American Institute of Mathematical Sciences

September  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

* 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.

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
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.
Networked System Architecture
Structure of block row/column-sparse SOF gains for different values of $\Psi_s$ and $\Psi_p$
 [1] Xingyue Liang, Jianwei Xia, Guoliang Chen, Huasheng Zhang, Zhen Wang. $\mathcal{H}_{\infty}$ control for fuzzy markovian jump systems based on sampled-data control method. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1329-1343. doi: 10.3934/dcdss.2020368 [2] Liqiang Jin, Yanyan Yin, Kok Lay Teo, Fei Liu. Event-triggered mixed $H_\infty$ and passive control for Markov jump systems with bounded inputs. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1343-1355. doi: 10.3934/jimo.2020024 [3] Junlin Xiong, Wenjie Liu. $H_{\infty}$ observer-based control for large-scale systems with sparse observer communication network. Numerical Algebra, Control and Optimization, 2020, 10 (3) : 331-343. doi: 10.3934/naco.2020005 [4] Ramalingam Sakthivel, Palanisamy Selvaraj, Yeong-Jae Kim, Dong-Hoon Lee, Oh-Min Kwon, Rathinasamy Sakthivel. Robust $H_\infty$ resilient event-triggered control design for T-S fuzzy systems. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022028 [5] Zhaoxia Duan, Jinling Liang, Zhengrong Xiang. $H_{\infty}$ control for continuous-discrete systems in T-S fuzzy model with finite frequency specifications. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022064 [6] Jaume Llibre, Y. Paulina Martínez, Claudio Vidal. Phase portraits of linear type centers of polynomial Hamiltonian systems with Hamiltonian function of degree 5 of the form $H = H_1(x)+H_2(y)$. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 75-113. doi: 10.3934/dcds.2019004 [7] Dean Crnković, Nina Mostarac, Bernardo G. Rodrigues, Leo Storme. $s$-PD-sets for codes from projective planes $\mathrm{PG}(2,2^h)$, $5 \leq h\leq 9$. Advances in Mathematics of Communications, 2021, 15 (3) : 423-440. doi: 10.3934/amc.2020075 [8] Shengbing Deng. Construction solutions for Neumann problem with Hénon term in $\mathbb{R}^2$. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 2233-2253. doi: 10.3934/dcds.2019094 [9] Lakehal Belarbi. Ricci solitons of the $\mathbb{H}^{2} \times \mathbb{R}$ Lie group. Electronic Research Archive, 2020, 28 (1) : 157-163. doi: 10.3934/era.2020010 [10] Florin Diacu, Shuqiang Zhu. Almost all 3-body relative equilibria on $\mathbb S^2$ and $\mathbb H^2$ are inclined. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1131-1143. doi: 10.3934/dcdss.2020067 [11] Dongyi Liu, Genqi Xu. Input-output $L^2$-well-posedness, regularity and Lyapunov stability of string equations on networks. Networks and Heterogeneous Media, 2022  doi: 10.3934/nhm.2022007 [12] Lin Du, Yun Zhang. $\mathcal{H}_∞$ filtering for switched nonlinear systems: A state projection method. Journal of Industrial and Management Optimization, 2018, 14 (1) : 19-33. doi: 10.3934/jimo.2017035 [13] Raina Raj, Vidyottama Jain. Optimization of traffic control in $MMAP\mathit{[2]}/PH\mathit{[2]}/S$ priority queueing model with $PH$ retrial times and the preemptive repeat policy. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022044 [14] Rong Zhang. Nonexistence of Positive Solutions for high-order Hardy-H$\acute{e}$non Systems on $\mathbb{R}^{n}$. Communications on Pure and Applied Analysis, 2022, 21 (8) : 2857-2872. doi: 10.3934/cpaa.2022078 [15] Kwangseok Choe, Hyungjin Huh. Chern-Simons gauged sigma model into $\mathbb{H}^2$ and its self-dual equations. Discrete and Continuous Dynamical Systems, 2019, 39 (8) : 4613-4646. doi: 10.3934/dcds.2019189 [16] Yong Zhou, Jia Wei He. New results on controllability of fractional evolution systems with order $\alpha\in (1,2)$. Evolution Equations and Control Theory, 2021, 10 (3) : 491-509. doi: 10.3934/eect.2020077 [17] Canghua Jiang, Dongming Zhang, Chi Yuan, Kok Ley Teo. An active set solver for constrained $H_\infty$ optimal control problems with state and input constraints. Numerical Algebra, Control and Optimization, 2022, 12 (1) : 135-157. doi: 10.3934/naco.2021056 [18] Wensheng Yin, Jinde Cao, Guoqiang Zheng. Further results on stabilization of stochastic differential equations with delayed feedback control under $G$-expectation framework. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 883-901. doi: 10.3934/dcdsb.2021072 [19] Ruth F. Curtain, George Weiss. Strong stabilization of (almost) impedance passive systems by static output feedback. Mathematical Control and Related Fields, 2019, 9 (4) : 643-671. doi: 10.3934/mcrf.2019045 [20] N. U. Ahmed. Existence of optimal output feedback control law for a class of uncertain infinite dimensional stochastic systems: A direct approach. Evolution Equations and Control Theory, 2012, 1 (2) : 235-250. doi: 10.3934/eect.2012.1.235

Impact Factor: