LQG control for networked control systems in the presence of data packet drops

We study the linear-quadratic-Gaussian (LQG) control for multiple-input/multiple-output (MIMO) discrete-time networked control systems (NCSs) in the presence of data packet drops that are modeled as multiplicative noises, assumed to be white processes. We will first analyze the mean square (MS) stability problem for MIMO feedback systems in the presence of the multiplicative noises, and provide a new useful MS stability condition. The LQG control under packet data drops will then be studied in which the critical probability of the received data packet can be computed by solving a set of linear matrices inequalities (LMIs), beyond which the modified algebraic Riccati equations, associated with the LQG control, admit the stabilizing solutions. Finally a numerical example from the known literature is employed to illustrate our results.

[1]  Panos J. Antsaklis,et al.  Special Issue on Technology of Networked Control Systems , 2007 .

[2]  Graham C. Goodwin,et al.  Control over unreliable networks affected by packet erasures and variable transmission delays , 2008, IEEE Journal on Selected Areas in Communications.

[3]  Sekhar Tatikonda,et al.  Control over noisy channels , 2004, IEEE Transactions on Automatic Control.

[4]  Richard H. Middleton,et al.  Feedback stabilization over signal-to-noise ratio constrained channels , 2007, Proceedings of the 2004 American Control Conference.

[5]  Guoxiang Gu,et al.  Generalized LQR control and Kalman filtering with relations to computations of inner-outer and spectral factorizations , 2006, IEEE Transactions on Automatic Control.

[6]  Keyou You,et al.  Minimum Data Rate for Mean Square Stabilizability of Linear Systems With Markovian Packet Losses , 2011, IEEE Transactions on Automatic Control.

[7]  Bruno Sinopoli,et al.  Kalman Filtering With Intermittent Observations: Tail Distribution and Critical Value , 2012, IEEE Transactions on Automatic Control.

[8]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[9]  Petter Ögren,et al.  Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment , 2004, IEEE Transactions on Automatic Control.

[10]  Panos J. Antsaklis,et al.  Guest Editorial Special Issue on Networked Control Systems , 2004, IEEE Trans. Autom. Control..

[11]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[12]  Nicola Elia,et al.  Remote stabilization over fading channels , 2005, Syst. Control. Lett..

[13]  Bruno Sinopoli,et al.  Foundations of Control and Estimation Over Lossy Networks , 2007, Proceedings of the IEEE.

[14]  Peter J Seiler,et al.  Analysis of communication losses in vehicle control problems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[15]  Graham C. Goodwin,et al.  Control system design subject to SNR constraints , 2010, Autom..

[16]  Lihua Xie,et al.  The sector bound approach to quantized feedback control , 2005, IEEE Transactions on Automatic Control.