Foundations of Control and Estimation Over Lossy Networks

This paper considers control and estimation problems where the sensor signals and the actuator signals are transmitted to various subsystems over a network. In contrast to traditional control and estimation problems, here the observation and control packets may be lost or delayed. The unreliability of the underlying communication network is modeled stochastically by assigning probabilities to the successful transmission of packets. This requires a novel theory which generalizes classical control/estimation paradigms. The paper offers the foundations of such a novel theory. The central contribution is to characterize the impact of the network reliability on the performance of the feedback loop. Specifically, it is shown that for network protocols where successful transmissions of packets is acknowledged at the receiver (e.g., TCP-like protocols), there exists a critical threshold of network reliability (i.e., critical probabilities for the successful delivery of packets), below which the optimal controller fails to stabilize the system. Further, for these protocols, the separation principle holds and the optimal LQG controller is a linear function of the estimated state. In stark contrast, it is shown that when there is no acknowledgement of successful delivery of control packets (e.g., UDP-like protocols), the LQG optimal controller is in general nonlinear. Consequently, the separation principle does not hold in this circumstance

[1]  David Bailey,et al.  Practical SCADA for industry , 2003 .

[2]  J. Geromel,et al.  Solutions for the Linear-Quadratic Control Problem of Markov Jump Linear Systems , 1999 .

[3]  João Pedro Hespanha,et al.  Stabilization of nonlinear systems with limited information feedback , 2005, IEEE Transactions on Automatic Control.

[4]  Daniel Liberzon,et al.  On stabilization of linear systems with limited information , 2003, IEEE Trans. Autom. Control..

[5]  Bruno Sinopoli,et al.  Optimal linear LQG control over lossy networks without packet acknowledgment , 2008 .

[6]  S. Sahai,et al.  The necessity and sufficiency of anytime capacity for control over a noisy communication link , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[7]  Bruno Sinopoli,et al.  Optimal LQG Control over Lossy Packet Networks , 2005 .

[8]  Jeff Wills.  Will HVAC Control Go Wireless , 2004 .

[9]  Christoforos N. Hadjicostis,et al.  Feedback control utilizing packet dropping network links , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[10]  Björn Wittenmark,et al.  Stochastic Analysis and Control of Real-time Systems with Random Time Delays , 1999 .

[11]  Gaurav S. Sukhatme,et al.  Connecting the Physical World with Pervasive Networks , 2002, IEEE Pervasive Comput..

[12]  M. Dahleh,et al.  Feedback stabilization of uncertain systems using a stochastic digital link , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[13]  T. Başar,et al.  Minimum rate coding for state estimation over noiseless channels , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  Per Capita,et al.  About the authors , 1995, Machine Vision and Applications.

[15]  Mingjun Zhang,et al.  Hybrid control of the Pendubot , 2002 .

[16]  Tamer Basar,et al.  Optimal control of dynamical systems over unreliable communication links , 2004 .

[17]  Donal Heffernan,et al.  Expanding Automotive Electronic Systems , 2002, Computer.

[18]  Johan Nilsson,et al.  Real-Time Control Systems with Delays , 1998 .

[19]  I. Petersen,et al.  Robust Filtering with Missing Data and a Deterministic Description of Noise and Uncertainty , 1996 .

[20]  Daniel W. C. Ho,et al.  Variance-constrained filtering for uncertain stochastic systems with missing measurements , 2003, IEEE Trans. Autom. Control..

[21]  Guanrong Chen,et al.  Linear Stochastic Control Systems , 1995 .

[22]  Michael Cw Kintner-Meyer.  Opportunities of Wireless Sensors and Controls for Building Operation , 2005 .

[23]  J. Hespanha,et al.  Towards the Control of Linear Systems with Minimum Bit-Rate , 2002 .

[24]  W. L. De Koning,et al.  Infinite horizon optimal control of linear discrete time systems with stochastic parameters , 1982, Autom..

[25]  John N. Tsitsiklis,et al.  Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

[26]  Sekhar Tatikonda,et al.  Control under communication constraints , 2004, IEEE Transactions on Automatic Control.

[27]  Kristofer S. J. Pister,et al.  Smart Dust: Communicating with a Cubic-Millimeter Computer , 2001, Computer.

[28]  A. Goldsmith,et al.  Kalman filtering with partial observation losses , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[29]  Richard M. Murray,et al.  Optimal LQG control across packet-dropping links , 2007, Syst. Control. Lett..

[30]  T. Katayama.  On the matrix Riccati equation for linear systems with random gain , 1976 .

[31]  Johan Nilsson,et al.  Stochastic Analysis and Control of Real-Time Systems with Random Time Delays , 1996 .

[32]  Nicola Elia,et al.  Stabilization of linear systems with limited information , 2001, IEEE Trans. Autom. Control..

[33]  Gabor Karsai,et al.  Smart Dust: communicating with a cubic-millimeter computer , 2001 .

[34]  S. Sastry,et al.  Optimal control with unreliable communication: the TCP case , 2005, Proceedings of the 2005, American Control Conference, 2005..

[35]  Ian F. Akyildiz,et al.  Sensor Networks , 2002, Encyclopedia of GIS.

[36]  R. Murray,et al.  Optimal LQG Control Across a Packet-Dropping Link , 2004 .

[37]  Peter Seiler,et al.  Estimation with lossy measurements: jump estimators for jump systems , 2003, IEEE Trans. Autom. Control..

[38]  Raja Sengupta,et al.  An H/sub /spl infin// approach to networked control , 2005, IEEE Transactions on Automatic Control.

[39]  Babak Hassibi,et al.  On LQG control across a stochastic packet-dropping link , 2005, Proceedings of the 2005, American Control Conference, 2005..

[40]  Qiang Ling,et al.  Optimal dropout compensation in networked control systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[41]  Tamer Basar,et al.  Optimal control of LTI systems over unreliable communication links , 2006, Autom..

[42]  J.P. Hespanha,et al.  Estimation under uncontrolled and controlled communications in Networked Control Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[43]  Wing Shing Wong,et al.  Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback , 1999, IEEE Trans. Autom. Control..

[44]  Alberto L. Sangiovanni-Vincentelli,et al.  Electronic-System Design in the Automobile Industry , 2003, IEEE Micro.

[45]  EstrinDeborah,et al.  Connecting the Physical World with Pervasive Networks , 2002 .

[46]  R.H. Middleton,et al.  Feedback Stabilization Over Signal-to-Noise Ratio Constrained Channels , 2007, IEEE Transactions on Automatic Control.

[47]  A. Daneels,et al.  Selection and evaluation of commercial SCADA systems for the controls of the CERN LHC experiments , 1999 .

[48]  Oswaldo Luiz V. Costa,et al.  Stationary filter for linear minimum mean square error estimator of discrete-time Markovian jump systems , 2002, IEEE Trans. Autom. Control..

[49]  Daniel W. C. Ho,et al.  Variance-constrained control for uncertain stochastic systems with missing measurements , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[50]  Anant Sahai,et al.  The Necessity and Sufficiency of Anytime Capacity for Stabilization of a Linear System Over a Noisy Communication Link—Part I: Scalar Systems , 2006, IEEE Transactions on Information Theory.

[51]  N. Elia,et al.  Limitations of linear remote control over packet drop networks , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

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

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

[54]  Long Wang,et al.  Stabilization of networked control systems with data packet dropout via switched system approach , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).