T echnical Report: Results on Continuous and Discrete Model-Based Networked Control Systems with Intermittent Feedback, Part I: Stability

The aim of this technical report is to provide a thorough compendium of our results in stability of model-based networked control systems with intermittent feedback. The first set of sections deal with continuous time results, while the latter sections focus on discrete time. We apply the concept of Intermittent Feedback to a class of net-worked control systems known as Model-Based Networked Control Systems (MB-NCS). Model-Based Networked Control Systems use an explicit model of the plant in order to reduce the network traffic while attempting to prevent excessive performance degradation, while Intermittent Feedback consists of the loop remaining closed for some fixed interval, then open for another interval. We begin by introducing the basic architecture for model-based control with intermittent feedback, then address the case with output feedback (through the use of a state observer), providing a full description of the state response of the system, as well as a necessary and sufficient condition for stability in each case. Examples are provided to complement the theoretical results. Extensions of our results to cases with nonlinear plants are also presented. Next, we investigate the situation where the update 2 times τ and h are time-varying, first addressing the case where they have upper and lower bounds, then moving on to the case where their distributions are i.i.d or driven by a Markov chain. We then shift our focus to the stability of discrete-time plants in Model-Based Networked Control Systems with Intermittent Feedback. We provide a full description of the output, as well as a necessary and sufficient condition for stability of the system. We also extend our results to the case where the full state of the plant is not known, so that we resort to a state observer. Finally, as for the continuous time case, we investigate the situation where the update times are time-varying, first addressing the case where they have upper and lower bounds, then moving on to the case where their distributions are i.i.d or driven by a Markov chain.

[1]  P.J. Antsaklis,et al.  Model-Based Control with Intermittent Feedback , 2006, 2006 14th Mediterranean Conference on Control and Automation.

[2]  Panos J. Antsaklis,et al.  Stability of Model-Based Networked Control Systems with Intermittent Feedback , 2009 .

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

[4]  Wei Zhang,et al.  Scheduling and feedback co-design for networked control systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[5]  D. Delchamps.  Stabilizing a linear system with quantized state feedback , 1990 .

[6]  Panos J. Antsaklis,et al.  Control and Communication Challenges in Networked Real-Time Systems , 2007, Proceedings of the IEEE.

[7]  Panos J. Antsaklis,et al.  Linear Systems , 1997 .

[8]  G. Bugmann,et al.  Compensating Intermittent Delayed Visual Feedback in Robot Navigation , 2004 .

[9]  Peter F. Al-Hokayem.  Stability Analysis of Networked Control Systems , 2003 .

[10]  David John Hill,et al.  Open-Loop Intermittent Feedback Optimal Predictive Control: a human movement control model , 1999, NIPS 1999.

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

[12]  Alexander S. Mikhailov,et al.  Controlling Chemical Turbulence by Global Delayed Feedback: Pattern Formation in Catalytic CO Oxidation on Pt(110) , 2001, Science.

[13]  R. Evans,et al.  Communication-limited stabilization of linear systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[14]  B L Hopkins,et al.  The effect of intermittent feedback and intermittent contingent access to play on printing of kindergarten children. , 1971, Journal of applied behavior analysis.

[15]  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).

[16]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

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

[18]  Panos J. Antsaklis,et al.  MODEL-BASED NETWORKED CONTROL SYSTEMS – NECESSARY AND SUFFICIENT CONDITIONS FOR STABILITY , 2002 .

[19]  Panos J. Antsaklis,et al.  Networked Control Systems: A Model-Based Approach , 2005, Handbook of Networked and Embedded Control Systems.

[20]  P.J. Antsaklis,et al.  Stability of discrete-time plants using model-based control with intermittent feedback , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[21]  Nandit Soparkar,et al.  Trading computation for bandwidth: reducing communication in distributed control systems using state estimators , 2002, IEEE Trans. Control. Syst. Technol..

[22]  D. Hristu-Varsakelis.  Feedback control systems as users of a shared network: communication sequences that guarantee stability , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[23]  Panos J. Antsaklis,et al.  State and output feedback control in model-based networked control systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..