-
Previous Article
Nonlinear conjugate gradient methods with sufficient descent properties for unconstrained optimization
- JIMO Home
- This Issue
-
Next Article
A log-exponential regularization method for a mathematical program with general vertical complementarity constraints
On the robust control design for a class of nonlinearly affine control systems: The attractive ellipsoid approach
1. | Department of Control and Automation, CINVESTAV, Av, Instituto Politecnico Nacional 2508, Mexico D.F., Mexico, Mexico, Mexico |
References:
[1] |
V. Azhmyakov, Stability of differential inclusions: A computational approach,, Mathematical Problems in Engineering, 2006 (2006), 1.
doi: 10.1155/MPE/2006/17837. |
[2] |
V. Azhmyakov, V. G. Boltyanski and A. Poznyak, Optimal control of impulsive hybrid systems,, Nonlinear Analysis: Hybrid Systems, 2 (2008), 1089.
doi: 10.1016/j.nahs.2008.09.003. |
[3] |
V. Azhmyakov, An approach to controlled mechanical systems based on the multiobjective optimization technique,, Journal of Industrial and Management Optimization, 4 (2008), 697.
doi: 10.3934/jimo.2008.4.697. |
[4] |
V. Azhmyakov, A gradient-type algorithm for a class of optimal control processes governed by hybrid dynamical systems,, IMA Journal of Mathematical Control and Information, 28 (2011), 291.
doi: 10.1093/imamci/dnr010. |
[5] |
V. Azhmyakov, On the geometric aspects of the invariant ellipsoid method: Application to the robust control design,, in, (2011), 1353.
doi: 10.1109/CDC.2011.6161180. |
[6] |
V. Azhmyakov, M. V. Basin and J. Raisch, Proximal point based approach to optimal control of affine switched systems,, Discrete Event Dynamic Systems, 22 (2012), 61.
doi: 10.1007/s10626-011-0109-8. |
[7] |
A. E. Barabanov and O. N. Granichin, Optimal controller for linear plants with bounded noise,, Automation and Remote Control, 45 (1984), 39.
|
[8] |
M. Basin and D. Calderon-Alvarez, Optimal filtering over linear observations with unknown parameters,, Journal of The Franklin Institute, 347 (2010), 988.
doi: 10.1016/j.jfranklin.2010.01.006. |
[9] |
M. Basin, J. Rodriguez-Gonzalez and L. Fridman, Optimal and robust control for linear state-delay systems,, Journal of The Franklin Institute, 344 (2007), 830.
doi: 10.1016/j.jfranklin.2006.10.002. |
[10] |
F. Blanchini and S. Miani, "Set-Theoretic Methods in Control,", Birkhäuser, (2008).
|
[11] |
S. Boyd, E. Ghaoui, E. Feron and V. Balakrishnan, "Linear Matrix Inequalities in System and Control Theory,", SIAM, (1994).
doi: 10.1137/1.9781611970777. |
[12] |
P. Chen, H. Qin and J. Huang, Local stabilization of a class of nonlinear systems by dynamic output feedback,, Automatica, 37 (2001), 969.
doi: 10.1016/S0005-1098(01)00047-4. |
[13] |
D. F. Coutinho, A. Trofino and K. A. Barbosa, Robust linear dynamic output feedback controllers for a class of nonlinear systems,, in, (2003), 374. Google Scholar |
[14] |
M. A. Dahleh, J. B. Pearson and J. Boyd, Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization,, IEEE Transactions on Automatic Control, 33 (1988), 722.
doi: 10.1109/9.1288. |
[15] |
G. J. Duncan and F. C. Schweppe, Control of linear dynamic systems with set constrained disturbances,, IEEE Transactions on Automatic Control, AC-16 (1971), 411.
|
[16] |
E. Fridman and Y. Orlov, On stability of linear parabolic distributed parameter systems with time-varying delays,, in, (2007), 1597.
doi: 10.1109/CDC.2007.4434196. |
[17] |
E. Fridman, A refined input delay approach to sampled-data control,, Automatica, 46 (2010), 421.
doi: 10.1016/j.automatica.2009.11.017. |
[18] |
L. El Ghaoui and S. Niculescu, "Advances in Linear Matrix Inequalities in Control,", SIAM, (2000).
doi: 10.1137/1.9780898719833. |
[19] |
W. Haddad and V. Chellaboina, "Nonlinear Dynamical Systems and Control,", Princeton University Press, (2008).
|
[20] |
A. Isidori, A. R. Teel and L. Praly, A note on the problem of semiglobal practical stabilization of uncertain nonlinear systems via dynamic output feedback,, System and Control Letters, 39 (2000), 165.
doi: 10.1016/S0167-6911(99)00083-3. |
[21] |
I. Karafyllis and Z.-P. Jiang, "Stability and Stabilization of Nonlinear Systems,", Springer, (2011).
doi: 10.1007/978-0-85729-513-2. |
[22] |
C. T. Kelley, L. Qi, X. Tong and H. Yin, Finding a stable solution of a system of nonlinear equations arising from dynamic systems,, Journal of Industrial and Management Optimization, 7 (2011), 497.
doi: 10.3934/jimo.2011.7.497. |
[23] |
H. K. Khalil, "Nonlinear Systems,", Prentice Hall, (2002).
doi: 10.1007/s11071-008-9349-z. |
[24] |
A. B. Kurzhanski and P. Varaiya, Ellipsoidal techniques for reachability under state constraints,, SIAM Journal on Control and Optimization, 45 (2006), 1369.
doi: 10.1137/S0363012903437605. |
[25] |
A. B. Kurzhanski and V. M. Veliov, "Modeling Techniques and Uncertain Systems,", Birkhäuser, (1994).
|
[26] |
W. Lin and C. Qian, Semi-global robust stabilization of MIMO nonlinear systems by partial state and dynamic output feedback,, Automatica, 37 (2001), 1093.
doi: 10.1016/S0005-1098(01)00056-5. |
[27] |
M. Mera, A. Poznyak and V. Azhmyakov, On the robust control design for a class of continuous-time dynamical systems with a sample-data output,, in, (2011), 5819. Google Scholar |
[28] |
A. N. Michel, L. Hou and D. Liu, "Stability of Dynamical Systems,", Birkhäuser, (2007).
|
[29] |
P. Naghshtabrizi, J. P. Hespanha, and A. R. Teel, Exponential stability of impulsive systems with application to uncertain sampled-data systems,, Systems and Control Letters, 57 (2008), 378.
doi: 10.1016/j.sysconle.2007.10.009. |
[30] |
E. Polak, "Optimization,", Springer, (1997).
doi: 10.1007/978-1-4612-0663-7. |
[31] |
B. T. Polyak, S. A. Nazin, C. Durieu and E. Walter, Ellipsoidal parameter or state estimation under model uncertainty,, Automatica, 40 (2004), 1171.
doi: 10.1016/j.automatica.2004.02.014. |
[32] |
B. T. Polyak and M. V. Topunov, Suppression of bounded exogeneous disturbances: Output control,, Automation and Remote Control, 69 (2008), 801.
doi: 10.1134/S000511790805007X. |
[33] |
A. Polyakov and A. Poznyak, Lyapunov function design for finite-time convergence analysis: Twisting controller for second-order sliding mode realization,, Automatica, 45 (2009), 444.
doi: 10.1016/j.automatica.2008.07.013. |
[34] |
A. Poznyak, "Advanced Mathematical Tools for Automatic Control Engineers: Deterministic Techniques,", Elsevier, (2008).
|
[35] |
A. Poznyak, V. Azhmyakov and M. Mera, Practical output feedback stabilisation for a class of continuous-time dynamic systems under sample-data outputs,, International Journal of Control, 84 (2011), 1408.
doi: 10.1080/00207179.2011.603097. |
[36] |
E. Sontag, "Mathematical Control Theory,", Springer, (1998).
|
[37] |
E. D. Sontag, Further facts about input to state stabilization,, IEEE Transactions on Automatic Control, AC-35 (1990), 473.
doi: 10.1109/9.52307. |
[38] |
A. R. Teel, D. Nesic and P. V. Kokotovic, A note on input-to-state stability of sampled-data nonlinear systems,, in, (1998), 2473.
doi: 10.1109/CDC.1998.757793. |
[39] |
A. R. Teel, L. Moreau and D. Nesic, A note on the robustness of input-to-state stability,, in, (2001), 875. Google Scholar |
[40] |
E. D. Yakubovich, Solution of the optimal control problem for the linear discrete systems,, Automation and Remote Control, 36 (1976), 1447.
|
[41] |
V. I. Zubov, "Mathematical Methods for the Study of Automatic Control Systems,", Pergamon Press, (1962).
|
show all references
References:
[1] |
V. Azhmyakov, Stability of differential inclusions: A computational approach,, Mathematical Problems in Engineering, 2006 (2006), 1.
doi: 10.1155/MPE/2006/17837. |
[2] |
V. Azhmyakov, V. G. Boltyanski and A. Poznyak, Optimal control of impulsive hybrid systems,, Nonlinear Analysis: Hybrid Systems, 2 (2008), 1089.
doi: 10.1016/j.nahs.2008.09.003. |
[3] |
V. Azhmyakov, An approach to controlled mechanical systems based on the multiobjective optimization technique,, Journal of Industrial and Management Optimization, 4 (2008), 697.
doi: 10.3934/jimo.2008.4.697. |
[4] |
V. Azhmyakov, A gradient-type algorithm for a class of optimal control processes governed by hybrid dynamical systems,, IMA Journal of Mathematical Control and Information, 28 (2011), 291.
doi: 10.1093/imamci/dnr010. |
[5] |
V. Azhmyakov, On the geometric aspects of the invariant ellipsoid method: Application to the robust control design,, in, (2011), 1353.
doi: 10.1109/CDC.2011.6161180. |
[6] |
V. Azhmyakov, M. V. Basin and J. Raisch, Proximal point based approach to optimal control of affine switched systems,, Discrete Event Dynamic Systems, 22 (2012), 61.
doi: 10.1007/s10626-011-0109-8. |
[7] |
A. E. Barabanov and O. N. Granichin, Optimal controller for linear plants with bounded noise,, Automation and Remote Control, 45 (1984), 39.
|
[8] |
M. Basin and D. Calderon-Alvarez, Optimal filtering over linear observations with unknown parameters,, Journal of The Franklin Institute, 347 (2010), 988.
doi: 10.1016/j.jfranklin.2010.01.006. |
[9] |
M. Basin, J. Rodriguez-Gonzalez and L. Fridman, Optimal and robust control for linear state-delay systems,, Journal of The Franklin Institute, 344 (2007), 830.
doi: 10.1016/j.jfranklin.2006.10.002. |
[10] |
F. Blanchini and S. Miani, "Set-Theoretic Methods in Control,", Birkhäuser, (2008).
|
[11] |
S. Boyd, E. Ghaoui, E. Feron and V. Balakrishnan, "Linear Matrix Inequalities in System and Control Theory,", SIAM, (1994).
doi: 10.1137/1.9781611970777. |
[12] |
P. Chen, H. Qin and J. Huang, Local stabilization of a class of nonlinear systems by dynamic output feedback,, Automatica, 37 (2001), 969.
doi: 10.1016/S0005-1098(01)00047-4. |
[13] |
D. F. Coutinho, A. Trofino and K. A. Barbosa, Robust linear dynamic output feedback controllers for a class of nonlinear systems,, in, (2003), 374. Google Scholar |
[14] |
M. A. Dahleh, J. B. Pearson and J. Boyd, Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization,, IEEE Transactions on Automatic Control, 33 (1988), 722.
doi: 10.1109/9.1288. |
[15] |
G. J. Duncan and F. C. Schweppe, Control of linear dynamic systems with set constrained disturbances,, IEEE Transactions on Automatic Control, AC-16 (1971), 411.
|
[16] |
E. Fridman and Y. Orlov, On stability of linear parabolic distributed parameter systems with time-varying delays,, in, (2007), 1597.
doi: 10.1109/CDC.2007.4434196. |
[17] |
E. Fridman, A refined input delay approach to sampled-data control,, Automatica, 46 (2010), 421.
doi: 10.1016/j.automatica.2009.11.017. |
[18] |
L. El Ghaoui and S. Niculescu, "Advances in Linear Matrix Inequalities in Control,", SIAM, (2000).
doi: 10.1137/1.9780898719833. |
[19] |
W. Haddad and V. Chellaboina, "Nonlinear Dynamical Systems and Control,", Princeton University Press, (2008).
|
[20] |
A. Isidori, A. R. Teel and L. Praly, A note on the problem of semiglobal practical stabilization of uncertain nonlinear systems via dynamic output feedback,, System and Control Letters, 39 (2000), 165.
doi: 10.1016/S0167-6911(99)00083-3. |
[21] |
I. Karafyllis and Z.-P. Jiang, "Stability and Stabilization of Nonlinear Systems,", Springer, (2011).
doi: 10.1007/978-0-85729-513-2. |
[22] |
C. T. Kelley, L. Qi, X. Tong and H. Yin, Finding a stable solution of a system of nonlinear equations arising from dynamic systems,, Journal of Industrial and Management Optimization, 7 (2011), 497.
doi: 10.3934/jimo.2011.7.497. |
[23] |
H. K. Khalil, "Nonlinear Systems,", Prentice Hall, (2002).
doi: 10.1007/s11071-008-9349-z. |
[24] |
A. B. Kurzhanski and P. Varaiya, Ellipsoidal techniques for reachability under state constraints,, SIAM Journal on Control and Optimization, 45 (2006), 1369.
doi: 10.1137/S0363012903437605. |
[25] |
A. B. Kurzhanski and V. M. Veliov, "Modeling Techniques and Uncertain Systems,", Birkhäuser, (1994).
|
[26] |
W. Lin and C. Qian, Semi-global robust stabilization of MIMO nonlinear systems by partial state and dynamic output feedback,, Automatica, 37 (2001), 1093.
doi: 10.1016/S0005-1098(01)00056-5. |
[27] |
M. Mera, A. Poznyak and V. Azhmyakov, On the robust control design for a class of continuous-time dynamical systems with a sample-data output,, in, (2011), 5819. Google Scholar |
[28] |
A. N. Michel, L. Hou and D. Liu, "Stability of Dynamical Systems,", Birkhäuser, (2007).
|
[29] |
P. Naghshtabrizi, J. P. Hespanha, and A. R. Teel, Exponential stability of impulsive systems with application to uncertain sampled-data systems,, Systems and Control Letters, 57 (2008), 378.
doi: 10.1016/j.sysconle.2007.10.009. |
[30] |
E. Polak, "Optimization,", Springer, (1997).
doi: 10.1007/978-1-4612-0663-7. |
[31] |
B. T. Polyak, S. A. Nazin, C. Durieu and E. Walter, Ellipsoidal parameter or state estimation under model uncertainty,, Automatica, 40 (2004), 1171.
doi: 10.1016/j.automatica.2004.02.014. |
[32] |
B. T. Polyak and M. V. Topunov, Suppression of bounded exogeneous disturbances: Output control,, Automation and Remote Control, 69 (2008), 801.
doi: 10.1134/S000511790805007X. |
[33] |
A. Polyakov and A. Poznyak, Lyapunov function design for finite-time convergence analysis: Twisting controller for second-order sliding mode realization,, Automatica, 45 (2009), 444.
doi: 10.1016/j.automatica.2008.07.013. |
[34] |
A. Poznyak, "Advanced Mathematical Tools for Automatic Control Engineers: Deterministic Techniques,", Elsevier, (2008).
|
[35] |
A. Poznyak, V. Azhmyakov and M. Mera, Practical output feedback stabilisation for a class of continuous-time dynamic systems under sample-data outputs,, International Journal of Control, 84 (2011), 1408.
doi: 10.1080/00207179.2011.603097. |
[36] |
E. Sontag, "Mathematical Control Theory,", Springer, (1998).
|
[37] |
E. D. Sontag, Further facts about input to state stabilization,, IEEE Transactions on Automatic Control, AC-35 (1990), 473.
doi: 10.1109/9.52307. |
[38] |
A. R. Teel, D. Nesic and P. V. Kokotovic, A note on input-to-state stability of sampled-data nonlinear systems,, in, (1998), 2473.
doi: 10.1109/CDC.1998.757793. |
[39] |
A. R. Teel, L. Moreau and D. Nesic, A note on the robustness of input-to-state stability,, in, (2001), 875. Google Scholar |
[40] |
E. D. Yakubovich, Solution of the optimal control problem for the linear discrete systems,, Automation and Remote Control, 36 (1976), 1447.
|
[41] |
V. I. Zubov, "Mathematical Methods for the Study of Automatic Control Systems,", Pergamon Press, (1962).
|
[1] |
Abdulrazzaq T. Abed, Azzam S. Y. Aladool. Applying particle swarm optimization based on Padé approximant to solve ordinary differential equation. Numerical Algebra, Control & Optimization, 2021 doi: 10.3934/naco.2021008 |
[2] |
Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83 |
[3] |
Marian Gidea, Rafael de la Llave, Tere M. Seara. A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold. Discrete & Continuous Dynamical Systems - A, 2020, 40 (12) : 6795-6813. doi: 10.3934/dcds.2020166 |
[4] |
Mohsen Abdolhosseinzadeh, Mir Mohammad Alipour. Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 321-332. doi: 10.3934/naco.2020028 |
[5] |
Peter Benner, Jens Saak, M. Monir Uddin. Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 1-20. doi: 10.3934/naco.2016.6.1 |
[6] |
Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021 |
[7] |
Y. Latushkin, B. Layton. The optimal gap condition for invariant manifolds. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 233-268. doi: 10.3934/dcds.1999.5.233 |
[8] |
Gelasio Salaza, Edgardo Ugalde, Jesús Urías. Master--slave synchronization of affine cellular automaton pairs. Discrete & Continuous Dynamical Systems - A, 2005, 13 (2) : 491-502. doi: 10.3934/dcds.2005.13.491 |
[9] |
Christopher Bose, Rua Murray. Minimum 'energy' approximations of invariant measures for nonsingular transformations. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 597-615. doi: 10.3934/dcds.2006.14.597 |
[10] |
Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonal-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 109-123. doi: 10.3934/dcdss.2016.9.109 |
[11] |
Xianchao Xiu, Ying Yang, Wanquan Liu, Lingchen Kong, Meijuan Shang. An improved total variation regularized RPCA for moving object detection with dynamic background. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1685-1698. doi: 10.3934/jimo.2019024 |
[12] |
Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim, Doo Seok Lee. Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021035 |
[13] |
Eduardo Casas, Christian Clason, Arnd Rösch. Preface special issue on system modeling and optimization. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021008 |
[14] |
Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 |
[15] |
Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023 |
[16] |
Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399 |
[17] |
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 |
[18] |
Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 209-220. doi: 10.3934/naco.2020022 |
[19] |
Wei Wang, Degen Huang, Haitao Yu. Word sense disambiguation based on stretchable matching of the semantic template. Mathematical Foundations of Computing, 2021, 4 (1) : 1-13. doi: 10.3934/mfc.2020022 |
[20] |
Wenmin Gong, Guangcun Lu. On coupled Dirac systems. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4329-4346. doi: 10.3934/dcds.2017185 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]