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September  2019, 9(3): 283-295. doi: 10.3934/naco.2019019

Optimal sparse output feedback for networked systems with parametric uncertainties

Ahmadreza Argha 1, , Steven W. Su 2,, , Lin Ye 2, and  Branko G. Celler 1,

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

* Corresponding author: steven.su@uts.edu.au

Received  May 2018 Revised  April 2019 Published  May 2019

Fund Project: An earlier version of the paper appears in the proceedings of American Control Conference 2018.

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 & Optimization, 2019, 9 (3) : 283-295. doi: 10.3934/naco.2019019
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. Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[14]

D. D. Šiljak and A. Zečević, Control of large-scale systems: Beyond decentralized feedback, Annual Reviews in Control, 29 (2005), 169-179.   Google Scholar

[15]

D. Siljak, Decentralized Control of Complex Systems, Dover Publications, 2012.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

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. Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[14]

D. D. Šiljak and A. Zečević, Control of large-scale systems: Beyond decentralized feedback, Annual Reviews in Control, 29 (2005), 169-179.   Google Scholar

[15]

D. Siljak, Decentralized Control of Complex Systems, Dover Publications, 2012.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

Figure 1.  Networked System Architecture
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Figure 2.  Structure of block row/column-sparse SOF gains for different values of $\Psi_s$ and $\Psi_p$
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