An introduction to event-triggered and self-triggered control

Recent developments in computer and communication technologies have led to a new type of large-scale resource-constrained wireless embedded control systems. It is desirable in these systems to limit the sensor and control computation and/or communication to instances when the system needs attention. However, classical sampled-data control is based on performing sensing and actuation periodically rather than when the system needs attention. This paper provides an introduction to event- and self-triggered control systems where sensing and actuation is performed when needed. Event-triggered control is reactive and generates sensor sampling and control actuation when, for instance, the plant state deviates more than a certain threshold from a desired value. Self-triggered control, on the other hand, is proactive and computes the next sampling or actuation instance ahead of time. The basics of these control strategies are introduced together with a discussion on the differences between state feedback and output feedback for event-triggered control. It is also shown how event- and self-triggered control can be implemented using existing wireless communication technology. Some applications to wireless control in process industry are discussed as well.

[1]  James Moyne,et al.  Using deadbands to reduce communication in networked control systems , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[2]  Randy Cogill,et al.  Event-based control using quadratic approximate value functions , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

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

[4]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[5]  W. P. M. H. Heemels,et al.  Periodic event-triggered control based on state feedback , 2011, IEEE Conference on Decision and Control and European Control Conference.

[6]  George A. Bekey,et al.  Adaptive sampling based on amplitude sensitivity , 1966 .

[7]  M. Velasco,et al.  The Self Triggered Task Model for Real-Time Control Systems , 2003 .

[8]  Sang Jeong Lee,et al.  Event-based modeling and control for the burnthrough point in sintering processes , 1999, IEEE Trans. Control. Syst. Technol..

[9]  Michael D. Lemmon,et al.  Weakly coupled event triggered output feedback control in wireless networked control systems , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

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

[11]  Hong Ye,et al.  Scheduling of networked control systems , 2001 .

[12]  Karl Henrik Johansson,et al.  Optimal stopping for event-triggered sensing and actuation , 2008, 2008 47th IEEE Conference on Decision and Control.

[13]  Sandra Hirche,et al.  Structural characterization of optimal event-based controllers for linear stochastic systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[14]  Valentina Orsini,et al.  Event-Triggered Internally Stabilizing Sporadic Control for MIMO Plants with Non Measurable State , 2011 .

[15]  S. Gupta Increasing the sampling efficiency for a control system , 1963 .

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

[17]  W. P. M. H. Heemels,et al.  Asynchronous measurement and control : a case study on motor synchronisation Running title : Asynchronous measurement and control , 2011 .

[18]  G. Bekey,et al.  Sensitivity of discrete systems to variation of sampling interval , 1966 .

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

[20]  J. Mitchell,et al.  Adaptive sampling technique , 1969 .

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

[22]  Anton Cervin,et al.  Sporadic event-based control of first-order linear stochastic systems , 2008, Autom..

[23]  Marek Miskowicz,et al.  Send-On-Delta Concept: An Event-Based Data Reporting Strategy , 2006, Sensors (Basel, Switzerland).

[24]  Karl Henrik Johansson,et al.  On the dual effect in state-based scheduling of networked control systems , 2011, Proceedings of the 2011 American Control Conference.

[25]  W. P. M. H. Heemels,et al.  Analysis and experimental validation of a sensor-based event-driven controller , 2007, 2007 American Control Conference.

[26]  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.

[27]  Karl-Erik Årzén,et al.  A simple event-based PID controller , 1999 .

[28]  K. Åström,et al.  Comparison of Periodic and Event Based Sampling for First-Order Stochastic Systems , 1999 .

[29]  Jorge Cortes,et al.  Self-triggered coordination of robotic networks for optimal deployment , 2012, Autom..

[30]  W. P. M. H. Heemels,et al.  Model-based periodic event-triggered control for linear systems , 2013, Autom..

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

[32]  Karl Henrik Johansson,et al.  Scheduling packets for Event-triggered control , 2009, 2009 European Control Conference (ECC).

[33]  Karl Johan Åström,et al.  Log-concave Observers , 2006 .

[34]  A. Liff,et al.  On the optimum sampling rate for discrete-time modeling of continuous-time systems , 1966 .

[35]  Mato Baotic,et al.  Multi-Parametric Toolbox (MPT) , 2004, HSCC.

[36]  Manuel Mazo,et al.  Input-to-state stability of self-triggered control systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[37]  Elbert Hendricks,et al.  Problems in event based engine control , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[38]  Paulo Tabuada,et al.  Periodic event-triggered control for nonlinear systems , 2013, 52nd IEEE Conference on Decision and Control.

[39]  Maria Domenica Di Benedetto,et al.  Digital self triggered robust control of nonlinear systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[40]  J.H. Braslavsky,et al.  Level Crossing Sampling in Feedback Stabilization under Data-Rate Constraints , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[41]  Daniel Lehmann,et al.  Event-based output-feedback control , 2011, 2011 19th Mediterranean Conference on Control & Automation (MED).

[42]  A. Pascoal,et al.  Self-Triggered Output Feedback Control of Linear Plants in the Presence of Unknown Disturbances , 2011, IEEE Transactions on Automatic Control.

[43]  Paulo Tabuada,et al.  A unifying Lyapunov-based framework for the event-triggered control of nonlinear systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[44]  Carlo Fischione,et al.  Modeling and stability analysis of hybrid multiple access in the IEEE 802.15.4 protocol , 2013, TOSN.

[45]  A. Girotra,et al.  Performance Analysis of the IEEE 802 . 11 Distributed Coordination Function , 2005 .

[46]  Michael D. Lemmon,et al.  Weakly coupled event triggered output feedback system in wireless networked control systems , 2011, Discrete Event Dynamic Systems.

[47]  Manuel Mazo,et al.  On self-triggered control for linear systems: Guarantees and complexity , 2009, 2009 European Control Conference (ECC).

[48]  Paulo Tabuada,et al.  On the Benefits of Relaxing the Periodicity Assumption for Networked Control Systems over CAN , 2009, 2009 30th IEEE Real-Time Systems Symposium.

[49]  Wassim M. Haddad,et al.  Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control , 2006 .

[50]  Anton Cervin,et al.  Comparison of LTI and event-based control for a moving cart with quantized position measurements , 2009, 2009 European Control Conference (ECC).

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

[52]  Panos J. Antsaklis,et al.  Stability of model-based networked control systems with time-varying transmission times , 2004, IEEE Transactions on Automatic Control.

[53]  Daniel Lehmann,et al.  Extension and experimental evaluation of an event-based state-feedback approach , 2011 .

[54]  Mircea Lazar,et al.  On Event Based State Estimation , 2009, HSCC.

[55]  W. P. M. H. Heemels,et al.  Analysis of event-driven controllers for linear systems , 2008, Int. J. Control.

[56]  W. P. M. H. Heemels,et al.  On integration of event-based estimation and robust MPC in a feedback loop , 2010, HSCC '10.

[57]  W. Brockett,et al.  Minimum attention control , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[58]  Karl Henrik Johansson,et al.  Steady state performance analysis of multiple state-based schedulers with CSMA , 2011, IEEE Conference on Decision and Control and European Control Conference.

[59]  Paulo Tabuada,et al.  Exploiting Isochrony in Self-Triggered Control , 2010, IEEE Transactions on Automatic Control.

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

[61]  Manuel Mazo,et al.  Self-triggered control over wireless sensor and actuator networks , 2011, 2011 International Conference on Distributed Computing in Sensor Systems and Workshops (DCOSS).

[62]  Xiaofeng Wang,et al.  Self-Triggering Under State-Independent Disturbances , 2010, IEEE Transactions on Automatic Control.

[63]  Carlos Silvestre,et al.  Self-triggered state feedback control of linear plants under bounded disturbances , 2010, 49th IEEE Conference on Decision and Control (CDC).

[64]  W. P. M. H. Heemels,et al.  Periodic Event-Triggered Control for Linear Systems , 2013, IEEE Trans. Autom. Control..

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

[66]  Paulo Tabuada,et al.  On the minimum attention control problem for linear systems: A linear programming approach , 2011, IEEE Conference on Decision and Control and European Control Conference.

[67]  D. Ciscato,et al.  On increasing sampling efficiency by adaptive sampling , 1967, IEEE Transactions on Automatic Control.

[68]  George A. Perdikaris Computer Controlled Systems , 1991 .