On the trade-off between communication and control cost in event-triggered deadbeat control

We consider a stochastic system where the communication between the controller and the actuator is triggered by a thresholdbased rule. The communication is performed across an unreliable link that stochastically erases transmitted packets. To decrease the communication burden, and as a partial protection against dropped packets, the controller sends a sequence of control commands to the actuator in each packet. These commands are stored in a buffer and applied sequentially until the next control packet arrives. In this context, we study dead-beat control laws and compute the expected linear-quadratic loss of the closed-loop system for any given event-threshold. Furthermore, we provide analytical expressions that quantify the trade-off between the communication cost and the control performance of event-triggered control systems. Numerical examples demonstrate the effectiveness of the proposed technique.

[1]  Tongwen Chen,et al.  Optimal Sampling and Performance Comparison of Periodic and Event Based Impulse Control , 2012, IEEE Transactions on Automatic Control.

[2]  Vijay Gupta,et al.  On the trade-off between control performance and communication cost for event-triggered control over lossy networks , 2013, 2013 European Control Conference (ECC).

[3]  Luca Schenato,et al.  To Zero or to Hold Control Inputs With Lossy Links? , 2009, IEEE Transactions on Automatic Control.

[4]  John Odentrantz,et al.  Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues , 2000, Technometrics.

[5]  Frank Allgöwer,et al.  The performance of event-based control for scalar systems with packet losses , 2012, 2012 IEEE 51st 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]  Tamás Linder,et al.  On Rates of Convergence for Markov Chains Under Random Time State Dependent Drift Criteria , 2016, IEEE Transactions on Automatic Control.

[8]  João Pedro Hespanha,et al.  Linear Systems Theory , 2009 .

[9]  Manjunath B. G.,et al.  Moments Calculation for the Double Truncated Multivariate Normal Density , 2009, Journal of Behavioral Data Science.

[10]  M. T. Qureshi,et al.  Lyapunov Matrix Equation in System Stability and Control , 2008 .

[11]  Panos J. Antsaklis,et al.  Networked state estimation over a shared communication medium , 2013, 2013 American Control Conference.

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

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

[14]  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).

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

[16]  Ling Shi,et al.  A Stochastic Online Sensor Scheduler for Remote State Estimation With Time-Out Condition , 2014, IEEE Transactions on Automatic Control.

[17]  Uwe D. Hanebeck,et al.  Event-based LQG Control over Networks with Random Transmission Delays and Packet Losses , 2013 .

[18]  Daniel E. Quevedo,et al.  Robust stability of packetized predictive control of nonlinear systems with disturbances and Markovian packet losses , 2012, Autom..

[19]  Vijay Gupta,et al.  On Stability in the Presence of Analog Erasure Channel Between the Controller and the Actuator , 2010, IEEE Transactions on Automatic Control.

[20]  Tamer Basar,et al.  Optimal control with limited controls , 2006, 2006 American Control Conference.

[21]  Marcelo D. Fragoso,et al.  Optimal Control for Continuous-Time Linear Quadratic Problems with Infinite Markov Jump Parameters , 2001, SIAM J. Control. Optim..

[22]  Daniel E. Quevedo,et al.  Stochastic Stability of Event-Triggered Anytime Control , 2013, IEEE Transactions on Automatic Control.

[23]  Maben Rabi,et al.  Packet based Inference and Control , 2006 .

[24]  John O'Reilly,et al.  The discrete linear time invariant time-optimal control problem - An overview , 1981, Autom..

[25]  Vijay Gupta,et al.  Input-to-state stability of hybrid systems with receding horizon control in the presence of packet dropouts , 2012, Autom..

[26]  K. Åström,et al.  Comparison of Riemann and Lebesgue sampling for first order stochastic systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..