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Stability of a class of risk-averse multistage stochastic programs and their distributionally robust counterparts
September
2021, 17(5): 2441-2450.
doi: 10.3934/jimo.2020076
Probabilistic robust anti-disturbance control of uncertain systems
| 1. | Key laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, China |
| 2. | School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, Western Australia, 6102, Australia |
| 3. | School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, GPO Box U1987, Perth, WA6845, Australia |
| 4. | Shenzhen Audencia Business School, WeBank Institute of Fintech, Guangdong Laboratory of Artificial Intelligence and Digital Economics (SZ), Shenzhen University, Shenzhen, 518060, China |
We propose a novel method for constructing probabilistic robust disturbance rejection control for uncertain systems in which a scenario optimization method is used to deal with the nonlinear and unbounded uncertainties. For anti-disturbance, a reduced order disturbance observer is considered and a state-feedback controller is designed. Sufficient conditions are presented to ensure that the resulting closed-loop system is stable and a prescribed $ H_{\infty} $ performance index is satisfied. A numerical example is presented to illustrate the effectiveness of the techniques proposed and analyzed.
Keywords:
Uncertain systems,
discrete time systems,
scenario optimization method,
probabilistic control,
disturbance rejection.
Mathematics Subject Classification:
Primary: 93C55, 93D09; Secondary: 93B05.
Citation:
Peng Cheng, Feng Pan, Yanyan Yin, Song Wang. Probabilistic robust anti-disturbance control of uncertain systems. Journal of Industrial and Management Optimization,
2021, 17
(5)
: 2441-2450.
doi: 10.3934/jimo.2020076
![]()
References:
| [1] |
J. Ackermann, Robust Control: The Parameter Space Approach, Springer-Verlag, London, 2002.
doi: 10.1007/978-1-4471-0207-6. |
| [2] |
T. Alamo, R. Tempo, A. Luque and D. R. Ramirez,
Randomized methods for design of uncertain systems: Sample complexity and sequential algorithms, Automatica J. IFAC, 52 (2015), 160-172.
doi: 10.1016/j.automatica.2014.11.004. |
| [3] |
B. R. Barmish, New Tools for Robustness of Linear Systems, MacMillan, New York, 1994. |
| [4] |
S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, 15, SIAM, Philadelphia, PA, 1994.
doi: 10.1137/1.9781611970777. |
| [5] |
M. C. Campi, S. Garatti and and M. Prandini,
The scenario approach for systems and control design, Ann. Rev. Control, 33 (2009), 149-157.
doi: 10.1016/j.arcontrol.2009.07.001. |
| [6] |
G. C. Calafiore and M. C. Campi,
The scenario approach to robust control design,, IEEE Trans. Automat. Control, 51 (2006), 742-753.
doi: 10.1109/TAC.2006.875041. |
| [7] |
G. Grimm, M. J. Messina, S. E. Tuna and A. R. Teel,
Nominally robust model predictive control with state constraints, IEEE Trans. Automat. Control, 52 (2007), 1856-1870.
doi: 10.1109/TAC.2007.906187. |
| [8] |
P. Gahinet,
Explicit controller formulas for LMI-based $H_{\infty}$ synthesis, Automatica J. IFAC, 32 (1996), 1007-1014.
doi: 10.1016/0005-1098(96)00033-7. |
| [9] |
L. Guo and W. Chen,
Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach, Internat. J. Robust Nonlinear Control, 15 (2005), 109-125.
doi: 10.1002/rnc.978. |
| [10] |
X. Ji, M. Ren and H. Su,
Comment on "Further enhancement on robust ${H_\infty }$ control design for discrete-time singular systems", IEEE Trans. Automat. Control, 60 (2015), 3119-3120.
doi: 10.1109/TAC.2015.2409951. |
| [11] |
L. Jin, Y. Yin, K. L. Teo and F. Liu, Event-triggered mixed $H\infty$ and passive control for Markov jump systems with bounded inputs, J. Ind. Manag. Optim..
doi: 10.3934/jimo.2020024. |
| [12] |
Y. Liu, Y. Yin, K. L. Teo, S. Wang and F. Liu,
Probabilistic control of Markov jump systems by scenario optimization approach, J. Ind. Manag. Optim., 15 (2019), 1447-1453.
doi: 10.3934/jimo.2018103. |
| [13] |
H. Melkote, F. Khorrami, S. Jain and M. S. Mattice,
Robust adaptive control of variable reluctance stepper motors, IEEE Trans. Control Systems Tech., 7 (1999), 212-221.
doi: 10.1109/87.748147. |
| [14] |
A. Nemirovski and A. Shapiro,
Convex approximations of chance constrained programs, SIAM J. Optim., 17 (2006), 969-996.
doi: 10.1137/050622328. |
| [15] |
R. E. Skelton, T. Iwasaki and K. Grigoriadis, A Unified Algebraic Approach to Linear Control Design, The Taylor & Francis Systems and Control Book Series, Taylor & Francis Group, London, 1998. |
| [16] |
H. Sun and L. Guo,
Neural network-based DOBC for a class of nonlinear systems with unmatched disturbances, IEEE Trans. Neural Networks Learning Systems, 28 (2017), 482-489.
doi: 10.1109/TNNLS.2015.2511450. |
| [17] |
E. Tian, Z. Wang, L. Zou and D. Yue,
Chance-constrained $H_{\infty}$ control for a class of time-varying systems with stochastic nonlinearities: The finite-horizon case, Automatica J. IFAC, 107 (2019), 296-305.
doi: 10.1016/j.automatica.2019.05.039. |
| [18] |
E. Tian, Z. Wang, L. Zou and D. Yue,
Probabilistic constrained filtering for a class of nonlinear systems with improved static event-triggered communication, Internat. J. Robust Nonlinear Control, 29 (2019), 1484-1498.
doi: 10.1002/rnc.4447. |
| [19] |
B. Yao, M. Al-Majed and M. Tomizuka,
High-performance robust motion control of machine tools: An adaptive robust control approach and comparative experiments, IEEE/ASME Trans. Mechatronics, 2 (1997), 63-76.
doi: 10.1109/ACC.1997.611956. |
| [20] |
Y. Yin, P. Shi, F. Liu, K. L. Teo and C. C. Lim,
Robust filtering for nonlinear nonhomogeneous Markov jump systems by fuzzy approximation approach, IEEE Trans on Cybernetics, 45 (2015), 1706-1716.
doi: 10.1109/TCYB.2014.2358680. |
| [21] |
Y. Yin, Z. Lin, Y. Liu and K. L. Teo,
Event-triggered constrained control of positive systems with input saturation, Internat. J. Robust Nonlinear Control, 28 (2018), 3532-3542.
doi: 10.1002/rnc.4097. |
| [22] |
Y. Yin and Z. Lin,
Constrained control of uncertain nonhomogeneous Markovian jump systems, Internat. J. Robust Nonlinear Control, 27 (2017), 3937-3950.
doi: 10.1002/rnc.3774. |
| [23] |
J. Yang, B. Wu, S. Li and X. Yu,
Design and qualitative robustness analysis of an DOBC approach for DC-DC buck converters with unmatched circuit parameter perturbations, IEEE Trans. Circuits Systems I: Regular Papers, 63 (2016), 551-560.
doi: 10.1109/TCSI.2016.2529238. |
show all references
References:
| [1] |
J. Ackermann, Robust Control: The Parameter Space Approach, Springer-Verlag, London, 2002.
doi: 10.1007/978-1-4471-0207-6. |
| [2] |
T. Alamo, R. Tempo, A. Luque and D. R. Ramirez,
Randomized methods for design of uncertain systems: Sample complexity and sequential algorithms, Automatica J. IFAC, 52 (2015), 160-172.
doi: 10.1016/j.automatica.2014.11.004. |
| [3] |
B. R. Barmish, New Tools for Robustness of Linear Systems, MacMillan, New York, 1994. |
| [4] |
S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, 15, SIAM, Philadelphia, PA, 1994.
doi: 10.1137/1.9781611970777. |
| [5] |
M. C. Campi, S. Garatti and and M. Prandini,
The scenario approach for systems and control design, Ann. Rev. Control, 33 (2009), 149-157.
doi: 10.1016/j.arcontrol.2009.07.001. |
| [6] |
G. C. Calafiore and M. C. Campi,
The scenario approach to robust control design,, IEEE Trans. Automat. Control, 51 (2006), 742-753.
doi: 10.1109/TAC.2006.875041. |
| [7] |
G. Grimm, M. J. Messina, S. E. Tuna and A. R. Teel,
Nominally robust model predictive control with state constraints, IEEE Trans. Automat. Control, 52 (2007), 1856-1870.
doi: 10.1109/TAC.2007.906187. |
| [8] |
P. Gahinet,
Explicit controller formulas for LMI-based $H_{\infty}$ synthesis, Automatica J. IFAC, 32 (1996), 1007-1014.
doi: 10.1016/0005-1098(96)00033-7. |
| [9] |
L. Guo and W. Chen,
Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach, Internat. J. Robust Nonlinear Control, 15 (2005), 109-125.
doi: 10.1002/rnc.978. |
| [10] |
X. Ji, M. Ren and H. Su,
Comment on "Further enhancement on robust ${H_\infty }$ control design for discrete-time singular systems", IEEE Trans. Automat. Control, 60 (2015), 3119-3120.
doi: 10.1109/TAC.2015.2409951. |
| [11] |
L. Jin, Y. Yin, K. L. Teo and F. Liu, Event-triggered mixed $H\infty$ and passive control for Markov jump systems with bounded inputs, J. Ind. Manag. Optim..
doi: 10.3934/jimo.2020024. |
| [12] |
Y. Liu, Y. Yin, K. L. Teo, S. Wang and F. Liu,
Probabilistic control of Markov jump systems by scenario optimization approach, J. Ind. Manag. Optim., 15 (2019), 1447-1453.
doi: 10.3934/jimo.2018103. |
| [13] |
H. Melkote, F. Khorrami, S. Jain and M. S. Mattice,
Robust adaptive control of variable reluctance stepper motors, IEEE Trans. Control Systems Tech., 7 (1999), 212-221.
doi: 10.1109/87.748147. |
| [14] |
A. Nemirovski and A. Shapiro,
Convex approximations of chance constrained programs, SIAM J. Optim., 17 (2006), 969-996.
doi: 10.1137/050622328. |
| [15] |
R. E. Skelton, T. Iwasaki and K. Grigoriadis, A Unified Algebraic Approach to Linear Control Design, The Taylor & Francis Systems and Control Book Series, Taylor & Francis Group, London, 1998. |
| [16] |
H. Sun and L. Guo,
Neural network-based DOBC for a class of nonlinear systems with unmatched disturbances, IEEE Trans. Neural Networks Learning Systems, 28 (2017), 482-489.
doi: 10.1109/TNNLS.2015.2511450. |
| [17] |
E. Tian, Z. Wang, L. Zou and D. Yue,
Chance-constrained $H_{\infty}$ control for a class of time-varying systems with stochastic nonlinearities: The finite-horizon case, Automatica J. IFAC, 107 (2019), 296-305.
doi: 10.1016/j.automatica.2019.05.039. |
| [18] |
E. Tian, Z. Wang, L. Zou and D. Yue,
Probabilistic constrained filtering for a class of nonlinear systems with improved static event-triggered communication, Internat. J. Robust Nonlinear Control, 29 (2019), 1484-1498.
doi: 10.1002/rnc.4447. |
| [19] |
B. Yao, M. Al-Majed and M. Tomizuka,
High-performance robust motion control of machine tools: An adaptive robust control approach and comparative experiments, IEEE/ASME Trans. Mechatronics, 2 (1997), 63-76.
doi: 10.1109/ACC.1997.611956. |
| [20] |
Y. Yin, P. Shi, F. Liu, K. L. Teo and C. C. Lim,
Robust filtering for nonlinear nonhomogeneous Markov jump systems by fuzzy approximation approach, IEEE Trans on Cybernetics, 45 (2015), 1706-1716.
doi: 10.1109/TCYB.2014.2358680. |
| [21] |
Y. Yin, Z. Lin, Y. Liu and K. L. Teo,
Event-triggered constrained control of positive systems with input saturation, Internat. J. Robust Nonlinear Control, 28 (2018), 3532-3542.
doi: 10.1002/rnc.4097. |
| [22] |
Y. Yin and Z. Lin,
Constrained control of uncertain nonhomogeneous Markovian jump systems, Internat. J. Robust Nonlinear Control, 27 (2017), 3937-3950.
doi: 10.1002/rnc.3774. |
| [23] |
J. Yang, B. Wu, S. Li and X. Yu,
Design and qualitative robustness analysis of an DOBC approach for DC-DC buck converters with unmatched circuit parameter perturbations, IEEE Trans. Circuits Systems I: Regular Papers, 63 (2016), 551-560.
doi: 10.1109/TCSI.2016.2529238. |
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