Cooperative adaptive finite‐time control for stochastic multi‐agent systems with input quantisation

Zhang, Yanhui; Sun, Jian; He, Wei; Li, Hongyi

doi:10.1049/iet-cta.2018.5330

Cited by 13 publications

(9 citation statements)

References 39 publications

(35 reference statements)

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“…Definition 1. (Consensus with probability one [29][30][31][32][33][34] : For system (3), the system is said to be consensus with probability one if for any initial states, there exists ax such that lim…”

Section: Consensus Protocolmentioning

confidence: 99%

“…To state our main results, Some necessary definitions are to be listed subsequently. Similar to finite‐time consensus in probability in [29–31, –34] , the definition of fixed‐time consensus in probability is described by means of consensus with probability one and the stochastic settling time function.Definition (Consensus with probability one [29–34] : For system (3), the system is said to be consensus with probability one if for any initial states, there exists a

\overset{x}{true}

such that

\begin{matrix} true \\ right \lim_{t \to \infty} normalP (() ∥ x_{i} false(t false) - \bar{x} ∥ = 0) = 1 \forall i \in I_{n} . \end{matrix}

…”

Section: Problem Formulationmentioning

confidence: 99%

“…Lemma [1, 13 29–34]: For the following stochastic differential equation:

\begin{matrix} true \\ right d x = g (x) d x + h (x) d ω (t), x (0) = x_{0}, \end{matrix}

where

ω (t)

denotes m‐dimensional Brown motion defined on a complete probability space

(Ω, F_{t}, P)

with the augmented filtration

{false{F false}}_{false(t \geq 0 false)}

generated by

ω (t)

, and functions

f : R_{+} \times R^{n} \to R^{n}

and

h : R_{+} \times R^{n} \to R^{n \times m}

are also called the coefficient of the equation, which are Borel measurable, continuous in x, and satisfy

f (t, 0) = 0

g (t, 0) = 0

for

t \geq 0

. If there exist a

C_{2}^{0} false(R^{n} false)

function

V : R^{n} \to R_{> 0}

, two

K_{\infty}

class functions

κ_{1}, κ_{2}

and positive numbers

k_{1}

α

with …”

Section: Problem Formulationmentioning

confidence: 99%

“…Moreover, as a kind of important problem of networked system, finite-time and fixed-time consensus problem of SMASs has been paid attentions from many researchers recently. For instance, [29][30][31][32] investigated finite-time consensus problem of first-order SMASs and second-order SMASs, respectively. Compared with [29][30][31][32], [-34] investigated fixed-time consensus of stochastic systems, and corresponding settling time satisfies conditions whose expectation is upper bounded by a constant regardless of initial conditions.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems

Yan

2020

IET Control Theory & Appl

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The paper devotes to study fixed‐time stability of stochastic nonlinear systems and fixed‐time consensus of stochastic multi‐agent systems (SMASs). Firstly, a new fixed‐time stability theorem is established and a high‐precise estimation of settling time is provided. Secondly, as an application, the fixed‐time consensus problem of SMASs is discussed in virtue of the established theorem. A new class of fixed‐time nonlinear consensus protocols with stochastic perturbation is designed by employing the neighbour's information. Based on graph theory, matrix theory and fixed‐time stability theorem, we prove that fixed‐time consensus of SMASs is achieved under the designed protocol. Moreover, some sufficient conditions are proposed to guarantee fixed‐time consensus of SMAS. It is shown that the settling time is not only independent of the initial conditions, but also it has higher precise. In the end, three numerical examples are provided to illustrate correctness of our theoretical results.

show abstract

Section: Consensus Protocolmentioning

confidence: 99%

\overset{x}{true}

such that

\begin{matrix} true \\ right \lim_{t \to \infty} normalP (() ∥ x_{i} false(t false) - \bar{x} ∥ = 0) = 1 \forall i \in I_{n} . \end{matrix}

…”

Section: Problem Formulationmentioning

confidence: 99%

“…Lemma [1, 13 29–34]: For the following stochastic differential equation:

\begin{matrix} true \\ right d x = g (x) d x + h (x) d ω (t), x (0) = x_{0}, \end{matrix}

where

ω (t)

denotes m‐dimensional Brown motion defined on a complete probability space

(Ω, F_{t}, P)

with the augmented filtration

{false{F false}}_{false(t \geq 0 false)}

generated by

ω (t)

, and functions

f : R_{+} \times R^{n} \to R^{n}

and

h : R_{+} \times R^{n} \to R^{n \times m}

are also called the coefficient of the equation, which are Borel measurable, continuous in x, and satisfy

f (t, 0) = 0

g (t, 0) = 0

for

t \geq 0

. If there exist a

C_{2}^{0} false(R^{n} false)

function

V : R^{n} \to R_{> 0}

, two

K_{\infty}

class functions

κ_{1}, κ_{2}

and positive numbers

k_{1}

α

with …”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems

Yan

2020

IET Control Theory & Appl

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show abstract

“…[31][32][33][34] Specifically, in the work of Zhang et al 31 a quantized control scheme was proposed to solve the stabilization problem of nonlinear networked systems with time-delay. Wei et al 32 and Zhang et al 33 studied the problem of finite-time stabilization for SISO stochastic systems with input quantization. However, most of the existing ETC schemes were developed without considering the influence of quantized signals.…”

Section: Introductionmentioning

confidence: 99%

Periodic event‐triggered control with multisource disturbances and quantized states

Zhao

Zheng

Ahn

et al. 2021

Intl J Robust & Nonlinear

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This study investigates periodic event-triggered (PET) output-feedback control method for nonlinear systems with quantized states and multisource disturbances. Based on a PET extended state observer, a novel PET composite control method is proposed. It not only can deal with the deterministic and stochastic disturbances but also can handle the quantization in the data transmission process. A PET extended state observer is used to simultaneously estimate the states and the disturbances. Moreover, both the static and dynamic event-triggered conditions are considered. Simulations and an experiment on a direct current brush motor are conducted to validate the proposed approach.

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Adaptive Finite-time Consensus for Second-order Nonlinear Multi-agent Systems with Input Quantization

Ren

Wang

Cai

2022

Int. J. Control Autom. Syst.

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Cooperative adaptive finite‐time control for stochastic multi‐agent systems with input quantisation

Cited by 13 publications

References 39 publications

Fixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems

Fixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems

Periodic event‐triggered control with multisource disturbances and quantized states

Adaptive Finite-time Consensus for Second-order Nonlinear Multi-agent Systems with Input Quantization

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