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2019, 9(3): 283-295.
doi: 10.3934/naco.2019019
Optimal sparse output feedback for networked systems with parametric uncertainties
| 1. | School of Electrical Engineering and Telecommunications, University of New South Wales, NSW 2052 Australia |
| 2. | Faculty of Engineering and Information Technology, University of Technology, Sydney (UTS), PO Box 123, Broadway, NSW 2007, Australia |
This paper investigates the design of block row/column-sparse distributed static output ${H}_2$ feedback control for interconnected systems with polytopic uncertainties. The proposed approach is applicable to the networked systems with publisher/subscriber communication topology. We added two additional terms into the optimisation index function to penalise the number of publishers and subscribers. To optimally select a subset of available publishers and/or subscribers in the network, we introduced both an explicit scheme and an iterative process to handle this problem. We demonstrated the effectiveness by using a numerical example. The example showed that the simultaneous identification of favourable networks topologies and design of controller strategy can be achieved by using the proposed method.
Keywords:
$ {H}_2 $ control,
polytope uncertain,
LMI,
static output feedback (SOF),
publisher/subscriber networked systems.
Mathematics Subject Classification:
Primary: 90C22, 90C35; Secondary: 93A15.
Citation:
Ahmadreza Argha, Steven W. Su, Lin Ye, Branko G. Celler. Optimal sparse output feedback for networked systems with parametric uncertainties. Numerical Algebra, Control and Optimization,
2019, 9
(3)
: 283-295.
doi: 10.3934/naco.2019019
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References:
| [1] |
R. Arastoo, Y. GhaedSharaf, M. V. Kothare and N. Motee, Optimal state feedback controllers with strict row sparsity constraints, in American Control Conference (ACC), IEEE, (2016), 1948–1953. |
| [2] |
A. Argha, S. W. Su, A. Savkin and B. Celler,
A framework for optimal actuator/sensor selection in a control system, International Journal of Control, 92 (2019), 242-260.
doi: 10.1080/00207179.2017.1350755. |
| [3] |
A. Argha, S. W. Su and A. Savkin, Optimal actuator/sensor selection through dynamic output feedback, in Decision and Control (CDC), IEEE, (2016), 3624–3629. |
| [4] |
A. Argha, L. Li and S. W. Su,
Design of $H_2$ ($H_{\infty}$)-based optimal structured and sparse static output feedback gains, Journal of the Franklin Institute, 354 (2017), 4156-4178.
doi: 10.1016/j.jfranklin.2017.03.011. |
| [5] |
A. Argha, S. W. Su, A. Savkin and B. G. Celler,
Mixed $H_2/H_{\infty}$-based actuator selection for uncertain polytopic systems with regional pole placement, International Journal of Control, 91 (2018), 320-336.
doi: 10.1080/00207179.2017.1279753. |
| [6] |
A. Argha, L. Li and S. W. Su,
$H_2$-based optimal sparse sliding mode control for networked control systems, International Journal of Robust and Nonlinear Control, 28 (2018), 16-30.
doi: 10.1002/rnc.3852. |
| [7] |
E. J. Candes, M. B. Wakin and S. P. Boyd,
Enhancing sparsity by reweighted $\ell_1$ minimization, Journal of Fourier Analysis and Applications, 14 (2008), 877-905.
doi: 10.1007/s00041-008-9045-x. |
| [8] |
M. Fardad, F. Lin and M. R. Jovanovic, Sparsity-promoting optimal control for a class of distributed systems, in Proc. the American Control Conference, San Francisco, CA, USA, (2011), 2050–2055. |
| [9] |
M. Fardad and M. R. Jovanovic, On the design of optimal structured and sparse feedback gains via sequential convex programming, in American Control Conference (ACC), IEEE, (2014), 2426–2431. |
| [10] |
F. Lin, M. Fardad and M. Jovanovic,
Augmented lagrangian approach to design of structured optimal state feedback gains, IEEE Trans. Autom. Control, 56 (2011), 2923-2929.
doi: 10.1109/TAC.2011.2160022. |
| [11] |
G. Pipeleers, B. Demeulenaere, J. Swevers and L. Vandenberghe,
Extended LMI characterizations for stability and performance of linear systems, Systems & Control Letters, 58 (2009), 510-518.
doi: 10.1016/j.sysconle.2009.03.001. |
| [12] |
M. Razeghi-Jahromi and A. Seyedi,
Stabilization of networked control systems with sparse observer-controller networks, IEEE Transactions on Automatic Control, 60 (2015), 1686-1691.
doi: 10.1109/TAC.2014.2360310. |
| [13] |
J. Rubió-Massegú, J. M. Rossell, H. R. Karimi and F. Palacios-Quiñonero,
Static output-feedback control under information structure constraints, Automatica, 49 (2013), 313-316.
doi: 10.1016/j.automatica.2012.10.012. |
| [14] |
D. D. Šiljak and A. Zečević,
Control of large-scale systems: Beyond decentralized feedback, Annual Reviews in Control, 29 (2005), 169-179.
|
| [15] |
D. Siljak, Decentralized Control of Complex Systems, Dover Publications, 2012. |
| [16] |
M. Staroswiecki and A. M. Amani, Fault-tolerant control of distributed systems by information pattern reconfiguration, International Journal of Adaptive Control and Signal Processing, 2014.
doi: 10.1002/acs.2497. |
| [17] |
S. Schuler, U. Münz and F. Allgöwer,
Decentralized state feedback control for interconnected systems with application to power systems, Journal of Process Control, 24 (2014), 379-388.
|
| [18] |
M. Van De Wal and B. De Jager,
A review of methods for input/output selection, Automatica, 37 (2001), 487-510.
doi: 10.1016/S0005-1098(00)00181-3. |
| [19] |
X. Wang and M. Lemmon,
Event-triggering in distributed networked control systems, IEEE Transactions on Automatic Control, 56 (2011), 586-601.
doi: 10.1109/TAC.2010.2057951. |
| [20] |
A. Zecevic and D. Siljak,
Global low-rank enhancement of decentralized control for large-scale systems, IEEE Transactions on Automatic Control, 50 (2005), 740-744.
doi: 10.1109/TAC.2005.847054. |
| [21] |
D. M. Zoltowski, N. Dhingra, F. Lin and M. R. Jovanovic, Sparsity-promoting optimal control of spatially-invariant systems, in American Control Conference (ACC) IEEE, (2014), 1255–1260. |
show all references
References:
| [1] |
R. Arastoo, Y. GhaedSharaf, M. V. Kothare and N. Motee, Optimal state feedback controllers with strict row sparsity constraints, in American Control Conference (ACC), IEEE, (2016), 1948–1953. |
| [2] |
A. Argha, S. W. Su, A. Savkin and B. Celler,
A framework for optimal actuator/sensor selection in a control system, International Journal of Control, 92 (2019), 242-260.
doi: 10.1080/00207179.2017.1350755. |
| [3] |
A. Argha, S. W. Su and A. Savkin, Optimal actuator/sensor selection through dynamic output feedback, in Decision and Control (CDC), IEEE, (2016), 3624–3629. |
| [4] |
A. Argha, L. Li and S. W. Su,
Design of $H_2$ ($H_{\infty}$)-based optimal structured and sparse static output feedback gains, Journal of the Franklin Institute, 354 (2017), 4156-4178.
doi: 10.1016/j.jfranklin.2017.03.011. |
| [5] |
A. Argha, S. W. Su, A. Savkin and B. G. Celler,
Mixed $H_2/H_{\infty}$-based actuator selection for uncertain polytopic systems with regional pole placement, International Journal of Control, 91 (2018), 320-336.
doi: 10.1080/00207179.2017.1279753. |
| [6] |
A. Argha, L. Li and S. W. Su,
$H_2$-based optimal sparse sliding mode control for networked control systems, International Journal of Robust and Nonlinear Control, 28 (2018), 16-30.
doi: 10.1002/rnc.3852. |
| [7] |
E. J. Candes, M. B. Wakin and S. P. Boyd,
Enhancing sparsity by reweighted $\ell_1$ minimization, Journal of Fourier Analysis and Applications, 14 (2008), 877-905.
doi: 10.1007/s00041-008-9045-x. |
| [8] |
M. Fardad, F. Lin and M. R. Jovanovic, Sparsity-promoting optimal control for a class of distributed systems, in Proc. the American Control Conference, San Francisco, CA, USA, (2011), 2050–2055. |
| [9] |
M. Fardad and M. R. Jovanovic, On the design of optimal structured and sparse feedback gains via sequential convex programming, in American Control Conference (ACC), IEEE, (2014), 2426–2431. |
| [10] |
F. Lin, M. Fardad and M. Jovanovic,
Augmented lagrangian approach to design of structured optimal state feedback gains, IEEE Trans. Autom. Control, 56 (2011), 2923-2929.
doi: 10.1109/TAC.2011.2160022. |
| [11] |
G. Pipeleers, B. Demeulenaere, J. Swevers and L. Vandenberghe,
Extended LMI characterizations for stability and performance of linear systems, Systems & Control Letters, 58 (2009), 510-518.
doi: 10.1016/j.sysconle.2009.03.001. |
| [12] |
M. Razeghi-Jahromi and A. Seyedi,
Stabilization of networked control systems with sparse observer-controller networks, IEEE Transactions on Automatic Control, 60 (2015), 1686-1691.
doi: 10.1109/TAC.2014.2360310. |
| [13] |
J. Rubió-Massegú, J. M. Rossell, H. R. Karimi and F. Palacios-Quiñonero,
Static output-feedback control under information structure constraints, Automatica, 49 (2013), 313-316.
doi: 10.1016/j.automatica.2012.10.012. |
| [14] |
D. D. Šiljak and A. Zečević,
Control of large-scale systems: Beyond decentralized feedback, Annual Reviews in Control, 29 (2005), 169-179.
|
| [15] |
D. Siljak, Decentralized Control of Complex Systems, Dover Publications, 2012. |
| [16] |
M. Staroswiecki and A. M. Amani, Fault-tolerant control of distributed systems by information pattern reconfiguration, International Journal of Adaptive Control and Signal Processing, 2014.
doi: 10.1002/acs.2497. |
| [17] |
S. Schuler, U. Münz and F. Allgöwer,
Decentralized state feedback control for interconnected systems with application to power systems, Journal of Process Control, 24 (2014), 379-388.
|
| [18] |
M. Van De Wal and B. De Jager,
A review of methods for input/output selection, Automatica, 37 (2001), 487-510.
doi: 10.1016/S0005-1098(00)00181-3. |
| [19] |
X. Wang and M. Lemmon,
Event-triggering in distributed networked control systems, IEEE Transactions on Automatic Control, 56 (2011), 586-601.
doi: 10.1109/TAC.2010.2057951. |
| [20] |
A. Zecevic and D. Siljak,
Global low-rank enhancement of decentralized control for large-scale systems, IEEE Transactions on Automatic Control, 50 (2005), 740-744.
doi: 10.1109/TAC.2005.847054. |
| [21] |
D. M. Zoltowski, N. Dhingra, F. Lin and M. R. Jovanovic, Sparsity-promoting optimal control of spatially-invariant systems, in American Control Conference (ACC) IEEE, (2014), 1255–1260. |
Figure 2.
Structure of block row/column-sparse SOF gains for different values of $\Psi_s$ and $\Psi_p$
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