Event-triggered sliding mode control of stochastic systems via output feedback

Wu, Ligang; Gao, Yabin; Liu, Jianxing; Li, Hongyi

doi:10.1016/j.automatica.2017.04.032

Cited by 483 publications

(213 citation statements)

References 45 publications

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“…From , Ξ 11 < 0, Q 1 > 0, Q > 0, that is,

P^{T} A + A^{T} P + F_{1} E + E^{T} F_{1}^{T} < 0 .

Then, pre and postmultiplying by V T and V , we have

([], \begin{matrix} center center \\ array # & array # \\ array # & array {\tilde{P}}_{22}^{T} {\tilde{A}}_{22} + {\tilde{A}}_{22}^{T} {\tilde{P}}_{22} \end{matrix}) < 0 .

This implies that

{\overset{A}{true}}_{22}

is nonsingular. Thus, the pair ( E , A ) is regular and impulse free . We construct a Lyapunov‐Krasovskii functional as

V false(t false) = I_{1} false(t false) + I_{2} false(t false) + I_{3} false(t false),

where

\begin{matrix} right I_{1} (t) & left = x^{T} (t) E^{T} P x (t) & right \\ right I_{2} (t) & left = \int_{t - τ_{m}}^{t} x^{T} (s) Q_{1} x (s) d s + \int_{t - \bar{τ}}^{t - τ_{m<...>}} \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

Network‐based integral sliding mode control for descriptor systems with event‐triggered sampling scheme

Wang

Zhang

Ren

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper investigates event‐triggered sliding mode control for descriptor systems subject to networked‐induced delay. For handling disturbance and saving data transmission in networks for descriptor systems, sliding model control and event‐triggered control are combined, whereas how to combine them to design a stable controller is challenging due to the complexity of descriptor systems. Firstly, a new discrete event‐triggered scheme is introduced for deciding whether sampled data is sent out or not for networked‐based descriptor systems. Secondly, integral‐type switching surface and event‐triggered scheme are integrated resulting in a novel time‐delay system. The existence condition of integral‐type switching surface and the stability condition of the sliding mode dynamic are presented. An event‐triggered sliding mode controller is derived for driving the closed‐loop system trajectories to the practical switching surface in finite time. Finally, two examples are employed to show the effectiveness and advantages of the proposed method.

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“…From , Ξ 11 < 0, Q 1 > 0, Q > 0, that is,

P^{T} A + A^{T} P + F_{1} E + E^{T} F_{1}^{T} < 0 .

Then, pre and postmultiplying by V T and V , we have

([], \begin{matrix} center center \\ array # & array # \\ array # & array {\tilde{P}}_{22}^{T} {\tilde{A}}_{22} + {\tilde{A}}_{22}^{T} {\tilde{P}}_{22} \end{matrix}) < 0 .

This implies that

{\overset{A}{true}}_{22}

is nonsingular. Thus, the pair ( E , A ) is regular and impulse free . We construct a Lyapunov‐Krasovskii functional as

V false(t false) = I_{1} false(t false) + I_{2} false(t false) + I_{3} false(t false),

where

\begin{matrix} right I_{1} (t) & left = x^{T} (t) E^{T} P x (t) & right \\ right I_{2} (t) & left = \int_{t - τ_{m}}^{t} x^{T} (s) Q_{1} x (s) d s + \int_{t - \bar{τ}}^{t - τ_{m<...>}} \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

Network‐based integral sliding mode control for descriptor systems with event‐triggered sampling scheme

Wang

Zhang

Ren

et al. 2019

Intl J Robust & Nonlinear

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“…for t ∈ [t k , t k+1 ). Now we want to point out the self-triggered mechanism (21) guarantees inequality (23) hold. The self-triggered mechanism is online forecasting device.…”

Section: Propositionmentioning

confidence: 99%

Tracking Control for Stochastic Multi‐Agent Systems Based on Hybrid Event‐Triggered Mechanism

Xing

Deng

2018

Asian Journal of Control

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This paper deals with the leader‐following consensus for nonlinear stochastic multi‐agent systems. To save communication resources, a new centralized/distributed hybrid event‐triggered mechanism (HETM) is proposed for nonlinear multi‐agent systems. HETMs can be regarded as a synthesis of continuous event‐triggered mechanism and time‐driven mechanism, which can effectively avoid Zeno behavior. To model the multi‐agent systems under centralized HETM, the switched system method is applied. By utilizing the property of communication topology, low‐dimensional consensus conditions are obtained. For the distributed hybrid event‐triggered mechanism, due to the asynchronous event‐triggered instants, the time‐varying system method is applied. Meanwhile, the effect of network‐induced time‐delay on the consensus is also considered. To further reduce the computational resources by constantly testing whether the broadcast condition has been violated, self‐triggered implementations of the proposed event‐triggered communication protocols are also derived. A numerical example is given to show the effectiveness of the proposed method.

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“…Remark Notice that the equivalent control law approach has been widely used to analyze the stability of the SMC systems (see, eg, other related works). However, it follows from and that

s false(k + 1 false) = F C false(A + normalΔ A false(k false) false) x false(k false) + F C B sans-serifg false(x, y false) + F C B ((), I - Φ_{σ false(k false)}) u false(k - 1 false) + F C B Φ_{σ false(k false)} ū false(k false),

from which one it is clear that the equivalent control law approach is no longer applicable here due to the singularity of the matrix F C B Φ σ ( k ) , and this makes the stability analysis of the SMC systems under the round‐robin protocol more challenging yet interesting.…”

Section: Design Of Static Output‐feedback Smc Under Round‐robin Protocolmentioning

confidence: 99%

Static output‐feedback sliding mode control under round‐robin protocol

Song

Wang

Niu

2018

Intl J Robust & Nonlinear

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Summary This paper addresses the static output‐feedback sliding mode control (SMC) problem for a class of uncertain control systems subject to the round‐robin protocol scheduling, in which the communication between the controller and the actuators is regulated by the round‐robin protocol, that is, only one actuator node gets the access to the transmission network at each instant and the other actuators utilize the values stored in the zero‐order holders. A key issue of the addressed problem is how to design both the sliding surface and the sliding mode controller subject to the kind of actuator signals depending on protocol scheduling and zero‐order holders. By only using the measured output information, a linear sliding surface is constructed, and then, a token‐dependent SMC law is designed properly with the aid of an updating rule on actuator input. Moreover, suitable token‐dependent Lyapunov functions are exploited to obtain sufficient conditions for guaranteeing the asymptotic stability of the closed‐loop systems and the reachability of the specified sliding surface. Furthermore, based upon a separation strategy, a convex optimization algorithm is proposed to obtain the controller gains. Finally, the effectiveness of the developed static output‐feedback SMC design scheme is verified in an industrial continuous‐stirred tank reactor system.

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Event-triggered sliding mode control of stochastic systems via output feedback

Cited by 483 publications

References 45 publications

Network‐based integral sliding mode control for descriptor systems with event‐triggered sampling scheme

Network‐based integral sliding mode control for descriptor systems with event‐triggered sampling scheme

Tracking Control for Stochastic Multi‐Agent Systems Based on Hybrid Event‐Triggered Mechanism

Static output‐feedback sliding mode control under round‐robin protocol

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