Stabilizing bit-rates in networked control systems with decentralized event-triggered communication

In a decentralized event-triggered networked control system (NCS), an agent samples and transmits its local state information to the controller when some local event occurs. Such event-triggered NCSs were expected to be more efficient than traditional periodically sampled system in terms of communication channel usage. This paper studies the stability of decentralized event-triggered NCS in the presence of quantization and delays. We point out some potential issues in decentralized event-triggered design and propose an alternative decentralized event with a linear-affine threshold, which avoids infinitely fast data transmission. Conditions on quantizer and communication channel are derived, which, when satisfied, can guarantee stability of the resulting NCS. Based on these conditions, finite stabilizing bit-rates are provided.

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

[2]  Xiaofeng Wang,et al.  Event-Triggering in Distributed Networked Control Systems , 2011, IEEE Transactions on Automatic Control.

[3]  Manuel Mazo,et al.  Decentralized event-triggered control with asynchronous updates , 2011, IEEE Conference on Decision and Control and European Control Conference.

[4]  Xiaofeng Wang,et al.  Self-Triggered Feedback Control Systems With Finite-Gain ${\cal L}_{2}$ Stability , 2009, IEEE Transactions on Automatic Control.

[5]  Xiaofeng Wang,et al.  Relaxing the consistency condition in distributed event-triggered networked control systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[6]  Paulo Tabuada,et al.  An introduction to event-triggered and self-triggered control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[7]  Fabian R. Wirth,et al.  On a small-gain approach to distributed event-triggered control , 2010, ArXiv.

[8]  Manuel Mazo,et al.  Decentralized event-triggered control with one bit communications , 2012, ADHS.

[9]  Panos J. Antsaklis,et al.  Event-triggered real-time scheduling for stabilization of passive and output feedback passive systems , 2011, Proceedings of the 2011 American Control Conference.

[10]  W. P. M. H. Heemels,et al.  Output-Based Event-Triggered Control With Guaranteed ${\cal L}_{\infty}$-Gain and Improved and Decentralized Event-Triggering , 2012, IEEE Transactions on Automatic Control.

[11]  P. Olver.  Nonlinear Systems , 2013 .

[12]  Xiaofeng Wang,et al.  Quantization Scheme Design in Distributed Event-Triggered Networked Control Systems , 2011 .

[13]  Prashant G. Mehta,et al.  Bode-Like Fundamental Performance Limitations in Control of Nonlinear Systems , 2010, IEEE Transactions on Automatic Control.

[14]  P. Antsaklis,et al.  : Event-Triggered Real-Time Scheduling For Stabilization of Passive / Output Feedback Passive Systems Technical Report of the ISIS Group at the University of Notre Dame isis-2010-001 October , 2010 , 2010 .

[15]  Karl Henrik Johansson,et al.  Control of Multi-Agent Systems via Event-based Communication , 2011 .

[16]  Karl Henrik Johansson,et al.  Event-triggered control for multi-agent systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[17]  Bernd Matschkal,et al.  Spherical logarithmic quantization and its application for DPCM , 2004 .

[18]  Paulo Tabuada,et al.  Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks , 2007, IEEE Transactions on Automatic Control.

[19]  Xiaofeng Wang,et al.  Asynchronous task execution in networked control systems using decentralized event-triggering , 2012, Syst. Control. Lett..

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

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

[22]  Manuel Mazo,et al.  On event-triggered and self-triggered control over sensor/actuator networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[23]  Xiaofeng Wang,et al.  Event-triggered broadcasting across distributed networked control systems , 2008, 2008 American Control Conference.

[24]  Manuel Mazo,et al.  An ISS self-triggered implementation of linear controllers , 2009, Autom..

[25]  Paulo Tabuada,et al.  To Sample or not to Sample: Self-Triggered Control for Nonlinear Systems , 2008, IEEE Transactions on Automatic Control.

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

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

[28]  Munther A. Dahleh,et al.  Feedback Control in the Presence of Noisy Channels: “Bode-Like” Fundamental Limitations of Performance , 2008, IEEE Transactions on Automatic Control.

[29]  Michael D. Lemmon,et al.  An event-triggered distributed primal-dual algorithm for Network Utility maximization , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[30]  Manuel Mazo,et al.  Decentralized Event-Triggered Control Over Wireless Sensor/Actuator Networks , 2010, IEEE Transactions on Automatic Control.

[31]  Xiaofeng Wang,et al.  Event-Triggering in Distributed Networked Systems with Data Dropouts and Delays , 2009, HSCC.

[32]  Stefan Pettersson,et al.  Analysis and Design of Hybrid Systems , 1999 .

[33]  Jan Lunze,et al.  A state-feedback approach to event-based control , 2010, Autom..

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

[35]  Xiaofeng Wang,et al.  Stabilizing bit-rates in quantized event triggered control systems , 2012, HSCC '12.