Data Transmission Over Networks for Estimation and Control

We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal linear-quadratic-Gaussian (LQG) controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network. We then determine the optimal information processing strategy that should be followed by each node in the network so that the estimator is able to compute the best possible estimate in the minimum mean squared error sense. The algorithm is optimal for any packet-dropping process and at every time step, even though it is recursive and hence requires a constant amount of memory, processing and transmission at every node in the network per time step. For the case when the packet drop processes are memoryless and independent across links, we analyze the stability properties and the performance of the closed loop system. The algorithm is an attempt to escape the viewpoint of treating a network of communication links as a single end-to-end link with the probability of successful transmission determined by some measure of the reliability of the network.

[1]  Bruno Sinopoli,et al.  Towards Receding Horizon Networked Control , 2007 .

[2]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

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

[4]  Dawn M. Tilbury,et al.  Packet-based control: The H2-optimal solution , 2006, Autom..

[5]  Joao P. Hespanha,et al.  Anticipative and non-anticipative controller design for network control systems , 2006 .

[6]  T. Kailath,et al.  Indefinite-quadratic estimation and control: a unified approach to H 2 and H ∞ theories , 1999 .

[7]  Qiang Ling,et al.  Power spectral analysis of networked control systems with data dropouts , 2004, IEEE Transactions on Automatic Control.

[8]  G. Baliga,et al.  Issues in the convergence of control with communication and computing: proliferation, architecture, design, services, and middleware , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

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

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

[11]  Peter J Seiler,et al.  Coordinated Control of Unmanned Aerial Vehicles , 2001 .

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

[13]  Panganamala Ramana Kumar,et al.  Control over Networks of Unreliable Links: Controller Location and Performance Bounds , 2007, 2007 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks and Workshops.

[14]  B. Azimi-Sadjadi,et al.  Stability of networked control systems in the presence of packet losses , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

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

[17]  James Moyne,et al.  Performance evaluation of control networks: Ethernet, ControlNet, and DeviceNet , 2001 .

[18]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[19]  J.P. Hespanha,et al.  Optimal communication logics in networked control systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

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

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

[22]  Panos J. Antsaklis,et al.  On the model-based control of networked systems , 2003, Autom..

[23]  Richard M. Murray,et al.  On a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage , 2006, Autom..

[24]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[25]  J.P. Hespanha,et al.  Estimation over Communication Networks: Performance Bounds and Achievability Results , 2007, 2007 American Control Conference.

[26]  A.G. Alleyne,et al.  Stability and performance of packet-based feedback control over a Markov channel , 2006, 2006 American Control Conference.

[27]  Babak Hassibi,et al.  Indefinite-Quadratic Estimation And Control , 1987 .

[28]  Klaus Dohmen,et al.  Inclusion-Exclusion and Network Reliability , 1998, Electron. J. Comb..

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

[30]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[31]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[32]  Mehryar Mohri,et al.  Semiring Frameworks and Algorithms for Shortest-Distance Problems , 2002, J. Autom. Lang. Comb..

[33]  Sekhar Tatikonda,et al.  Some scaling properties of large distributed control systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).