Dabo Xu

Consensus control of nonlinear leader–follower multi-agent systems with actuating disturbances

Abstract This paper studies a semi-global asymptotic consensus problem of nonlinear multi-agent systems with local actuating disturbances. For a modest nonlinear scenario, a consensus protocol is proposed based on a viable two-layer network. The consensus problem is treated as distributed output regulation, which is resolved by a joint decomposition of the zero-error constraint inputs and a configuration of a flexible internal model network. An illustrative example is also given to show the efficiency of the two-layer networked design.

Distributed Output Regulation of Nonlinear Multi-Agent Systems via Host Internal Model

This note presents a host internal model (h-IM) approach to distributed output regulation of reaching nonlinear leader-following consensus. Focusing on a basic nonlinear scenario of identical (or homogeneous) agents of a normal form, it is shown that the problem is solvable as long as its interaction digraph contains a certain directed spanning tree. A constructive Lyapunov protocol is proposed by incorporating a single h-IM. The result is also demonstrated by FitzHugh-Nagumo (FHN) and Lorenz type nonlinear dynamic networks.

Distributed node-to-node consensus of multi-agent systems with time-varying pinning links

In this paper, the distributed node-to-node consensus problem is addressed for a class of linear multi-agent systems with time-varying pinning links by using relative state feedback. The coordination goal in the present work is to make the states of each follower track those of its corresponding leader asymptotically where only a small fraction of followers can sense the states of their corresponding leaders through some switched communication channels. By using tools from M-matrix theory and stability analysis of switched systems theory, it is theoretically shown that such a node-to-node consensus in the closed-loop multi-agent systems can be guaranteed if each follower can be directly or indirectly influenced by at least one leader over some uniformly bounded time intervals, with the inner coupling matrix as well as the coupling strength being appropriately designed. Distributed node-to-node consensus for multi-agent systems with general Lipschitz-type nonlinear dynamics is also investigated. Numerical simulations are finally performed to verify the effectiveness of the theoretical results.

Output regulation of nonlinear output feedback systems with exponential parameter convergence

Abstract This paper revisits the global robust output regulation (GROR) problem of nonlinear output feedback systems with uncertain exosystems by error output feedback control. The problem was conventionally tackled by employing a linear canonical internal model and as a result, suitable adaptive stabilization has to be done for the augmented system to achieve output regulation. Distinguished from that, a novel nonlinear internal model approach is developed in the present study that successfully converts the GROR problem into a robust non-adaptive stabilization problem for the augmented system. The feature of the new approach is two-fold. On one hand, stabilization of augmented system is disentangled from any extra adaptive control law and thus the procedure is simplified. On the other hand, it leads to explicit strict Lyapunov characterization for the closed-loop system and consequently assures exponential parameter convergence.

Global adaptive output regulation for a class of nonlinear systems with iISS inverse dynamics using output feedback

Abstract This paper generalizes our recent results on global robust output regulation of output feedback systems with integral input-to-state stable (iISS) inverse dynamics in two aspects. First, we consider the general relative degree case instead of the unity relative degree case. For this purpose, the one step approach proposed previously has to be generalized to a recursive approach. Second, we allow the exosystem to be uncertain. For this purpose, we need to introduce an adaptive control technique to estimate the unknown parameter vector in the exosystem. A convergence analysis of the estimated parameter vector will also be given.

Cooperative Output Regulation of Heterogeneous Nonlinear Multi-Agent Systems With Unknown Control Directions

This technical note considers global cooperative output regulation for a class of heterogeneous nonlinear multi-agent systems. By using the internal model principle and the adaptive control technique, a novel distributed adaptive control scheme is developed. Contrary to most existing results, the proposed controller is applicable to multi-agent systems with agents of non-identical relative degrees and non-identical unknown control directions under a general digraph. Moreover, any existing Nussbaum-type functions can be adopted in the proposed control scheme, and the adopted Nussbaum-type functions can be non-identical for each agent. It is shown that global cooperative output regulation of the controlled multi-agent system can be achieved under some mild assumptions. A numerical example is finally presented to illustrate the effectiveness of the proposed controller.

Robust almost output consensus in networks of nonlinear agents with external disturbances

This paper considers robust almost output consensus control for heterogeneous and disturbed multi-agent nonlinear systems by distributed output feedback control. Taking the effect of inherent unmodeled disturbances into account, we develop a reduced order observer based consensus protocol with a performance constraint. Our study not only encompasses internal asymptotic output consensus, but also assures certain disturbance attenuation to the closed-loop system. Substantial difficulties due to nonidentical relative degrees and directed interaction graphs are surmounted in this result. Moreover, we show that in the linear case, it comes up with a novel H ∞ almost output consensus design that improves some results recently developed in the literature.

Global robust distributed output consensus of multi-agent nonlinear systems: An internal model approach

Abstract This paper studies the problem of global robust distributed output consensus of heterogeneous leader–follower multi-agent nonlinear systems by general directed output interactions. For a class of minimum-phase single-input single-output nonlinear agents having unity relative degree, it is shown that the problem is solvable by an internal model approach under certain mild conditions. A Lyapunov function based output-feedback control law is developed by converting the global output consensus into a global distributed stabilization problem for an augmented network.

Global robust stabilization of nonlinear cascaded systems with integral ISS dynamic uncertainties

Abstract The authors consider a global robust asymptotic stabilization problem (GRS) for cascaded systems having dynamic uncertainties that are not necessarily input-to-state stable (ISS). Specifically, a recursive Lyapunov design approach is developed by induction on the system relative degree, providing a smoothly globally stabilizing controller. It is applicable to nonlinear cascaded systems having multiple distinct iISS dynamic uncertainties. The proposed design is constructive and leads to an iISS-Lyapunov characterization in a superposition form for the closed-loop system.

Node-to-node consensus of multi-agent systems with switched pinning links

This paper considers the problem of distributed node-to-node consensus for general linear multi-agent systems with switched pinning links. The control goal in the present work is to make each follower track the corresponding leader asymptotically under the condition that only a small fraction of followers can sense their corresponding leaders through some switched communication channels. By using tools from M-matrix theory and switched systems theory, it is proved that such a node-to-node consensus can be achieved if each follower can be directly or indirectly influenced by at least one leader, and the inner linking matrix as well as coupling strength are appropriately designed.