A QSR-Dissipativity Based Design for Event-Triggered Networked Systems

Compositional control methods are well-suited for the design of large-scale control systems. QSR-dissipativity and passivity are closely related to stability and may be utilized to show Lyapunov and finite-gain stability for dynamical systems under certain conditions. Additionally, passivity is preserved under feedback and parallel interconnections of passive systems and may be utilized to build larger stable systems. In this paper, we present a QSR-dissipativity and passivity based analysis for event-triggered networked control systems (NCSs). We characterize QSR-dissipativity, passivity, and stability conditions for an event-triggered NCS in cases where an input–output event-triggering sampler is located on the plant's side, controller's side, or both sides leading to a considerable decrease in the communication load among subunits. We calculate passivity levels for the entire NCS. We show that the general passivity and stability conditions of the NCS depend on passivity properties of the plant and controller. Our results illustrate the tradeoffs amongst passivity levels, stability, and the rates of communication between subsystems. The motivation behind our work is that by designing and connecting individual stable passive event-triggered NCSs with desired passivity levels, one can design larger stable passive compositional networked systems that are suitable for the design and control of large-scale systems, such as cyber-physical systems.

[1]  Panos J. Antsaklis,et al.  SOS methods for demonstrating dissipativity for switched systems , 2014, 2014 American Control Conference.

[2]  Panos J. Antsaklis,et al.  Passivity-Based Design for Event-Triggered Networked Control Systems , 2018, IEEE Transactions on Automatic Control.

[3]  Michael D. Lemmon,et al.  Event-Triggered Feedback in Control, Estimation, and Optimization , 2010 .

[4]  Panos J. Antsaklis,et al.  Passivation and performance optimization using an extremum seeking co-simulation framework with application to Adaptive Cruise Control systems , 2016, 2016 American Control Conference (ACC).

[5]  Peter L. Lee,et al.  Process Control: The Passive Systems Approach , 2010 .

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

[7]  Mrdjan J. Jankovic,et al.  Constructive Nonlinear Control , 2011 .

[8]  Panos J. Antsaklis,et al.  A QSR-dissipativity and passivity based analysis of event-triggered networked control systems , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[9]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .

[10]  Sandra Hirche,et al.  Human-Oriented Control for Haptic Teleoperation , 2012, Proceedings of the IEEE.

[11]  Feng Zhu,et al.  Passivity analysis and passivation of feedback systems using passivity indices , 2014, 2014 American Control Conference.

[12]  Karl Johan Åström,et al.  Event Based Control , 2008 .

[13]  Panos J. Antsaklis,et al.  Event-triggered output feedback control for networked control systems using passivity: Achieving L2 stability in the presence of communication delays and signal quantization , 2013, Autom..

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

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

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

[17]  Ricardo G. Sanfelice,et al.  Input-output triggered control using Lp -stability over finite horizons , 2015 .

[18]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[19]  Panos J. Antsaklis,et al.  QSR-Dissipativity and Passivity Analysis of Event-Triggered Networked Control Cyber-Physical Systems , 2016, 1607.00553.

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

[21]  Edward A. Lee,et al.  Introduction to Embedded Systems - A Cyber-Physical Systems Approach , 2013 .