Quantized Feedback Control for Networked Control Systems Under Communication Constraints

  • Qing-Quan Liu School of Information Science and Engineering Shenyang Ligong University No. 6, Nan Ping Zhong Road, Hun Nan Xin District, Shenyang, 110159, China
  • Guang-Hong Yang College of Information Science and Engineering Northeastern University Shenyang, 110004, China

Abstract

This paper investigates the feedback stabilization problem for networked control systems (NCSs) with unbound process noise, where sensors and controllers are connected via noiseless digital channels carrying a finite number of bits per unit time. A sufficient condition for stabilization of NCSs, which relies on a variable-rate digital link used to transmit state measurements, is derived. A lower bound of data rates, above which there exists a quantization, coding and control scheme to guarantee both stabilization and a prescribed control performance of the unstable discrete-time plant, is presented. An illustrative example is given to demonstrate the effectiveness of the proposed method.

References

[1] W. S. Wong and R. W. Brockett, Systems with finite communication bandwidth constraints I: Stabilization with limited information feedback, IEEE Trans. Automat. Control, 4(5):1049-1053, May 1999.
http://dx.doi.org/10.1109/9.763226

[2] J. Baillieul, Feedback designs for controlling device arrays with communication channel andwidth constraints, in ARO Workshop on Smart Structures, Pennsylvania State Univ, ug. 1999.

[3] J. Baillieul, Feedback designs in information based control, in Stochastic Theory and Control roceedings of a Workshop Held in Lawrence, Kansas, B. Pasik-Duncan, Ed. New York: pringer-Verlag, 2001, pp. 35-57.

[4] J. Baillieul, Data-rate requirements for nonlinear feedback control, in Proc. 6th IFAC Symp. onlinear Control Syst., Stuttgart, Germany, 2004, pp. 1277-1282.

[5] K. Li and J. Baillieul, Robust quantization for digital finite communication bandwidth (DFCB) control, IEEE Trans. Automat. Control, 49(9):1573-1584, Sep. 2004.
http://dx.doi.org/10.1109/TAC.2004.834106

[6] G. N. Nair and R. J. Evans, Stabilizability of stochastic linear systems with finite feedback ata rates, SIAM J. Control Optim., 43(2):413-436, Jul. 2004.
http://dx.doi.org/10.1137/S0363012902402116

[7] N. Elia and S. K. Mitter, Stabilization of linear systems with limited information, IEEE rans. Automat. Control, 46(9):1384-1400, Sep. 2001.

[8] N. Elia, When Bode meets Shannon: Control-oriented feedback communication schemes, EEE Trans. Automat. Control, 49(9):1477-1488, Sep. 2004.
http://dx.doi.org/10.1109/TAC.2004.834119

[9] S. Tatikonda and S. K. Mitter, Control under communication constraints, IEEE Trans. utomat. Control, 49(7):1056-1068, Jul. 2004.

[10] S. Tatikonda and S. K. Mitter, Control over noisy channels, IEEE Trans. Automat. Control, 9(7):1196-1201, Jul. 2004.
http://dx.doi.org/10.1109/TAC.2004.831102

[11] S. Tatikonda, A. Sahai and S. K. Mitter, Stochastic linear control over a communication hannel, IEEE Trans. Automat. Control, 49(9):1549-1561, Sep. 2004.
http://dx.doi.org/10.1109/TAC.2004.834430

[12] N. C. Martins, M. A. Dahleh, and N. Elia, Feedback stabilization of uncertain systems in he presence of a direct link, IEEE Trans. Automat. Control, 51(3):438-447, Mar. 2006.
http://dx.doi.org/10.1109/TAC.2006.871940

[13] N. C. Martins and M. A. Dahleh, Feedback control in the presence of noisy channels: 'Bodelike' undamental limitations of performance, IEEE Trans. Automat. Control, 53(7):1604- 615, Jul. 2008.
http://dx.doi.org/10.1109/TAC.2008.929361

[14] G. N. Nair, S. Dey, and R. J. Evans, Infimum data rates for stabilizing Markov jump linear ystems, in Proc. IEEE Conf. Decision and Control, 2003, pp. 1176-1181.

[15] A. Sahai and S. Mitter, The necessity and sufficiency of anytime capacity for stabilization f a linear system over a noisy communication link Part I: Scalar systems, IEEE Trans. utomat. Control, 52(8):3369-3395, Aug. 2006.

[16] J. Q. Sun and S. M. Djouadi, Robust stabilization over communication channels in the resence of unstructured uncertainty, IEEE Trans. Automat. Control, 54(4):830-834, Apr. 009.

[17] S. Y¨uksel and T. Basar, Communication constraints for decentralized stabilizability with ime-invariant policies, IEEE Trans. Automat. Control, 52(6):1060-1066, Jun. 2007.
http://dx.doi.org/10.1109/TAC.2007.899085

[18] C.D. Charalambous, A. Farhadi, and S.Z. Denic, Control of continuous-time linear Gaussian ystems over additive Gaussian wireless fading channels: A separation principle, IEEE rans. Automat. Control, 53(4):1013-1019, Apr. 2008.

[19] P. Minero, M. Franceschetti, S. Dey, and G. N. Nair, Data rate theorem for stabilization ver time-varying feedback channels, IEEE Trans. Automat. Control, 54(2):243-255, Feb. 009.

[20] J. Baillieul and P. Antsaklis, Control and communication challanges in networked real time ystems, in Proceedings of IEEE Special Iss. Emerg. Technol. Netw. Control Syst, USA: EEE, 2007, pp. 9-28.

[21] G. N. Nair, F. Fagnani, S. Zampieri, and R. J. Evans, Feedback control under data rate onstraints: An overview, in Proceedings of IEEE Special Iss. Emerg. Technol. Netw. Control yst, USA: IEEE, 2007, pp. 108-137.

[22] Y. L. Wang and G. H. Yang, H∞ control of networked control systems with time delay and acket disordering, IET Control Theory & Applications, 1(5):1344-1354, May. 2007.

[23] Y. L. Wang and G. H. Yang, Multiple communication channels-based packet dropout compensation or networked control system, IET Control Theory & Applications, 2(8):717-727, ug. 2008.

[24] T. Cover and J. Thomas, Elements of Information Theory. New York: Wiley, 2006.
Published
2012-03-01
How to Cite
LIU, Qing-Quan; YANG, Guang-Hong. Quantized Feedback Control for Networked Control Systems Under Communication Constraints. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 7, n. 1, p. 90-100, mar. 2012. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/1425>. Date accessed: 08 july 2020. doi: https://doi.org/10.15837/ijccc.2012.1.1425.

Keywords

networked control systems (NCSs), quantized feedback control, communication constraints, feedback stabilization