In this paper, we investigate leader-follower consensus (LFC) of multiple Euler-Lagrange systems (MELSs) under the case that followers can only measure partial output information of leader system, and the communication network among followers is switching and jointly connected. Firstly, in order to accurately estimate complete state information of the leader system in real time, we propose a distributed reduced-order observer, which is valid over a jointly connected switching network. Then, by applying this distributed reduced-order observer, we further design an observer-based controller for multiple Euler-Lagrange systems (MELSs) to reach leader-follower consensus (LFC). Distinct with the existing controllers for LFC of MELSs, this controller is robust for bounded external disturbances, and independent of the structure and features of Euler-Lagrange (EL) system. At last, a simulation example is given to confirm the effectiveness of the proposed distributed reduced-order observer and robust controller.Note to Practitioners—Many practical engineering applications (such as spacecrafts, mobile robot manipulators) can be modeled as multiple uncertain Euler-Lagrange systems, where each agent suffers external input disturbances, and only a portion of followers can measure partial components of leader’s output. However, most relevant works assumed that the dynamic information of each agent is completely known, agents do not suffer external input disturbances, and all follower agents can measure full-dimensional output of leader. How to achieve LFC for such MELSs has become a main focus of control researches. Thus, this paper proposes an adaptive distributed reduced-order observer-based consensus algorithm for such MELSs, whose communication network is switching and jointly connected. Finally, the effectiveness of the proposed algorithm is illustrated by a simulation example.

This article investigates the leader-follower consensus problem of multiple Euler-Lagrange (EL) systems, where each agent suffers uncertain external disturbances, and the communication links among agents experience faults. Besides, we consider a more general case that only a portion of followers can measure partial components of leader's output and access the dynamic information of leader. The main idea of solving the consensus problem in this article is proceeded in two steps. First, we design an adaptive distributed observer to estimate the full state information of leader in real time with resilience to communication link faults. Second, based on the proposed distributed observer, we propose a proportional-integral (PI) control protocol for each agent to track the trajectory of leader, which is model-independent and robust to uncertain external disturbances. Distinct from the existing leader-follower consensus protocols of multiple EL systems, the proposed distributed observer-based PI consensus protocol in this article is model-independent, which is irrelevant to the structures or features of EL system model. Finally, we present a simulation example to show the resilience of the above adaptive distributed observer and the robustness of the distributed observer-based consensus protocol.

In this article, we introduce adaptive robust observers for the estimation of comprehensive state variables and model parameters of a leader system. In particular, we suppose that the communication network among followers suffers communication link faults (CLFs), and the leader contains uncertainty, which means no follower knows the model parameters of leader system. Then, by applying the proposed observers, we elaborate on the design of a robust model-independent controller tailored for the leader-follower consensus problem (LFCP) of multiple Euler-Lagrange systems (MELSs). In contrast to the controllers currently employed for the LFCP in MELSs, the controller developed herein exhibits robustness against bounded external disturbances. Besides, the controller does not rely on the specific structure or characteristics of the Euler-Lagrange (EL) system model. At last, we provide simulation examples to demonstrate the validity of the proposed observers and the robust controller in the context of the LFCP for MELSs.

This article proposes a Q -learning (QL)-based algorithm for global consensus of saturated discrete-time multiagent systems (DTMASs) via output feedback. According to the low-gain feedback (LGF) theory, control inputs of the saturated DTMASs can avoid the saturation by utilizing the control policies with LGF matrices, which were computed from the modified algebraic Riccati equation (MARE) by requiring the information of system dynamics in most previous works. However, in this article, we first find the lower bound on the real part of Laplacian matrices' nonzero eigenvalues of directed network topologies. Then, we define a test control input and propose a Q -function to derive a QL Bellman equation, which plays an essential part of the QL algorithm. Subsequently, different from the previous works, the output-feedback gain (OFG) matrix of this article can be obtained by limited iterations of the QL algorithm without requiring the information of agent dynamics and network topologies of the saturated DTMASs. Furthermore, the saturated DTMASs can achieve global consensus rather than the semiglobal consensus of the previous results. Finally, the effectiveness of the QL algorithm is confirmed via two simulations.

In this article, we propose two model-free algorithms using state or output feedback for saturated discrete-time multiagent systems (SDTMASs) to attain global containment control. In most previous works, the control input can avoid saturation by utilizing the low gain feedback (LGF) method whereas requiring the knowledge of agent dynamics, and SDTMASs just can attain semi-global containment control. Distinct with the previous works, first, based on the$Q$-learning (QL) technique, this article defines a$Q$-function and deduces the corresponding QL Bellman equation, which is the most important part of the QL algorithm. Then, in order to solve the QL Bellman equation, we propose two iterative model-free algorithms using state and output feedback, and the LGF matrix can be acquired from that solution directly. Furthermore, under the state and output feedback control protocols with the feedback matrices obtained from the proposed model-free algorithms, the SDTMASs can achieve global containment control instead of semi-global containment control. Finally, we present some simulations to confirm the validity of the proposed algorithms.

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.

In this paper, the controllability problem is addressed for a two-time-scale discrete-time system with multiple agents. First, the system is described by a singularly perturbed difference equation expressed on fast timescale. Then, to eliminate the singular perturbation parameter, by using the iterative method and approximate approach, the two-time-scale system is separated into slow and fast subsystems. Subsequently, some sufficient and/or necessary conditions of controllability for the systems are derived by using matrix theory. Moreover, under three special network topologies, the necessary criteria for controllability are proposed via graph theory. Finally, we give a simulation example to illustrate the effectiveness of the proposed theoretical results.