Optimal state feedback control for wireless networked control systems with decentralised controllers
- Author(s): Zhuwei Wang 1, 2 ; Xiaodong Wang 1, 3 ; Lihan Liu 4 ; Mo Huang 5
-
-
View affiliations
-
Affiliations:
1:
Department of Electrical Engineering, Columbia University, New York 10027, NY, USA;
2: College of Electronic Information and Control Engineering, Beijing University ofTechnology, Beijing 100124, People's Republic of China;
3: King Abdulaziz University, Jeddah, Saudi Arabia;
4: School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing 100876, People's Republic of China;
5: Institute of Electronics, Chinese Academy of Science, Beijing 100190, People's Republic of China
-
Affiliations:
1:
Department of Electrical Engineering, Columbia University, New York 10027, NY, USA;
- Source:
Volume 9, Issue 6,
13 April 2015,
p.
852 – 862
DOI: 10.1049/iet-cta.2014.0418 , Print ISSN 1751-8644, Online ISSN 1751-8652
In this study, the design of the optimal decentralised full-state-feedback controllers is derived for wireless networked control systems with network-induced delays. In particular, the authors formulate the optimal decentralised control problem as a non-cooperative linear quadratic game. Then, the optimal control strategy of each controller is obtained that is based on the current plant state and the last control strategies of decentralised controllers. The proposed optimal decentralised controllers reduce to the known controller under certain conditions. Moreover, the authors illustrate the application of the proposed decentralised state feedback control to load frequency control in power grid systems.
Inspec keywords: control system synthesis; optimal control; delays; power grids; networked control systems; game theory; frequency control; decentralised control; state feedback
Other keywords: power grid systems; optimal decentralised controllers; optimal state feedback control; noncooperative linear quadratic game; network-induced delays; wireless networked control systems; optimal decentralised full-state-feedback controller design; load frequency control
Subjects: Control system analysis and synthesis methods; Distributed parameter control systems; Frequency control; Multivariable control systems; Game theory; Optimal control
References
-
-
1)
- R. Olfati-Saber , R.M. Murray . Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control , 9 , 1520 - 1533
-
2)
- Z. Qu , J. Wang , R. Hull . Cooperative control of dynamical systems with application to autonomous vehicles. IEEE Trans. Autom. Control , 4 , 894 - 911
-
3)
-
30. Fosha, C.E., Elgerd, O.I.: ‘The megawatt frequency control problem: a new approach via optimal control theory’, IEEE Trans. Power Appl., Syst., 1970, PAS-89, (4), pp. 563–577 (doi: 10.1109/TPAS.1970.292603).
-
-
4)
-
13. Gu, D.: ‘A differential game approach to formation control’, IEEE Trans. Control Syst. Technol., 2008, 16, (1), pp. 85–93 (doi: 10.1109/TCST.2007.899732).
-
-
5)
-
26. Chai, S., Liu, G.P., Rees, D., Xia, Y.: ‘Design and practical implementation of internet-based predictive control of a servo system’, IEEE Trans. Control Syst. Technol., 2008, 16, (1), pp. 158–168 (doi: 10.1109/TCST.2007.903095).
-
-
6)
- J. Liang , Z. Wang , Y. Liu , X. Liu . Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances. IEEE Trans. Syst. Man Cybern., B , 4 , 1073 - 1083
-
7)
- R.M. Murray . Recent research in cooperative control of multivehicle systems. J. Dyn. Syst., Meas., Control , 5 , 571 - 583
-
8)
-
31. Dong, L., Zhang, Y.: ‘On design of a robust load frequency controller for interconnected power systems’. Proc. of 2010 American Control Conf., Baltimore, USA, 2010, pp. 1731–1736.
-
-
9)
-
29. Astrom, K.J., Wittenmark, B.: ‘Computer-controlled systems theory and design’ (Prentice-Hall, 1997, 3rd edn.).
-
-
10)
-
10. Engwerda, J.C.: ‘LQ dynamic optimization and differential games’ (Wiley, Chichester, 2005).
-
-
11)
-
12. Mukaidani, H.: ‘Local feedback Pareto strategy for weakly coupled large-scale discrete-time stochastic systems’, IET Control Theory Appl., 2011, 5, (7), pp. 2005–2014 (doi: 10.1049/iet-cta.2010.0469).
-
-
12)
-
26. Vokharaie, V.S., Mason, O., Verwoerd, M.: ‘D-stability and delay-independent stability of homogeneous cooperative systems’, IEEE Trans. Autom. Control, 2010, 55, (12), pp. 2882–2885 (doi: 10.1109/TAC.2010.2076334).
-
-
13)
-
3. Bullo, F., Cortes, J., Martinez, S.: ‘Distributed control of robotic networks: a mathematical approach to motion coordination algorithms’ (Princeton University Press, 2009).
-
-
14)
-
20. Liu, X., Goldsmith, A.: ‘Wireless medium access control in networked control systems’. Proc. of 2004 American Control Conf., Boston, USA, 2004, pp. 688–694.
-
-
15)
-
27. Li, H., Lai, L., Poor, H.V.: ‘Multicast routing for decentralized control of cyber physical systems with an application in smart grid’, IEEE J. Sel. Areas Commun., 2012, 30, (6), pp. 1097–1107 (doi: 10.1109/JSAC.2012.120708).
-
-
16)
- J. Nilsson , B. Bernhardsson , B. Wittenmark . Stochastic analysis and control of real-time systems with random time delays. Automatica , 1 , 57 - 64
-
17)
- G. Ferrari-Trecate , L. Galbusera , M.P.E. Marciandi , R. Scattolini . Model predictive control schemes for consensus in multi-agent systems with single- and double-integrator dynamics. IEEE Trans. Autom. Control , 11 , 2560 - 2572
-
18)
- W. Semsar-Kazerooni , K. Khorasani . Multi-agent team cooperation: a game theory approach. Automatica , 10 , 2205 - 2213
-
19)
-
1. ISO New England Inc.: ‘Overview of the smart grid: policies, initiatives and needs’, 2009, pp. 1–46.
-
-
20)
-
8. Chen, W., Qiu, L.: ‘Stabilization of networked control systems with multirate sampling’, Automatica, 2013, 49, (6), pp. 1528–1537 (doi: 10.1016/j.automatica.2013.02.010).
-
-
21)
- F. Borrelli , T. Keviczky . Distributed LQR design for identical dynamically decoupled systems. IEEE Trans. Autom. Control , 8 , 1901 - 1912
-
22)
- F. Xiao , L. Wang . State consensus for multi-agent systems with switching topologies and time-varying delays. Int. J. Control , 10 , 1277 - 1284
-
23)
-
14. Cao, Y., Ren, W.: ‘Optimal linear consensus algorithms: an LQR perspective’, IEEE Trans. Syst., Man Cybern., 2010, 40, (3), pp. 819–830 (doi: 10.1109/TSMCB.2009.2030495).
-
-
24)
- H. Shousong , Z. Qixin . Stochastic optimal control and analysis of stability of networked control systems with long delay. Automatica , 1877 - 1884
-
25)
-
6. Hespanha, J., Naghshtabrizi, P., Xu, Y.: ‘A survey of recent results in networked control systems’, Automatica, 2007, 95, (1), pp. 138–162.
-
-
26)
-
21. Pajic, M., Sundaram, S., Pappas, G.J., Mangharam, R.: ‘The wireless control network: a new approach for control over networks’, IEEE Trans. Autom. Control, 2011, 56, (10), pp. 2305–2318 (doi: 10.1109/TAC.2011.2163864).
-
-
27)
-
22. Wang, Z., Ding, D., Dong, H., Shu, H.: ‘H∞ consensus control for multi-agent systems with missing measurements: the finite-horizon case’, Syst. Control Lett., 2013, 62, (10), pp. 827–836 (doi: 10.1016/j.sysconle.2013.06.004).
-
-
28)
-
1. Sun, J.D., Jiang, J. P.: ‘Delay and data packet dropout separately related stability and state feedback stabilisation of networked control systems’, IET Control Theory Appl., 2013, 7, (3), pp. 333–342 (doi: 10.1049/iet-cta.2011.0391).
-
-
29)
- C.Q. Ma , J.F. Zhang . Necessary and sufficient conditions for consensusability of linear multi-agent systems. IEEE Trans. Autom. Control , 5 , 1263 - 1268
-
30)
- Y. Tian , C. Liu . Consensus of multi-agent systems with diverse input and communication delays. IEEE Trans. Autom. Control , 9 , 2122 - 2128
-
31)
-
16. Gupta, V., Hassibi, B., Murray, R.M.: ‘A sub-optimal algorithm to synthesize control laws for a network of dynamic agents’, Int. J. Control, 2005, 78, (16), pp. 1302–1313 (doi: 10.1080/00207170500324175).
-
-
1)