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In this paper, the leader–follower robust synchronization issue is mainly addressed for reaction–diffusion neural networks (RDNNs) with multiple leaders and external disturbances under directed graphs. Based on the σ modification approach, we propose a novel distributed adaptive controller by adding a term − θ i (c i − 1) 2 to avoid the phenomenon of parameter drift, that is, the adaptive parameters grow to infinity. Meanwhile, different from the adaptive control algorithm proposed in the undirected graph, we introduce a new function χ i (t) to provide additional freedom for the design to achieve robust containment when confronted with external disturbances. Further, the robustness of tracking synchronization with one leader is guaranteed by the proposed adaptive controller when the external disturbances concerning L 2 norm are bounded. Finally, relevant numerical simulation graphics are displayed separately to verify the correctness of the related theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we study the consensus issues of multiagent systems (MASs) without any information of the system model by using the reinforcement learning (RL) method and event-based control strategy. First, we design an adaptive event-based consensus control protocol using the local sampled state information so that the consensus errors of all agents are uniformly ultimately bounded. The validity of the above event-triggered adaptive control protocol is confirmed by excluding the Zeno behavior within finite time. Then, based on the RL approach, we present a model-free algorithm to get the feedback gain matrix, and accomplish constructing the adaptive event-triggered control strategy without the knowledge of model information. Distinct with the existing related works, this RL-based event-triggered adaptive control algorithm only relies on the local sampled state information, irrelevant to any model information or global network information. Finally, we provide some examples to demonstrate the validity of the above adaptive event-based consensus algorithm. [ABSTRACT FROM AUTHOR]

In this article, we investigate the distributed adaptive consensus problem of parabolic partial differential equation (PDE) agents by output feedback on undirected communication networks, in which two cases of no leader and leader–follower with a leader are taken into account. For the leaderless case, a novel distributed adaptive protocol, namely, the vertex-based protocol, is designed to achieve consensus by taking advantage of the relative output information of itself and its neighbors for any given undirected connected communication graph. For the case of leader–follower, a distributed continuous adaptive controller is put forward to converge the tracking error to a bounded domain by using the Lyapunov function, graph theory, and PDE theory. Furthermore, a corollary that the tracking error tends to zero by replacing the continuous controller with the discontinuous controller is given. Finally, the relevant simulation results are further demonstrated to demonstrate the theoretical results obtained. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of distributed adaptive leader-follower coordination of partial differential systems (i.e., reaction-diffusion neural networks, RDNNs) with directed communication topology in the case of multiple leaders. Different from the dynamical networks with ordinary differential dynamics, the design of adaptive protocols is more difficult due to the existence of spatial variables and nonlinear terms in the model. Under directed networks, a novel adaptive control protocol is proposed to solve the containment control problem of RDNNs. By constructing proper Lyapunov functional and adopting some important prior knowledge, the stability of containment for coupled RDNNs is theoretically proved. Furthermore, a corollary about the leader-follower synchronization with a leader for coupled RDNNs with directed communication topology is given. In the end, two numerical examples are provided to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This article mainly solves the consensus issue of parabolic partial differential equation (PDE) agents with switching topology by output feedback. A novel edge-based adaptive control protocol is designed to reach consensus under the condition that the switching graphs are always connected at any switching instants. Different from the existing adaptive protocol associated with partial differential dynamics, the proposed adaptive observer-type law relies on the relative output information rather than relative state information. A proper Lyapunov functional is constructed and some important lemmas are used, then a sufficient condition is obtained for the consensus of parabolic PDE agents on switching graphs. Besides, a corollary about the distributed adaptive consensus of parabolic PDE agents on fixed undirected communication networks is given. Finally, the theoretical results are demonstrated by two numerical simulations. [ABSTRACT FROM AUTHOR]

In this study, a novel decentralized adaptive full-order sliding mode control framework is proposed for the robust synchronized formation motion of multiple unmanned aerial vehicles (UAVs) subject to system uncertainty. First, a full-order sliding mode surface in a decentralized manner is designed to incorporate both the individual position tracking error and the synchronized formation error while the UAV group is engaged in building a certain desired geometric pattern in three dimensional space. Second, a decentralized virtual plant controller is constructed which allows the embedded low-pass filter to attain the chattering free property of the sliding mode controller. In addition, robust adaptive technique is integrated in the decentralized chattering free sliding control design in order to handle unknown bounded uncertainties, without requirements for assuming a priori knowledge of bounds on the system uncertainties as stated in conventional chattering free control methods. Subsequently, system robustness as well as stability of the decentralized full-order sliding mode control of multiple UAVs is synthesized. Numerical simulation results illustrate the effectiveness of the proposed control framework to achieve robust 3D formation flight of the multi-UAV system. [ABSTRACT FROM AUTHOR]

In this study, the authors investigate the cluster synchronisation of coupled harmonic oscillators with multiple leaders in an undirected fixed network. Unlike many existing algorithms for cluster synchronisation of complex dynamical networks or group consensus of multi‐agent systems, which require global information of the underlying network such as eigenvalues of the coupling matrix or centralised control protocols, we propose a novel decentralised adaptive cluster synchronisation protocol for coupled harmonic oscillators. By using the decentralised adaptive cluster synchronisation protocol and without using any global information of the underlying network, all oscillators in the same group asymptotically synchronise with the corresponding leader even when only one oscillator in each group has access to the information of the corresponding leader. Numerical simulation results are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates fully distributed scaled non-negative edge-consensus problems of networked systems with actuator saturation and unmeasurable internal states. By using the adaptive control method, output-feedback-based low-gain technique, and graph theory, a new adaptive algorithm is designed to obtain scaled edge-consensus conditions, under which the difficulties caused by the constraints on edge states and controllers are overcome. There are three interesting characteristics that any global information of networks is not used in this paper's algorithm and result, including the number of vertexes and edges; the feasible solutions of the scaled edge-consensus conditions exist and can be easily obtained; the convergence rate of the controller is adjustable. Furthermore, the designed algorithm is expanded in the cases without actuator saturation. Finally, three examples are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates second-order consensus of multi-agent systems with heterogeneous nonlinear dynamics and time-varying delays by introducing novel decentralized adaptive strategies to both the coupling strengths and the feedback gains. Based on the Lyapunov stability theory, it is proved that the position and the velocity of each agent can converge to those of the virtual leader respectively, when the network is connected and at least one agent is informed, without any global information of the multi-agent system. Finally, some numerical simulations are presented to verify the theoretical results. [Copyright &y& Elsevier]

This paper investigates flocking problems with uncertain nonlinear multi-agent systems. Two distributed adaptive event-triggered control algorithms are proposed for leaderless and leader-follower flocking, separately. According to Lyapunov stability theory, under the proposed control protocols, we obtain some sufficient conditions to ensure stable flocking motion and maintain connectivity of network topology. And it is proven that there is a positive lower limit of the interval between any two trigger events, which indicates that the Zeno behavior will not occur. As a result, communication bandwidth resources are effectively saved on the premise of stable flocking. Lastly, numerical simulations are presented to verify the availability of the theoretical results. [ABSTRACT FROM AUTHOR]