To Zero or to Hold Control Inputs With Lossy Links?

This technical note studies the linear quadratic (LQ) performance of networked control systems where control packets are subject to loss. In particular we explore the two simplest compensation strategies commonly found in the literature: the zero-input strategy, in which the input to the plant is set to zero if a packet is dropped, and the hold-input strategy, in which the previous control input is used if packet is lost. We derive expressions for computing the optimal static gain for both strategies and we compare their performance on some numerical examples. Interestingly, none of the two can be claimed superior to the other, even for simple scalar systems, since there are scenarios where one strategy performs better then the other and scenarios where the converse occurs.

[1]  Haitao Mo,et al.  Feedback control over packet dropping network links , 2007, 2007 Mediterranean Conference on Control & Automation.

[2]  Guanrong Chen,et al.  Linear Stochastic Control Systems , 1995 .

[3]  Richard M. Murray,et al.  Control over a network: Using actuation buffers to reduce transmission frequency , 2007, 2007 European Control Conference (ECC).

[4]  E. Yaz,et al.  Linear and nonlinear estimation with uncertain observations , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[5]  Nicola Elia,et al.  Limitations of Linear Control Over Packet Drop Networks , 2011, IEEE Transactions on Automatic Control.

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

[7]  Luca Schenato,et al.  Optimal Estimation in Networked Control Systems Subject to Random Delay and Packet Drop , 2008, IEEE Transactions on Automatic Control.

[8]  Bruno Sinopoli,et al.  Distributed control applications within sensor networks , 2003, Proc. IEEE.

[9]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[10]  Tamer Basar,et al.  Optimal control of LTI systems over unreliable communication links , 2006, Autom..

[11]  Bruno Sinopoli,et al.  Towards Receding Horizon Networked Control , 2007 .

[12]  Oswaldo Luiz V. Costa,et al.  Stationary filter for linear minimum mean square error estimator of discrete-time Markovian jump systems , 2002, IEEE Trans. Autom. Control..

[13]  N. Elia,et al.  Limitations of linear remote control over packet drop networks , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  Johan Nilsson,et al.  Real-Time Control Systems with Delays , 1998 .

[15]  Qiang Ling,et al.  Optimal dropout compensation in networked control systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[16]  Tamer Basar,et al.  Optimal control of dynamical systems over unreliable communication links , 2004 .

[17]  Peter Seiler,et al.  Estimation with lossy measurements: jump estimators for jump systems , 2003, IEEE Trans. Autom. Control..

[18]  Bruno Sinopoli,et al.  Kalman filtering with intermittent observations , 2004, IEEE Transactions on Automatic Control.

[19]  D.M. Tilbury,et al.  Packet-based control , 2004, Proceedings of the 2004 American Control Conference.

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

[21]  Christoforos N. Hadjicostis,et al.  Feedback control utilizing packet dropping network links , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[22]  Björn Wittenmark,et al.  Stochastic Analysis and Control of Real-time Systems with Random Time Delays , 1999 .

[23]  Bruno Sinopoli,et al.  Foundations of Control and Estimation Over Lossy Networks , 2007, Proceedings of the IEEE.

[24]  Nasser E. Nahi,et al.  Optimal recursive estimation with uncertain observation , 1969, IEEE Trans. Inf. Theory.

[25]  Nicola Elia,et al.  Remote stabilization over fading channels , 2005, Syst. Control. Lett..

[26]  L. Schenato.  Kalman Filtering for networked control systems with random delay and packet loss , 2005 .