TY - JOUR

T1 - Networked control with stochastic scheduling

AU - Liu, Kun

AU - Fridman, Emilia

AU - Johansson, Karl Henrik

N1 - Publisher Copyright:
© 1963-2012 IEEE.

PY - 2015/11/1

Y1 - 2015/11/1

N2 - This note develops the time-delay approach to networked control systems with scheduling protocols, variable delays and variable sampling intervals. The scheduling of sensor communication is defined by a stochastic protocol. Two classes of protocols are considered. The first one is defined by an independent and identically-distributed stochastic process. The activation probability of each sensor node for this protocol is a given constant, whereas it is assumed that collisions occur with a certain probability. The resulting closed-loop system is a stochastic impulsive system with delays both in the continuous dynamics and in the reset equations, where the system matrices have stochastic parameters with Bernoulli distributions. The second scheduling protocol is defined by a discrete-time Markov chain with a known transition probability matrix taking into account collisions. The resulting closed-loop system is a Markovian jump impulsive system with delays both in the continuous dynamics and in the reset equations. Sufficient conditions for exponential mean-square stability of the resulting closed-loop system are derived via a Lyapunov-Krasovskii-based method. The efficiency of the method is illustrated on an example of a batch reactor. It is demonstrated how the time-delay approach allows treating network-induced delays larger than the sampling intervals in the presence of collisions.

AB - This note develops the time-delay approach to networked control systems with scheduling protocols, variable delays and variable sampling intervals. The scheduling of sensor communication is defined by a stochastic protocol. Two classes of protocols are considered. The first one is defined by an independent and identically-distributed stochastic process. The activation probability of each sensor node for this protocol is a given constant, whereas it is assumed that collisions occur with a certain probability. The resulting closed-loop system is a stochastic impulsive system with delays both in the continuous dynamics and in the reset equations, where the system matrices have stochastic parameters with Bernoulli distributions. The second scheduling protocol is defined by a discrete-time Markov chain with a known transition probability matrix taking into account collisions. The resulting closed-loop system is a Markovian jump impulsive system with delays both in the continuous dynamics and in the reset equations. Sufficient conditions for exponential mean-square stability of the resulting closed-loop system are derived via a Lyapunov-Krasovskii-based method. The efficiency of the method is illustrated on an example of a batch reactor. It is demonstrated how the time-delay approach allows treating network-induced delays larger than the sampling intervals in the presence of collisions.

KW - Lyapunov functional

KW - Networked control systems

KW - Stochastic impulsive system

KW - Stochastic protocols

UR - http://www.scopus.com/inward/record.url?scp=84946781697&partnerID=8YFLogxK

U2 - 10.1109/TAC.2015.2414812

DO - 10.1109/TAC.2015.2414812

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84946781697

SN - 0018-9286

VL - 60

SP - 3071

EP - 3076

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 11

M1 - 7063933

ER -