In this paper, we introduce a nonlinear time-varying coupling law, which can be designed in a fully decentralized manner and achieves approximate synchronization with arbitrary precision, under only mild assumptions on the individual vector fields and the underlying (undirected) graph structure. The proposed coupling law is motivated by the so-called funnel control method studied in adaptive control under the observation that arbitrary precision synchronization can be achieved for heterogeneous multi-agent systems by a high-gain coupling; consequently we call our novel synchronization method `(node-wise) funnel coupling.' By adjusting the conventional proof technique in the funnel control study, we are even able to obtain asymptotic synchronization with the same funnel coupling law. Moreover, the emergent collective behavior that arises for a heterogeneous multi-agent system when enforcing arbitrary precision synchronization by the proposed funnel coupling law, is analyzed in this paper. In particular, we introduce a single scalar dynamics called `emergent dynamics' which describes the emergent synchronized behavior of the multi-agent system under funnel coupling. Characterization of the emergent dynamics is important because, for instance, one can design the emergent dynamics first such that the solution trajectory behaves as desired, and then, provide a design guideline to each agent so that the constructed vector fields yield the desired emergent dynamics. We illustrate this idea via the example of a distributed median solver based on funnel coupling.
Beijing Institute of Technology（北京理工大学）；Beijing Institute of Control Engineering（北京控制工程研究所）
This work proposes a force control strategy with prescribed transient performance for the legs of a wheel-legged robotic system to realize the posture adjustment on uneven roads. A dynamic model of the robotic system is established with the body postures as inputs and the leg forces as outputs, such that the desired forces for the wheel-legs are calculated by the posture reference and feedback. Based on the funnel control scheme, the legs realize force tracking with prescribed transient performance. To improve the robustness of the force control system, an event-based mechanism is designed for…
In this note, we study the prescribed-time (PT) synchronization of multiweighted and directed complex networks (MWDCNs) via pinning control. Unlike finite-time and fixed-time synchronization, the time for synchronization can be preset as needed, which is independent of initial values and parameters like coupling strength. First and foremost, we reveal the essence of PT stability by improper integral, L'Hospital rule and Taylor expansion theory. Many controllers established previously for PT stability can be included in our new model. Then, we apply this new result on MWDCNs as an application. …
This paper considers the fixed-time control problem of a multi-agent system composed of a class of Euler-Lagrange dynamics with parametric uncertainty and a dynamic leader under a directed communication network. A distributed fixed-time observer is first proposed to estimate the desired trajectory and then a fixed-time controller is constructed by transforming uncertain Euler-Lagrange systems into second-order systems and utilizing the backstepping design procedure. The overall design guarantees that the synchronization errors converge to zero in a prescribed time independent of initial condit…
Distributed Safe Consensus Under Asymmetric Input and Time-Varying Output Constraints
Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati（智能系统引导、自主、学习与控制实验室，航空航天工程与工程力学系，辛辛那提大学）；Intelligent Systems and Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay（智能系统与控制实验室，航空航天工程系，印度班加罗尔理工学院）
