Continuous-time stochastic consensus: Stochastic approximation and Kalman–Bucy filtering based protocols

Tang, Huaibin; Li, Tao

doi:10.1016/j.automatica.2015.08.007

Cited by 40 publications

(16 citation statements)

References 23 publications

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“…Remark The stochastic approximation control gain γ ( t ) satisfying α 1 t − ς ≤ γ ( t ) ≤ α 2 t − ς or

γ false(t false) = \frac{d}{{false(t + b false)}^{ς}}

ς \in false(\frac{1}{2}, 1 false]

has been used in the works of Tang and Li and Chen et al Similarly, we can choose the control gain as

γ false(t false) = a false(t false) = \frac{d}{{false(ϕ t + b false)}^{ς}}

with

ς \in false(\frac{1}{τ}, 1 false]

and ϕ , b , d >0, such that all the conditions in Theorem are fulfilled. In addition, Theorem also indicates that if ρ ∈(1,2),

a false(t false) = \frac{d}{{false(ϕ t + b false)}^{ς}}

with

ς \in false(\frac{1}{ρ}, 1 false]

and ϕ , b , d >0, then the containment control can be achieved by

\int_{t_{0}}^{\infty} \frac{d}{{false(ϕ t + b false)}^{ς}} = \infty

and

\int_{t_{0}}^{\infty} \frac{d}{{false(ϕ t + b false)}^{ς ρ}} < \infty

.…”

Section: Containment Control With Multiplicative and Additive Noisesmentioning

confidence: 99%

“…In practical applications, the common cooperative control protocols for MASs in other works cannot be directly applied for solving the consensus problem with communication noises. In order to deal with the negative effect of additive noise, whose intensity is independent of agents' states, a noise attenuation technique was developed based on the stochastic approximation . The stochastic approximation with a time‐varying gain function is used for distributed control with communication noises such that each agent can reduce the weights to its neighbors gradually and then weakens the effect of noises.…”

Section: Introductionmentioning

confidence: 99%

“…In order to deal with the negative effect of additive noise, whose intensity is independent of agents' states, a noise attenuation technique was developed based on the stochastic approximation. 14 The stochastic approximation with a time-varying gain function is used for distributed control with communication noises such that each agent can reduce the weights to its neighbors gradually and then weakens the effect of noises. For instance, in the work of Li and Zhang, 15 a stochastic approximation-type time-varying gain (t) (∫ ∞ 0 (t)dt = ∞ and ∫ ∞ 0 (t) 2 dt < ∞) was first given and some necessary and sufficient conditions in mean square sense with additive noises were derived.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Containment control for distributed networks subject to multiplicative and additive noises with stochastic approximation–type protocols

Wang

Zuo

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper is concerned with the stochastic containment control problem for distributed network with multiplicative and additive noises, in which the stochastic approximation technique is utilized. A major challenge, compared with the existing results with multiplicative and additive noises, is that the involving leaders are dynamically changing. It is shown that finite boundedness for dynamical leaders is of great importance for addressing the stochastic containment control issue. A suitable approach is proposed to handle multiplicative and additive noises based on the stochastic approximation, and some necessary/sufficient conditions are derived for mean square convergence with mild requirements. Furthermore, the convergence rates are studied for both dynamical leaders and static leaders scenarios. We conclude this paper by using two illustrative examples to verify the effectiveness of the theoretical results.

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“…Remark The stochastic approximation control gain γ ( t ) satisfying α 1 t − ς ≤ γ ( t ) ≤ α 2 t − ς or

γ false(t false) = \frac{d}{{false(t + b false)}^{ς}}

ς \in false(\frac{1}{2}, 1 false]

has been used in the works of Tang and Li and Chen et al Similarly, we can choose the control gain as

γ false(t false) = a false(t false) = \frac{d}{{false(ϕ t + b false)}^{ς}}

with

ς \in false(\frac{1}{τ}, 1 false]

and ϕ , b , d >0, such that all the conditions in Theorem are fulfilled. In addition, Theorem also indicates that if ρ ∈(1,2),

a false(t false) = \frac{d}{{false(ϕ t + b false)}^{ς}}

with

ς \in false(\frac{1}{ρ}, 1 false]

and ϕ , b , d >0, then the containment control can be achieved by

\int_{t_{0}}^{\infty} \frac{d}{{false(ϕ t + b false)}^{ς}} = \infty

and

\int_{t_{0}}^{\infty} \frac{d}{{false(ϕ t + b false)}^{ς ρ}} < \infty

.…”

Section: Containment Control With Multiplicative and Additive Noisesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Containment control for distributed networks subject to multiplicative and additive noises with stochastic approximation–type protocols

Wang

Zuo

et al. 2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…It was shown that if the noise-attenuating noise gain is infinitesimal and of the same order with t  , where ∈(0.5,1), all the agents' states converge to the same value in the mean square sense at a rate of O(t  ). Extensions to the almost-sure consensus were made in [19]. The convergence rate of a linear SISO MAS with the leader-following structure was studied in [20], where each agent is allowed to have its own noise-attenuation gain.…”

mentioning

confidence: 99%

“…In all the aforementioned papers, only the asymptotic properties of the MASs were analyzed, while this paper also investigates the convergence rate (transient performance) of the MAS. Recently, a few papers [18][19][20] have made some early attempts to understand the convergence rate of MASs with communication noise. The convergence rate of a single-integrator MAS is studied in [18], where all agents share the same noiseattenuation gain.…”

mentioning

confidence: 99%

Reaching a stochastic consensus in the noisy networks of linear MIMO agents: Dynamic output-feedback and convergence rate

Wang

Cheng

Yang

et al. 2015

Sci. China Technol. Sci.

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This paper addresses the leader-following consensus problem of linear multi-agent systems (MASs) with communication noise. Each agent's dynamical behavior is described by a linear multi-input and multi-output (MIMO) system, and the agent's full state is assumed to be unavailable. To deal with this challenge, a state observer is constructed to estimate the agent's full state. A dynamic output-feedback based protocol that is based on the estimated state is proposed. To mitigate the effect of communication noise, noise-attenuation gains are also introduced into the proposed protocol. In this study, each agent is allowed to have its own noise-attenuation gain. It is shown that the proposed protocol can solve the mean square leader-following consensus problem of a linear MIMO MAS. Moreover, if all noise-attenuation gains are of (t  ), where ∈(0,1), the convergence rate of the MAS can be quantitatively analyzed. It turns out that all followers' states converge to the leader's state in the mean square sense at a rate of O(t  ). multi-agent system, mean square consensus, communication noise, noise-attenuation gain, convergence rate Citation:Wang Y P, Cheng L, Yang C G, et al. Reaching a stochastic consensus in the noisy networks of linear MIMO agents: Dynamic output-feedback and convergence rate.

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Scaled consensus for MASs with compound noises over Markovian switched topologies

Liang

Liu

et al. 2023

Asian Journal of Control

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This article aims to address the stochastic scaled consensus issue in almost surely and mean square sense of stochastic multiagent systems (SMASs) with compound noises in a Markovian switching setting. At first, based on stochastic approximation technique and nearest‐neighbor interaction rules, the stochastic scaled consensus controller is built for SMASs in presence of multiplicative and additive noise by designing a time‐varying gain. Meanwhile, some consensus criterions of SMASs are addressed if the union of the graph and time‐varying gain fulfill some mild requirements. Furthermore, the scaled consensus means that the agents' state variables tend to a prescribed proportion rather than the common value, so this behavior can be seen as non‐convergent behavior. The difference with most of excellent literatures is that the coexistence of noncooperative behavior and multiplicative noise generates that it is not easy to transform the multiplicative noise term into the form of an error equation, which means that the Lyapunov methods cannot be directly utilized in our article. To cope with this, we first demonstrate the boundedness for each agent's state, and hence the convergence can be achieved. Finally, in order to reveal the efficiency of our proposed protocol, the corresponding example is given in the simulation part.

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Continuous-time stochastic consensus: Stochastic approximation and Kalman–Bucy filtering based protocols

Cited by 40 publications

References 23 publications

Containment control for distributed networks subject to multiplicative and additive noises with stochastic approximation–type protocols

Containment control for distributed networks subject to multiplicative and additive noises with stochastic approximation–type protocols

Reaching a stochastic consensus in the noisy networks of linear MIMO agents: Dynamic output-feedback and convergence rate

Scaled consensus for MASs with compound noises over Markovian switched topologies

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