Quantized predictive control over erasure channels

We study a control architecture for linear time-invariant plants which are affected by random disturbances. The distinguishing aspect of the situation at hand is that an unreliable data-rate limited network is placed between controller and the plant input. To achieve robustness with respect to i.i.d. dropouts, the controller transmits data packets containing quantized plant input predictions. These minimize a finite horizon cost function and are provided by an appropriate optimal entropy coded dithered lattice vector quantizer. Within this context, we derive an equivalent noise-shaping model of the closed loop system. This model is employed for the design and analysis of the vector quantizer used by the controller.

[1]  Yuval Kochman,et al.  Achieving the Gaussian Rate–Distortion Function by Prediction , 2007, IEEE Transactions on Information Theory.

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

[3]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[4]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

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

[6]  W. Fischer,et al.  Sphere Packings, Lattices and Groups , 1990 .

[7]  Alberto Bemporad,et al.  Predictive control of teleoperated constrained systems with unbounded communication delays , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

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

[9]  Graham C. Goodwin,et al.  Optimal coding for bit-rate limited networked control systems in the presence of data loss , 2007, 2007 46th IEEE Conference on Decision and Control.

[10]  D.E. Quevedo,et al.  Packetized Predictive Control over Erasure Channels , 2007, 2007 American Control Conference.

[11]  Dawn M. Tilbury,et al.  The Emergence of Industrial Control Networks for Manufacturing Control, Diagnostics, and Safety Data , 2007, Proceedings of the IEEE.

[12]  Clarence W. de Silva,et al.  Stability validation of a constrained model predictive networked control system with future input buffering , 2007, Int. J. Control.

[13]  T. Parisini,et al.  Stabilization of Networked Control Systems by Nonlinear Model Predictive Control: A Set Invariance Approach , 2009 .

[14]  Alexander Vardy,et al.  Closest point search in lattices , 2002, IEEE Trans. Inf. Theory.

[15]  Graham C. Goodwin,et al.  On Optimal Perfect Reconstruction Feedback Quantizers , 2008, IEEE Transactions on Signal Processing.

[16]  Jing Wu,et al.  Design of Networked Control Systems With Packet Dropouts , 2007, IEEE Transactions on Automatic Control.

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

[18]  Meir Feder,et al.  On universal quantization by randomized uniform/lattice quantizers , 1992, IEEE Trans. Inf. Theory.

[19]  G. Goodwin,et al.  Finite constraint set receding horizon quadratic control , 2004 .

[20]  Guo-Ping Liu,et al.  Improved predictive control approach to networked control systems , 2008 .

[21]  Graham C. Goodwin,et al.  The Quadratic Gaussian Rate-Distortion Function for Source Uncorrelated Distortions , 2008, Data Compression Conference (dcc 2008).

[22]  Senchun Chai,et al.  Design and stability analysis of networked control systems with random communication time delay using the modified MPC , 2006 .

[23]  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.

[24]  Meir Feder,et al.  On lattice quantization noise , 1996, IEEE Trans. Inf. Theory.

[25]  Edoardo Mosca,et al.  Predictive teleoperation of constrained dynamic systems via Internet-like channels , 2006, IEEE Transactions on Control Systems Technology.

[26]  Robin J. Evans,et al.  Feedback Control Under Data Rate Constraints: An Overview , 2007, Proceedings of the IEEE.

[27]  Graham C. Goodwin,et al.  Architectures and coder design for networked control systems , 2008, Autom..

[28]  R. P. Marques,et al.  Discrete-Time Markov Jump Linear Systems , 2004, IEEE Transactions on Automatic Control.