Abstract
This work concerns discrete-time Linear Quadratic Gaussian (LQG) optimal control of a remote plant that communicates with the control unit by means of a packets dropping channel. Namely, the output measurements are sent to the control unit through an unreliable network and the actions decided by the control unit are sent to the plant actuator via the same network. Sensor and control packets may be randomly lost according to a Bernoulli process. In this work we focus on the importance of acknowledgments in the communication between the control unit and the actuators. In the literature two extreme cases have been considered: either guaranteed acknowledgment or complete lack of it. Although very common in practice, the case where the acknowledgment packets can be lost has not been dealt with a sufficient level of detail. In this work we focus on such a case by assuming that also the acknowledgment packets can be lost according to a Bernoulli process. We can show how the partial loss of acknowledgements yields a non classical information pattern [1], making the optimal control law a nonlinear function of the information set. For the special case each observation packet contains the complete state information, we can prove linearity of the optimal controller. Furthermore, we can compute the control law in closed form and show that the stability range increases monotonically with the arrival rate of the acknowledgement packets.
This research was supported in part by CyLab at Carnegie Mellon under grant DAAD19-02-1-0389 from the Army Research Office, and grant CNS-0509004 from the National Science Foundation. The views and conclusions contained here are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either express or implied, of ARO, CMU, NSF, or the U.S. Government or any of its agencies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Witsenhausen, H.: A counterexample in stochastic optimum control. SIAM Journal of Control 6 (1968)
Murray, R.M., Astrom, K.J., Boyd, S.P., Brockett, R.W., Stein, G.: Control in an information rich world. IEEE Control System Magazine 23 (2003)
Hespanha, J., Naghshtabrizi, P., Xu, Y.: A survey of recent results in networked control systems. Proceedings of the IEEE, special issue 95(1) (2007)
Yang, T.C.: Networked control system: a brief survey. IEE Proceedings of Control Theory and Applications (2006)
Wong, W.S., Brockett, R.E.: Systems with finite communication bandwidth constraints.II: Stabilization with limited information feedback. IEEE Transaction on Automatic Control 44(5) (1999)
Nair, G.N., Evans, R.J.: Exponential stabilisability of finite-dimensional linear systems with limited data rates. Automatica 39(4) (2003)
Braslavsky, J.H., Middleton, R.H., Freudenberg, J.S.: Feedback stabilization over signal-to-noise ratio constrained channels. In: American Control Conference (2004)
Zhang, W., Branicky, M.S., Phillips, S.M.: Stability of networked control systems. IEEE Control System Magazine 21(1) (2001)
Luck, R., Ray: An observer-based compensator for distributed delays. Automatica 26(5) (1990)
Montestruque, L.A., Antsaklis, P.J.: Stability of model-based networked control systems with time-varying transmission times. IEEE Transaction on Automatic Control 49(9) (2004)
Walsh, G.C., Ye, H., Bushnell, L.: Stability analysis of networked control systems. IEEE Transaction on Control System Technology 10(3) (2001)
Nesic, D., Teel, A.: Input-output stability properties of networked control systems. IEEE Transaction on Automatic Control 49(10) (2004)
Hadjicostis, C.N., Touri, R.: Feedback control utilizing packet dropping network links. In: IEEE Conference on Decision and Control, Las Vegas (2002)
Nilsson, J.: Real-time control systems with delays. Ph.D. dissertation, Dept. Automatic Control, Lund Inst. Technology, Lund, Sweden (1998)
Schenato, L.: To hold or to zero control inputs with lossy links? Accepted for publication in IEEE Transactions on Automatic Control (2008)
Imer, O.C., Yuksel, S., Basar, T.: Optimal Control of dynamical systems over unreliable communicaion links. In: NOLCOS, Stutgart, Germany (2004)
Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Jordan, M., Sastry, S.: Optimal Control wih unreliable communication: the TCP case. In: American Control Conference, Portland, OR, USA (2005)
Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Sastry, S.: LQG control with missing observation and control packets. In: IFAC World Congress, Prague, Czech Republic (2005)
Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Sastry, S.: An LQG optimal linear controller for control system with packet losses. In: Conference on Decision and Control, Sevilla, Spain (2005)
Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Sastry, S.: Optimal Linear LQG control over lossy networks wihout packet acknowledgment. In: Conference on Decision and Control, San Diego, CA, USA (2006)
Epstein, M., Shi, L., Murray, R.M.: An estimation algorithm for a class of networked control systems using UDP-like communication scheme. In: Conference on Decision and Control, San Diego, CA, USA (2006)
Padmasola, P., Elia, N.: Mean Square Stabilization of LTI Systems over Packet-drop Networks with Imperfect Side Information. In: American Control Conference Minneapolis (2006)
Tanenbaum, A.: Computer Networks. Prentice-Hall, Englewood Cliffs (1981)
Gupta, V., Spanos, D., Hassibi, B., Murray, R.M.: Optimal LQG control across a packet-dropping link. System and Control Letters 56 (2007)
Xu, Y., Hespanha, J.: Estimation under controlled and uncontrolled communications in networked control system. In: Conference on Decision and Control, Sevilla, Spain (2007)
Smith, S., Seiler, P.: Estimation with lossy measurements: jump estimators for jump systems. IEEE Transaction on Automatic Control 48 (2003)
Huang, M., Dey, S.: Stability of Kalman filtering with Markovian packet losses. Automatica 43 (2007)
Drew, M., Liu, X., Goldsmith, A., Hedrick, J.: Control system design over a wireless lan. In: Conference on Decision and Control, Sevilla, Spain (2005)
Liu, X., Goldsmith, A.: Cross-layer Design of Distributed Control over Wireless Networks. In: Basar, T. (ed.). Birkhauser, Basel (2005)
Elia, N., Eisembeis, J.: Limitation of linear control over packet drop networks. In: Conference on Decision and Control, Bahamas (2004)
Elia, N.: Remote stabilization over fading channels. System and Control Letters 54 (2005)
Schenato, L., Sinopoli, B., Franceschetti, M., Poolla, K., Sastry, S.: Foundations of Control and estimation over lossy Networks. Proceedings of the IEEE 95 (2007)
Garone, E., Sinopoli, B., Casavola, A., Goldsmith, A.: LGQ control for distributed systems over TCP-like erasure channels. In: Conference on Decision and Control, New Orleans, LS, USA (2007)
Green, M., Limebeer, D.J.N.: Linear Robust Control. Prentice-Hall, Englewood Cliffs (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Garone, E., Sinopoli, B., Casavola, A. (2009). On the Effect of Packet Acknowledgment on the Stability and Performance of Networked Control Systems. In: Chiuso, A., Fortuna, L., Frasca, M., Rizzo, A., Schenato, L., Zampieri, S. (eds) Modelling, Estimation and Control of Networked Complex Systems. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03199-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-03199-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03198-4
Online ISBN: 978-3-642-03199-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)