arXiv subjects

Shimin Wang

Publications and source records attributed to Shimin Wang.

26 records · Page 2Linked to original sources

arXiv2023

Nonlinear Bipartite Output Regulation with Application to Turing Pattern

In this paper, a bipartite output regulation problem is solved for a class of nonlinear multi-agent systems subject to static signed communication networks. A nonlinear distributed observer is proposed for a nonlinear exosystem with cooperation-competition interactions to address the problem. Sufficient conditions are provided to guarantee its existence and stability. The exponential stability of the observer is established. As a practical application, a leader-following bipartite consensus problem is solved for a class of nonlinear multi-agent systems based on the observer. Finally, a network of multiple pendulum systems is treated to support the feasibility of the proposed design. The possible application of the approach to generate specific Turing patterns is also presented.

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arXiv2023

Distributed Time- and Event-Triggered Observers for Linear Systems: Non-Pathological Sampling and Inter-Event Dynamics

For an autonomous linear time-invariant (LTI) system, a distributed observer with time-triggered periodic observations and event-triggered communication is proposed to estimate the state of the system. It is shown that the sampling period is critical for the existence of desirable observers. A necessary and sufficient condition is established to give all feasible sampling periods that lead to convergent error dynamics and characterize delicate relationships among sampling periods, topologies, and system matrices. An event-triggering mechanism based on locally sampled data is designed to regulate the communication among agents, and the convergence of the estimation errors under the mechanism holds for a class of positive and convergent triggering functions, which include the commonly used exponential function as a special case. The mixed time- and event-triggered architecture naturally excludes the existence of Zeno behavior as the system updates at discrete instants. When the triggering function is bounded by exponential functions, analytical characterization of the relationship among sampling, event triggering, and inter-event behaviour is established. Finally, several examples are provided to illustrate the effectiveness and merits of the theoretical results.

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arXiv2023

Leaderless Consensus of Heterogeneous Multiple Euler-Lagrange Systems with Unknown Disturbance

This paper studies the leaderless consensus problem of {heterogeneous} multiple networked Euler-Lagrange systems subject to persistent disturbances with unknown constant biases, amplitudes, initial phases, and frequencies. The main characteristic of this study is that none of the agents has information of a common reference model or of a common reference trajectory. Therefore, the agents must simultaneously and in a distributed way: achieve consensus to a common reference model (group model); achieve consensus to a common reference trajectory; {and} reject the unknown disturbances. We show that this is possible via a suitable combination of techniques of distributed `observers', internal model principle, and adaptive regulation. The proposed design generalizes recent results on group model learning, which have been studied for linear agents over undirected networks. In this work, group model learning is achieved for Euler-Lagrange dynamics over directed networks in the presence of persistent unknown disturbances.

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arXiv2022

Invariant tori for area-preserving maps with ultra-differentiable perturbation and Liouvillean frequency

We prove the existence of invariant tori to the area-preserving maps defined on $ \mathbb{R}^2\times\mathbb{T} $ \begin{equation*} \bar{x}=F(x,θ), \qquad \barθ=θ+α\, \,(α\in \mathbb{R}\setminus\mathbb{Q}), \end{equation*} where $ F $ is closed to a linear rotation, and the perturbation is ultra-differentiable in $ θ\in \mathbb{T},$ which is very closed to $C^{\infty}$ regularity. Moreover, we assume that the frequency $α$ is any irrational number without other arithmetic conditions and the smallness of the perturbation does not depend on $α$. Thus, both the difficulties from the ultra-differentiability of the perturbation and Liouvillean frequency will appear in this work. The proof of the main result is based on the Kolmogorov-Arnold-Moser (KAM) scheme about the area-preserving maps with some new techniques.

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arXiv2022

Learning nonlinear dynamics in synchronization of knowledge-based leader-following networks

Knowledge-based leader-following synchronization of heterogeneous nonlinear multi-agent systems is a challenging problem since the leader's dynamic information is unknown to any follower node. This paper proposes a learning-based fully distributed observer for a class of nonlinear leader systems, which can simultaneously learn the leader's dynamics and states. This class of leader dynamics is rather general and does not require a bounded Jacobian matrix. Based on this learning-based distributed observer, we further synthesize an adaptive distributed control law for solving the leader-following synchronization problem of multiple Euler-Lagrange systems subject to an uncertain nonlinear leader system. The results are illustrated by a simulation example.

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arXiv2022

Adaptive Cooperative Tracking and Parameter Estimation of an Uncertain Leader over General Directed Graphs

This paper studies cooperative tracking problem of heterogeneous Euler-Lagrange systems with an uncertain leader. Different from most existing works, system dynamic knowledge of the leader node is unaccessible to any follower node in our paper. Distributed adaptive observers are designed for all follower nodes, simultaneously estimate the state and parameters of the leader node. The observer design does not rely on the frequency knowledge of the leader node, and the estimation errors are shown to converge to zero exponentially. Moreover, the results are applied to general directed graphs, where the symmetry of Laplacian matrix does not hold. This is due to two newly developed Lyapunov equations, which solely depend on communication network topologies. Interestingly, using these Lyapunov equations, many results of multi-agent systems over undirected graphs can be extended to general directed graphs. Finally, this paper also advances the knowledge base of adaptive control systems by providing a main tool in the analysis of parameter convergence for adaptive observers.

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arXiv2020

Adaptive Consensus and Parameter Estimation of Multi-Agent Systems with An Uncertain Leader

In this note, the problem of simultaneous leader-following consensus and parameter estimation is studied for a class of multi-agent systems subject to an uncertain leader system. The leader system is described by a sum of sinusoids with unknown amplitudes, frequencies and phases. A distributed adaptive observer is established for each agent to estimate the unknown frequencies of the leader. It is shown that if the signal of the leader is sufficiently rich, the estimation errors of the unknown frequencies converge to zero asymptotically for all the agents. Based on the designed distributed adaptive observer, a distributed adaptive control law is synthesized for each agent to solve the leader-following consensus problem.

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arXiv2019

Adaptive Leader-Following Consensus for Multiple Euler-Lagrange Systems with an Uncertain Leader System

In this paper, we study the leader-following consensus problem of multiple Euler-Lagrange systems subject to an uncertain leader system. We first establish an adaptive distributed observer for a neutrally stable linear leader system whose system matrix is not known exactly. Under standard assumptions, this adaptive distributed observer can estimate and pass the leader's state to each follower through the communication network of the system without knowing the leader's system matrix exactly. Under the additional assumption that the leader's state is persistently exciting, this adaptive distributed observer can also asymptotically learn the parameters of the leader's system matrix. On the basis of this adaptive distributed observer, we further synthesize an adaptive distributed control law to solve our problem via the certainty equivalence principle. Our result allows the leader-following consensus problem of multiple Euler-Lagrange systems to be solved even if none of the followers knows the system matrix of the leader system exactly.

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