Output feedback control of discrete‐time systems with self‐triggered controllers

This paper deals with the stability of discrete-time networked systems with multiple sensor nodes under dynamic scheduling protocols. Access to the communication medium is orchestrated by a weighted try-once-discard or by an independent and identically-distributed stochastic protocol that determines which sensor node can access the network at each sampling instant and transmit its corresponding data. Through a time-delay approach, a unified discrete-time hybrid system with time-varying delays in the dynamics and in the reset conditions is formulated under both scheduling protocols. Then, a new stability criterion for discrete-time systems with time-varying delays is proposed by the discrete counterpart of the second-order Bessel-Legendre integral inequality. The developed approach is applied to guarantee the stability of the resulting discrete-time hybrid system model with respect to the full state under try-once-discard or independent and identically-distributed scheduling protocol. The communication delays can be larger than the sampling intervals. Finally, the efficiency of the presented approach is illustrated by a cart-pendulum system. KEYWORDS discrete-time networked control systems, dynamic protocols, Lyapunov method, multiple sensors INTRODUCTIONWith the development of communication techniques, network topologies, and control methods, networked control systems (NCSs) have received increasing attention in the past decades due to its widespread applications. 1 Meanwhile, because the network is usually shared by multiple sensor, controller and actuator nodes, these distributed nodes will compete for access to the network as a result of bandwidth limitations and interference channels. There is a need for network protocols to address communication constraints, which prohibit that sensor, controller, or actuator nodes transmits their corresponding values simultaneously. In the literature, there are two basic types of scheduling protocols, namely, static and dynamic protocols.Static protocols correspond to the situation where the order of the activated nodes is chosen initially and remains fixed at each transmission instant. The well-known Round-Robin (RR) communication protocol 2 is one of the static protocols, where the nodes take turns transmitting its corresponding data in a predetermined and cyclic manner. Compared to static protocols, the dynamic protocols, 3 such as the often used try-once-discard (TOD) protocol and stochastic protocol, usually achieve better system performance than the static ones. 4 In the TOD protocol, the node, corresponding to the largest error Int J Robust Nonlinear Control. 2018;28:4479-4499.wileyonlinelibrary.com/journal/rnc

Section: Illustrative Examplementioning

confidence: 99%

Improved stability conditions for discrete‐time systems under dynamic network protocols

Liu

Seuret

Fridman

et al. 2018

“…The core idea of STC is that the next update event of the controller depends on the current sampled data and does not need to detect the error all the time. More results about STC can be found in References 17‐22 and the references cited there.…”

Section: Introductionmentioning

confidence: 99%

Parametric Lyapunov equation based event‐triggered and self‐triggered control of input constrained linear systems

Zhang

Zhou

Jiang

2020

This article studies semiglobal stabilization of input constrained linear systems based on the static and dynamic event-triggered control (ETC) and self-triggered control (STC). First, a static ETC based on the parametric Lyapunov equation (PLE) is designed. Then the corresponding dynamic ETC is also proposed. The main advantage of the proposed static and dynamic ETC algorithms is that the minimum interexecution time (MIET) as a decreasing function of the parameter in the PLE is given, which allows us to find easily a trade-off between the interexecution times (IETs) and the control performance. The fact that the MIET of the dynamic ETC is never less than that of the static ETC is also guaranteed. Next, in order to avoid continuous monitoring of the states, both static and dynamic STC are designed. The influence of the parameters on IETs of the static and dynamic STC is analyzed in detail. The nonoccurrence of the Zeno phenomenon is proved in all the control algorithms. Finally, the proposed algorithms are applied to the design of spacecraft rendezvous. Numerical simulations on the original nonlinear model of the spacecraft rendezvous control system show the control system effectiveness of the algorithms.

“…In the discrete‐time, stability analysis of large‐scale nonlinear systems with application to a power system network was developed in Gielen and Lazar . Self‐triggered control of discrete‐time systems was studied in Zhang et al The time‐delay approach to discrete‐time NCS was developed in Liu and Fridman, where the scheduling protocols from sensors to controllers were considered. The results were confined to the case of 1‐plant and 2‐sensor nodes.…”

Section: Introductionmentioning

confidence: 99%

Decentralized networked control of discrete‐time systems with local networks

Freirich

Fridman

2017

SummaryThis paper considers discrete-time large-scale networked control systems with multiple local communication networks connecting sensors, controllers, and actuators. The local networks operate asynchronously and independently of each other in the presence of variable sampling intervals, transmission delays, and scheduling protocols (from sensors to controllers). The time-delay approach that was recently suggested to decentralized stabilization of large-scale networked systems in the continuous time is extended to H ∞ decentralized control in the discrete time. An appropriate Lyapunov-Krasovskii method is presented that leads to efficient LMI conditions for the exponential stability and l 2 -gain analysis of the closed loop large-scale system. Differences from the continuous-time results are discussed. A numerical example of decentralized control of 2 coupled cart-pendulum systems illustrates the efficiency of the results.