2020011

Fault-tolerant control against actuator failures for uncertain singular fractional order systems

School of Sciences, Northeastern University, Shenyang 110819, China

* Corresponding author: Xuefeng Zhang

Received  May 2019 Revised  August 2019 Published  February 2020

Fund Project: The first author is supported by NSFC under grant 61603055

A method of designing observer-based feedback controller against actuator failures for uncertain singular fractional order systems (SFOS) is presented in this paper. By establishing actuator fault model and state observer, an observer-based fault-tolerant state feedback controller is developed such that the closed-loop SFOS is admissible. The controller designed by the proposed method guarantees that the closed-loop system is regular, impulse-free and stable in the event of actuator failures. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.

Citation: Xuefeng Zhang, Yingbo Zhang. Fault-tolerant control against actuator failures for uncertain singular fractional order systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 1-12. doi: 10.3934/naco.2020011
References:
[1]

H. S. Ahn and Y. Q. Chen, Necessary and sufficient stability condition of fractional$-$order interval linear systems, Automatica, 44 (2008), 2985-2988.  doi: 10.1016/j.automatica.2008.07.003.  Google Scholar

[2]

M. Blanke, M. Kinnaert, J. Lunze and M. Staroswiecki, Diagnosisi and Fault-Tolerant Control, Springer, Berlin, Germany, 2006. doi: 10.1007/978-3-540-35653-0.  Google Scholar

[3]

M. BlankeR. Izadi-ZamanabadiS. A. Bogh and C. P. Lunau, Fault-tolerant control systems$-$a holistic view, Contol Engineering Prac., 5 (1997), 693-702.  doi: 10.1016/s0967-0661(97)00051-8.  Google Scholar

[4]

L. L. Fan and Y. D. Song, Neuro$-$adaptive model$-$referance fault$-$tolerant control with application to wind turbines, IET Control Theory & Appl., 6 (2012), 475-486.  doi: 10.1049/iet-cta.2011.0250.  Google Scholar

[5]

C. FargesM. Moze and J. Sabatier, Pseudo-state feedback stabilization of commensurate fractional order systems, Automatica, 46 (2010), 1730-1734.  doi: 10.1016/j.automatica.2010.06.038.  Google Scholar

[6]

C. Farges, J. Sabatier and M. Moze, Robust stability analysis and stabilization of fractional order polytopic systems , Preprints of the 18th IFAC World Congress, (2011), Milano, Italy, 10800-10805. doi: 10.3182/20110828-6-IT-1002.00779.  Google Scholar

[7]

Bin Guo and Yong Chen, Adaptive fault tolerant control for time-varying delay system withactuator fault and mismatched disturbance, ISA Transcation, 89 (2019), 122-130.  doi: 10.1016/j.isatra.2018.12.024.  Google Scholar

[8]

Q. HuB. Xiao and M. I. Friswll, Robust fault$-$tolerant control for spacecraft attitude stabilisation subject to input saturation, IET Control Theory & Appl., 5 (2011), 271-282.  doi: 10.1049/iet-cta.2009.0628.  Google Scholar

[9]

S. D. HuangJ. LamG. H. Yang and S. Y. Zhang, Fault tolerant decentralized $H_\infty$ control for symmetric composite systems, IEEE Trans. Autom. Control, 44 (1999), 2108-2114.  doi: 10.1109/9.802926.  Google Scholar

[10]

R. Isermann, Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer, Berlin, Germany, 2006. doi: 10.1007/3-540-30368-5.  Google Scholar

[11]

L. A. JacynthoM. C. M. Teixeira and E. Assunco, Identification of fractional-order transfer functions using a step excitation, IEEE Trans. Circuits Syst., 62 (2015), 896-900.  doi: 10.1109/tcsii.2015.2436052.  Google Scholar

[12]

Y. JiangQ. L. Hu and G. F. Ma, Adaptive backsteping fault$-$tolerant control for flexible spacecraft with unknown bounded disturbances and actuator failures, ISA Transcations, 49 (2010), 57-69.  doi: 10.1016/j.isatra.2009.08.003.  Google Scholar

[13]

E. Last, Linear matrix inequalities in system and control theory, Proceedings of the IEEE, 86 (1994), 2473-2474.  doi: 10.1109/JPROC.1998.735454.  Google Scholar

[14]

X. J. Li and G. H. Yang, Robust adaptive fault$-$tolerant control for uncertain linear systems with actuator failures, IET Control Theory & Appl., 6 (2012), 1544-1551.  doi: 10.1049/iet-cta.2011.0599.  Google Scholar

[15]

Y. LiY. Q. Chen and I. Podlubny, Stability of fractional order nonlinear dynamic systems, Automatica, 45 (2009), 1965-1969.  doi: 10.1016/j.automatica.2009.04.003.  Google Scholar

[16]

C. LinB. ChenP. Shi and J. P. Yu, Necessary and sufficient conditions of observer$-$based stabilization for a class of fractional$-$order descriptor systems, Systems & Control Letters, 112 (2018), 31-35.  doi: 10.1016/j.sysconle.2017.12.004.  Google Scholar

[17]

J. G. Lu and G. R. Chen, Robust stability and stabilization of fractional order interval systems: An LMI approach, IEEE Transactions on Automatic Control, 54 (2009), 1294-1299.  doi: 10.1109/tac.2009.2013056.  Google Scholar

[18]

J. G. Lu and Y. Q. Chen, Robust stability and stabilization of fractional order interval systems with the fractional order $\alpha$ : The $0 <\alpha<1$ case, IEEE Transactions on Automatic Control, 55 (2010), 152-158.  doi: 10.1109/TAC.2009.2033738.  Google Scholar

[19]

H. J. Ma and G. H. Yang, Detection and adaptive accommodation for actuator faults of a class of non$-$linear systems, IET Control Theory & Appl., 6 (2012), 2292-2307.  doi: 10.1049/iet-cta.2011.0265.  Google Scholar

[20]

S. MarirM. Chadli and D. Bouagada, New admissibility conditions for singular linear continuous$-$time fractional$-$order systems, Jouranl of the Franklin Institute, 354 (2017), 752-766.  doi: 10.1016/j.jfranklin.2016.10.022.  Google Scholar

[21]

S. MarirM. Chadli and D. Bouagada, A novel approach of admissibility for singular linear continuous$-$time fractional$-$order systems, International Journal of Control, Automation and Systems, 15 (2017), 959-964.  doi: 10.1007/s12555-016-0003-0.  Google Scholar

[22]

D. Matignon, Stability results for fractional differential equations with applications to control processing , Proc. Computational Engineering in Systems and Applications Multiconferences (IMACS), (1996), 963–868. Google Scholar

[23]

C. PengT. C. Yang and E. G. Tian, Robust fault-tolerant control of networked control systems with stochastic actuator failure, IET Control Theory & Appl., 4 (2012), 3003-3011.  doi: 10.1049/iet-cta.2009.0427.  Google Scholar

[24]

I. Podlubny, Fractional$-$order systems and $PI^\lambda D^\mu-$controllers, IEEE Transactions on Automat. Control, 44 (1999), 208-214.  doi: 10.1109/9.739144.  Google Scholar

[25] I. Podlubny, Fractional Differertial Equations, Academic Press, New York, 1999.  doi: 10.1007/978-3-642-39765-33.  Google Scholar
[26]

H. ShenX. N. Song and Z. Wang, Robust fault-tolerant control of uncertain fractional-order systems against actuator faults, IET Control Theory & Appl., 7 (2013), 1233-1241.  doi: 10.1049/iet-cta.2012.0822.  Google Scholar

[27]

J. Shen and J. D. Cao, Necessary and sufficient conditions for consensus of delayed fractional$-$order systems, Asian J. Control, 14 (2012), 1690-1697.  doi: 10.1002/asjc.492.  Google Scholar

[28]

X. N. Song, Y. Q. Chen and H. Shen, LMI fault tolerant control for interval fractional-order systems with sensor failures , Proc. Fourth IFAC Workshop Fractional Differentiation and its Applications, (2010), Article no. FDA10-126, Badajoz, Spain. Google Scholar

[29]

X. N. Song and H. Shen, Fault tolerant control for interval fractional-order systems with sensor failures, Advances in Mathematical Physics, 2013 (2013), 1-11.  doi: 10.1155/2013/836743.  Google Scholar

[30]

F. Tao and Q. Zhao, Synthesis of active fault$-$tolerant control based on Markovian jump system models, IET Control Theory & Appl., 1 (2007), 1160-1168.  doi: 10.1049/iet-cta:20050492.  Google Scholar

[31]

M. Tavakoli-Kakhki and M. S. Tavazoei, Estimation of the order and parameters of a fractional order model from a noisy step response data, Journal of Dynamic Systems, Measurement Control, 136 (2014), 1-7.  doi: 10.1115/1.4026345.  Google Scholar

[32]

E. Uezato and M. Ikeda, Strict LMI conditions for stability, robust stabilization, and $H_\infty$ control of descriptor systems , IEEE Conference on Decision & Contol. IEEE, (1994), 4092–4097. doi: 10.1109/CDC.1999.828001.  Google Scholar

[33]

Y. H. WeiP. W. TseY. Zhao and Y. Wang, The output feedback control synthesis for a class of singular fractional order systems, ISA Transactions, 69 (2017), 1-9.  doi: 10.1016/j.isatra.2017.04.020.  Google Scholar

[34]

Y. H. WeiJ. C. WangT. Y. Liu and Y. Wang, Sufficient and necessary conditions for stabilizing singular fractional order systems with partially measurable state, Jouranl of the Franklin Institute, 356 (2019), 1975-1990.  doi: 10.1016/j.jfranklin.2019.01.022.  Google Scholar

[35]

Z. G. WuP. ShiH. Y. Su and J. Chu, Reliable $H_\infty$ control for control for discrete$-$time fuzzy systems with infinite$-$distributed delay, IEEE Trans. on Fuzzy Syst., 20 (2012), 22-31.  doi: 10.1109/TFUZZ.2011.2162850.  Google Scholar

[36]

L. H. Xie, Output feedback $H_\infty$ control of systems with parameter uncertainty, International Journal of Control, 63 (1996), 741-750.  doi: 10.1080/00207179608921866.  Google Scholar

[37]

S. Y. Xu and J. Lam, Robust Control and Filtering of Singular Systems, Springer, Berlin, 2006. doi: 10.1080/00207721.2014.998751.  Google Scholar

[38]

G. H. YangJ. L. Wang and Y. C. Soh, Reliable $H_\infty$ controller design for linear systems, Automatica, 37 (2001), 717-725.  doi: 10.1016/S0005-1098(01)00007-3.  Google Scholar

[39]

H. YangV. Cocquempot and B. Jiang, Robust fault tolerant tracking control with application to hybrid nonlinear systems, Control Theory & Appl., 3 (2009), 211-224.  doi: 10.1049/iet-cta:20080015.  Google Scholar

[40]

T. Zhan and S. P. Ma, The controller design for singular fractional-order systems with fractional order $0<\alpha<1$, The ANZIAM Journal, 60 (2018), 230-248.  doi: 10.1017/S1446181118000202.  Google Scholar

[41]

X. F. Zhang and Y. Q. Chen, D$-$stability based LMI criteria of stability and stabilization for fractional order systems , ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2015-46692, (2015), 1–6. Google Scholar

[42]

X. F. Zhang and Y. Q. Chen, Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order $\alpha$: The $0<\alpha<1$ case, ISA Transcations, 82 (2018), 42-50.  doi: 10.1016/j.isatra.2017.03.008.  Google Scholar

show all references

References:
[1]

H. S. Ahn and Y. Q. Chen, Necessary and sufficient stability condition of fractional$-$order interval linear systems, Automatica, 44 (2008), 2985-2988.  doi: 10.1016/j.automatica.2008.07.003.  Google Scholar

[2]

M. Blanke, M. Kinnaert, J. Lunze and M. Staroswiecki, Diagnosisi and Fault-Tolerant Control, Springer, Berlin, Germany, 2006. doi: 10.1007/978-3-540-35653-0.  Google Scholar

[3]

M. BlankeR. Izadi-ZamanabadiS. A. Bogh and C. P. Lunau, Fault-tolerant control systems$-$a holistic view, Contol Engineering Prac., 5 (1997), 693-702.  doi: 10.1016/s0967-0661(97)00051-8.  Google Scholar

[4]

L. L. Fan and Y. D. Song, Neuro$-$adaptive model$-$referance fault$-$tolerant control with application to wind turbines, IET Control Theory & Appl., 6 (2012), 475-486.  doi: 10.1049/iet-cta.2011.0250.  Google Scholar

[5]

C. FargesM. Moze and J. Sabatier, Pseudo-state feedback stabilization of commensurate fractional order systems, Automatica, 46 (2010), 1730-1734.  doi: 10.1016/j.automatica.2010.06.038.  Google Scholar

[6]

C. Farges, J. Sabatier and M. Moze, Robust stability analysis and stabilization of fractional order polytopic systems , Preprints of the 18th IFAC World Congress, (2011), Milano, Italy, 10800-10805. doi: 10.3182/20110828-6-IT-1002.00779.  Google Scholar

[7]

Bin Guo and Yong Chen, Adaptive fault tolerant control for time-varying delay system withactuator fault and mismatched disturbance, ISA Transcation, 89 (2019), 122-130.  doi: 10.1016/j.isatra.2018.12.024.  Google Scholar

[8]

Q. HuB. Xiao and M. I. Friswll, Robust fault$-$tolerant control for spacecraft attitude stabilisation subject to input saturation, IET Control Theory & Appl., 5 (2011), 271-282.  doi: 10.1049/iet-cta.2009.0628.  Google Scholar

[9]

S. D. HuangJ. LamG. H. Yang and S. Y. Zhang, Fault tolerant decentralized $H_\infty$ control for symmetric composite systems, IEEE Trans. Autom. Control, 44 (1999), 2108-2114.  doi: 10.1109/9.802926.  Google Scholar

[10]

R. Isermann, Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer, Berlin, Germany, 2006. doi: 10.1007/3-540-30368-5.  Google Scholar

[11]

L. A. JacynthoM. C. M. Teixeira and E. Assunco, Identification of fractional-order transfer functions using a step excitation, IEEE Trans. Circuits Syst., 62 (2015), 896-900.  doi: 10.1109/tcsii.2015.2436052.  Google Scholar

[12]

Y. JiangQ. L. Hu and G. F. Ma, Adaptive backsteping fault$-$tolerant control for flexible spacecraft with unknown bounded disturbances and actuator failures, ISA Transcations, 49 (2010), 57-69.  doi: 10.1016/j.isatra.2009.08.003.  Google Scholar

[13]

E. Last, Linear matrix inequalities in system and control theory, Proceedings of the IEEE, 86 (1994), 2473-2474.  doi: 10.1109/JPROC.1998.735454.  Google Scholar

[14]

X. J. Li and G. H. Yang, Robust adaptive fault$-$tolerant control for uncertain linear systems with actuator failures, IET Control Theory & Appl., 6 (2012), 1544-1551.  doi: 10.1049/iet-cta.2011.0599.  Google Scholar

[15]

Y. LiY. Q. Chen and I. Podlubny, Stability of fractional order nonlinear dynamic systems, Automatica, 45 (2009), 1965-1969.  doi: 10.1016/j.automatica.2009.04.003.  Google Scholar

[16]

C. LinB. ChenP. Shi and J. P. Yu, Necessary and sufficient conditions of observer$-$based stabilization for a class of fractional$-$order descriptor systems, Systems & Control Letters, 112 (2018), 31-35.  doi: 10.1016/j.sysconle.2017.12.004.  Google Scholar

[17]

J. G. Lu and G. R. Chen, Robust stability and stabilization of fractional order interval systems: An LMI approach, IEEE Transactions on Automatic Control, 54 (2009), 1294-1299.  doi: 10.1109/tac.2009.2013056.  Google Scholar

[18]

J. G. Lu and Y. Q. Chen, Robust stability and stabilization of fractional order interval systems with the fractional order $\alpha$ : The $0 <\alpha<1$ case, IEEE Transactions on Automatic Control, 55 (2010), 152-158.  doi: 10.1109/TAC.2009.2033738.  Google Scholar

[19]

H. J. Ma and G. H. Yang, Detection and adaptive accommodation for actuator faults of a class of non$-$linear systems, IET Control Theory & Appl., 6 (2012), 2292-2307.  doi: 10.1049/iet-cta.2011.0265.  Google Scholar

[20]

S. MarirM. Chadli and D. Bouagada, New admissibility conditions for singular linear continuous$-$time fractional$-$order systems, Jouranl of the Franklin Institute, 354 (2017), 752-766.  doi: 10.1016/j.jfranklin.2016.10.022.  Google Scholar

[21]

S. MarirM. Chadli and D. Bouagada, A novel approach of admissibility for singular linear continuous$-$time fractional$-$order systems, International Journal of Control, Automation and Systems, 15 (2017), 959-964.  doi: 10.1007/s12555-016-0003-0.  Google Scholar

[22]

D. Matignon, Stability results for fractional differential equations with applications to control processing , Proc. Computational Engineering in Systems and Applications Multiconferences (IMACS), (1996), 963–868. Google Scholar

[23]

C. PengT. C. Yang and E. G. Tian, Robust fault-tolerant control of networked control systems with stochastic actuator failure, IET Control Theory & Appl., 4 (2012), 3003-3011.  doi: 10.1049/iet-cta.2009.0427.  Google Scholar

[24]

I. Podlubny, Fractional$-$order systems and $PI^\lambda D^\mu-$controllers, IEEE Transactions on Automat. Control, 44 (1999), 208-214.  doi: 10.1109/9.739144.  Google Scholar

[25] I. Podlubny, Fractional Differertial Equations, Academic Press, New York, 1999.  doi: 10.1007/978-3-642-39765-33.  Google Scholar
[26]

H. ShenX. N. Song and Z. Wang, Robust fault-tolerant control of uncertain fractional-order systems against actuator faults, IET Control Theory & Appl., 7 (2013), 1233-1241.  doi: 10.1049/iet-cta.2012.0822.  Google Scholar

[27]

J. Shen and J. D. Cao, Necessary and sufficient conditions for consensus of delayed fractional$-$order systems, Asian J. Control, 14 (2012), 1690-1697.  doi: 10.1002/asjc.492.  Google Scholar

[28]

X. N. Song, Y. Q. Chen and H. Shen, LMI fault tolerant control for interval fractional-order systems with sensor failures , Proc. Fourth IFAC Workshop Fractional Differentiation and its Applications, (2010), Article no. FDA10-126, Badajoz, Spain. Google Scholar

[29]

X. N. Song and H. Shen, Fault tolerant control for interval fractional-order systems with sensor failures, Advances in Mathematical Physics, 2013 (2013), 1-11.  doi: 10.1155/2013/836743.  Google Scholar

[30]

F. Tao and Q. Zhao, Synthesis of active fault$-$tolerant control based on Markovian jump system models, IET Control Theory & Appl., 1 (2007), 1160-1168.  doi: 10.1049/iet-cta:20050492.  Google Scholar

[31]

M. Tavakoli-Kakhki and M. S. Tavazoei, Estimation of the order and parameters of a fractional order model from a noisy step response data, Journal of Dynamic Systems, Measurement Control, 136 (2014), 1-7.  doi: 10.1115/1.4026345.  Google Scholar

[32]

E. Uezato and M. Ikeda, Strict LMI conditions for stability, robust stabilization, and $H_\infty$ control of descriptor systems , IEEE Conference on Decision & Contol. IEEE, (1994), 4092–4097. doi: 10.1109/CDC.1999.828001.  Google Scholar

[33]

Y. H. WeiP. W. TseY. Zhao and Y. Wang, The output feedback control synthesis for a class of singular fractional order systems, ISA Transactions, 69 (2017), 1-9.  doi: 10.1016/j.isatra.2017.04.020.  Google Scholar

[34]

Y. H. WeiJ. C. WangT. Y. Liu and Y. Wang, Sufficient and necessary conditions for stabilizing singular fractional order systems with partially measurable state, Jouranl of the Franklin Institute, 356 (2019), 1975-1990.  doi: 10.1016/j.jfranklin.2019.01.022.  Google Scholar

[35]

Z. G. WuP. ShiH. Y. Su and J. Chu, Reliable $H_\infty$ control for control for discrete$-$time fuzzy systems with infinite$-$distributed delay, IEEE Trans. on Fuzzy Syst., 20 (2012), 22-31.  doi: 10.1109/TFUZZ.2011.2162850.  Google Scholar

[36]

L. H. Xie, Output feedback $H_\infty$ control of systems with parameter uncertainty, International Journal of Control, 63 (1996), 741-750.  doi: 10.1080/00207179608921866.  Google Scholar

[37]

S. Y. Xu and J. Lam, Robust Control and Filtering of Singular Systems, Springer, Berlin, 2006. doi: 10.1080/00207721.2014.998751.  Google Scholar

[38]

G. H. YangJ. L. Wang and Y. C. Soh, Reliable $H_\infty$ controller design for linear systems, Automatica, 37 (2001), 717-725.  doi: 10.1016/S0005-1098(01)00007-3.  Google Scholar

[39]

H. YangV. Cocquempot and B. Jiang, Robust fault tolerant tracking control with application to hybrid nonlinear systems, Control Theory & Appl., 3 (2009), 211-224.  doi: 10.1049/iet-cta:20080015.  Google Scholar

[40]

T. Zhan and S. P. Ma, The controller design for singular fractional-order systems with fractional order $0<\alpha<1$, The ANZIAM Journal, 60 (2018), 230-248.  doi: 10.1017/S1446181118000202.  Google Scholar

[41]

X. F. Zhang and Y. Q. Chen, D$-$stability based LMI criteria of stability and stabilization for fractional order systems , ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2015-46692, (2015), 1–6. Google Scholar

[42]

X. F. Zhang and Y. Q. Chen, Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order $\alpha$: The $0<\alpha<1$ case, ISA Transcations, 82 (2018), 42-50.  doi: 10.1016/j.isatra.2017.03.008.  Google Scholar

Figure 1.  State responses of the closed-loop system in Example 1 with $ u(t) = 0. $
Figure 2.  Observation errors of the selected system in Example 1 with $ u(t) = Kx(t). $
Figure 3.  State responses of the closed-loop system in Example 1 with $ u(t) = Kx(t). $
[1]

John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021004

[2]

Daoyuan Fang, Ting Zhang. Compressible Navier-Stokes equations with vacuum state in one dimension. Communications on Pure & Applied Analysis, 2004, 3 (4) : 675-694. doi: 10.3934/cpaa.2004.3.675

[3]

Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311

[4]

Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1717-1746. doi: 10.3934/dcdss.2020451

[5]

W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349

[6]

Jan Prüss, Laurent Pujo-Menjouet, G.F. Webb, Rico Zacher. Analysis of a model for the dynamics of prions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 225-235. doi: 10.3934/dcdsb.2006.6.225

[7]

Sohana Jahan. Discriminant analysis of regularized multidimensional scaling. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 255-267. doi: 10.3934/naco.2020024

[8]

Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327

[9]

Vieri Benci, Sunra Mosconi, Marco Squassina. Preface: Applications of mathematical analysis to problems in theoretical physics. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : i-i. doi: 10.3934/dcdss.2020446

[10]

Martial Agueh, Reinhard Illner, Ashlin Richardson. Analysis and simulations of a refined flocking and swarming model of Cucker-Smale type. Kinetic & Related Models, 2011, 4 (1) : 1-16. doi: 10.3934/krm.2011.4.1

[11]

Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367

[12]

Seung-Yeal Ha, Shi Jin. Local sensitivity analysis for the Cucker-Smale model with random inputs. Kinetic & Related Models, 2018, 11 (4) : 859-889. doi: 10.3934/krm.2018034

[13]

Israa Mohammed Khudher, Yahya Ismail Ibrahim, Suhaib Abduljabbar Altamir. Individual biometrics pattern based artificial image analysis techniques. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2020056

[14]

Dan Wei, Shangjiang Guo. Qualitative analysis of a Lotka-Volterra competition-diffusion-advection system. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2599-2623. doi: 10.3934/dcdsb.2020197

[15]

Hailing Xuan, Xiaoliang Cheng. Numerical analysis and simulation of an adhesive contact problem with damage and long memory. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2781-2804. doi: 10.3934/dcdsb.2020205

[16]

Jiangxing Wang. Convergence analysis of an accurate and efficient method for nonlinear Maxwell's equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2429-2440. doi: 10.3934/dcdsb.2020185

[17]

Hailing Xuan, Xiaoliang Cheng. Numerical analysis of a thermal frictional contact problem with long memory. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021031

[18]

Carlos Fresneda-Portillo, Sergey E. Mikhailov. Analysis of Boundary-Domain Integral Equations to the mixed BVP for a compressible stokes system with variable viscosity. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3059-3088. doi: 10.3934/cpaa.2019137

[19]

Xiaoyi Zhou, Tong Ye, Tony T. Lee. Designing and analysis of a Wi-Fi data offloading strategy catering for the preference of mobile users. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021038

 Impact Factor: 

Metrics

  • PDF downloads (250)
  • HTML views (524)
  • Cited by (0)

Other articles
by authors

[Back to Top]