Dynamic Leader Research Articles

Scaled Tracking Consensus in Discrete-Time Second-Order Multiagent Systems With Random Packet Dropouts

This article focuses on the issue of scaled tracking consensus for discrete-time second-order multiagent systems under random packet dropouts, where the cases with a static leader and a dynamic leader are considered, respectively. The scaled tracking consensus means that all agents reach a consensus value determined by the leader but with different scales, and the phenomenon of packet dropout on each communication link is described as a Bernoulli variable independent of other communication links. By virtue of random environment-based scaled consensus algorithms, it is shown how to reconstruct the original system into augmented error systems with random coefficient matrices. With the kind assistance of substochastic matrix and super-stochastic matrix, sufficient conditions for the cases with a static leader and a dynamic leader are derived, respectively. Moreover, computer simulations are performed to demonstrate the dynamics of network agents under random packet dropouts.

Sampled-data containment control for double-integrator agents with dynamic leaders with nonzero inputs

The objective of containment control in multi-agent systems is to design control algorithms for the followers to converge to the convex hull spanned by the leaders. Sampled-data based containment control algorithms are suitable for the cases where the power supply and sensing capacity are limited, due to their low-cost and energy-saving features resulting from discrete sensing and interactions. In addition, sampled-data control has advantages in performance, price and generality. On the other hand, when the agents have double-integrator dynamics and the leaders are dynamic with nonzero inputs, the existing algorithms are not directly applicable in a sampled-data setting. To this end, this paper proposes a sampled-data based containment control algorithm for a group of double-integrator agents with dynamic leaders with nonzero inputs under directed communication networks. By applying the proposed control algorithm, the followers converge to the convex hull spanned by the dynamic leaders with bounded position and velocity containment control errors, and the ultimate bound of the overall containment error is proportional to the sampling period. A numerical simulation is presented to illustrate the proposed algorithm.

Time-varying formation tracking control for high-order nonlinear multi-agent systems in fixed-time framework

In this paper, we investigate the time-varying formation tracking control (TVFTC) problem for high-order uncertain nonlinear multi-agent systems (MASs) with a dynamic leader. Both unknown disturbances and uncertain nonlinear functions are considered. A novel fixed-time TVFTC strategy is proposed with two steps, which can avoid the communication loop problem. Firstly, a distributed fixed-time observer (DFTO) for the directed graph is introduced, such that the leader’s information can be accurately obtained by each agent within a bounded time. Secondly, by using fixed-time technique, a Lyapunov-function-based design process has been schemed to avoid the singularity problem. The developed TVFTC protocols can ensure all the followers achieve the desired time-varying formation and track the leader simultaneously. Furthermore, according to practical requirements, the configuration of formation can be chosen as arbitrary shape and the corresponding convergence time is allowed to be pre-estimated or preset. Stability analysis and some simulation examples for the control strategy are given, which further verify the validity.

Distributed event‐triggered tracking control with a dynamic leader for multiple Euler‐Lagrange systems under directed networks

SummaryThe distributed tracking control for multiple Euler‐Lagrange systems with a dynamic leader is investigated in this article via the event‐triggered approach. Only a portion of followers have access to the leader, and the communication topology among all agents is directed that contains a directed spanning tree rooted at the leader. The case that the leader's generalized velocity is constant is first considered, and a distributed event‐based control law is developed by using a velocity estimator. When the leader's generalized velocity is time‐varying, novel distributed continuous estimators are proposed to avoid the undesirable chattering effect while guaranteeing that the estimate errors converge to zeros. With the designed distributed estimators, another distributed event‐based control protocol is provided. Controller update frequency and resource consumption in our work can be reduced by applying the aforementioned two distributed control laws, and the tracking errors can converge to zeros. In addition, it is rigorously proved that no agent exhibits Zeno behavior. Finally, the effectiveness of the proposed distributed event‐based control laws is elucidated by a number of simulation examples.

Prescribed Performance Adaptive Fuzzy Containment Control for Nonlinear Multiagent Systems Using Disturbance Observer

This article focuses on the containment control problem for nonlinear multiagent systems (MASs) with unknown disturbance and prescribed performance in the presence of dead-zone output. The fuzzy-logic systems (FLSs) are used to approximate the unknown nonlinear function, and a nonlinear disturbance observer is used to estimate unknown external disturbances. Meanwhile, a new distributed containment control scheme is developed by utilizing the adaptive compensation technique without assumption of the boundary value of unknown disturbance. Furthermore, a Nussbaum function is utilized to cope with the unknown control coefficient, which is caused by the nonlinearity in the output mechanism. Moreover, a second-order tracking differentiator (TD) is introduced to avoid the repeated differentiation of the virtual controller. The outputs of the followers converge to the convex hull spanned by the multiple dynamic leaders. It is shown that all the signals are semiglobally uniformly ultimately bounded (SGUUB), and the local neighborhood containment errors can converge into the prescribed boundary. Finally, the effectiveness of the approach proposed in this article is illustrated by simulation results.

Quasi‐synchronization of multilayer heterogeneous networks with a dynamic leader

SummaryThis article considers the pinning quasi‐synchronization problem for a class of leader‐following multilayer heterogeneous complex networks. The leader has nonzero control inputs that are unavailable to the followers. Multilayer heterogeneous networks with heterogeneous node dynamics and two different layer structures are proposed in this article. Two types of discontinuous coupling laws are designed for achieving synchronization in multilayer heterogeneous networks. Based on Lyapunov stability theory and the matrix theory, some sufficient criteria for pinning quasi‐synchronization are derived, and the upper bound of quasi‐synchronization errors is solved. Finally, numerical simulations are performed to illustrate the effectiveness of the theoretical results.

Event-Triggered Fuzzy Adaptive Containment Control for Nonlinear Multiagent Systems With Unknown Bouc–Wen Hysteresis Input

This article investigates the event-triggered containment control problem for stochastic nonlinear multiagent systems with unknown Bouc–Wen hysteresis input. Based on the backstepping technique, an adaptive fuzzy event-triggered containment control scheme is proposed, which is conditionally updated only at the sampled instants. Fuzzy logic systems are used to approximate the unknown nonlinear functions. In addition, a Nussbaum function is utilized to eliminate the effect of unknown hysteresis. Moreover, an event-triggered mechanism is introduced to reduce the communication burden. By using stochastic Lyapunov stability theory and graph theory, it is proved that all signals in the closed-loop system are semiglobally uniformly ultimately bounded. Meanwhile, all the followers’ outputs converge to the dynamic convex hull spanned by the dynamic leaders. Finally, the effectiveness of the proposed control scheme is illustrated by some simulation results.

Personal reflections on 30 years of social work development in China

ABSTRACT China has developed modern social work over the past 30 years, introducing new theories and models of good practice that have been drawn from diverse parts of globe. It has also made extensive contributions to disaster interventions based on its engagement in numerous calamities that have affected the population in China, including the devastating Wenchuan earthquake of 2008. More recently, its dynamic leaders have supported the development of social work in other Asian countries. I have been privileged to have developed a long-standing relationship with China, its culture and its history for many decades, even before I became a social worker. My social work colleagues have honoured me by strengthening this interest by providing many opportunities to walk alongside them. This article considers my personal reflections on a profession’s development through momentous world events, and China rightly deserves to celebrate its 30 years of growth and development.

Optimal Model-Free Output Synchronization of Heterogeneous Multiagent Systems Under Switching Topologies

In this article, the output synchronization of discrete-time heterogeneous multiagent systems over directed switching topologies is investigated. For output synchronization problem, the optimal control protocols for all agents depend on the solutions of a series of algebraic Riccati equations (AREs), which are difficult to be solved analytically. Besides, both the agents' and the leader's dynamics are supposed to be unknown. The distributed adaptive observer for each agent is designed first to estimate the leader's state without requiring complete knowledge of the leader's dynamics. Based on the trained observers, the output synchronization problem is formulated to an optimal control problem. An observer-based Q-learning algorithm is developed to solve the AREs using system data rather than the accurate system models. The optimal analytic distributed control policies can be obtained by policy iteration combined least square method. It is proved theoretically that the output synchronization is ensured based on the distributed adaptive observers under switching topologies. Ultimately, the theoretical results are demonstrated via three simulation examples.

Distributed Tracking in Heterogeneous Networks With Asynchronous Sampled-Data Control

This article investigates distributed coordinated tracking problems of networked heterogeneous systems. Based on asynchronous sampling information, distributed sampled-data protocols are employed to realize leader-following synchronization and containment tracking in networked heterogeneous systems. In asynchronous sampled-data protocols, each node has different sampling instants with other nodes and only samples itself information at its own sampling instants. By utilizing the input-delay approach and Lyapunove–Krasovskii functional approach, some sufficient conditions for guaranteeing the coordinated tracking are presented. First, quasi-synchronization criteria are obtained for networked heterogeneous oscillator systems with a dynamic leader over the directed graph. Second, in the presence of multiple heterogeneous leaders for networked heterogeneous systems, sufficient conditions of quasi-containment tracking are derived. In a word, all followers can converge into a bounded level of convex hull spanned by the leader(s). The upper bounds of tracking errors are estimated for both quasi-synchronization and quasi-containment tracking. Finally, two numerical examples are given to verify the theoretical results.

Estimator-based MLP neuroadaptive dynamic surface containment control with prescribed performance for multiple quadrotors

This paper presents an estimator-based minimal learning parameter (EMLP) neuroadaptive dynamic surface containment control design capable of guaranteeing transient and steady-state behavior for multiple quadrotors with uncertainties, such that the followers can be driven into the convex hull constituted by multiple dynamic leaders with prescribed bounded errors. To facilitate the control design, the quadrotor dynamics is decomposed into translational and rotational subsystems. For each subsystem, in order to enable smooth and rapid learning of unknown system uncertainties and reduce the computational load in traditional neural network (NN), the estimation errors, instead of tracking errors, are used to regulate NN weights and only one NN learning parameter is required for adaptive neural approximation with the aid of MLP, which is more feasible for real-time implementation. Additionally, dynamic surface control (DSC) technique is introduced in control design to extract the time derivative of virtual control laws, and thus the issue of “explosion of complexity” can be circumvented. As an extension, prescribed performance function and error transformation technique are utilized to address the preselected containment synchronization error constraints problem. Finally, the stability analysis is established to prove that all error signals are uniformly ultimately bounded (UUB). Simulation results illustrate the effectiveness and superiority of the proposed control scheme.

Distributed Robust Global Containment Control of Second-Order Multiagent Systems With Input Saturation

In this paper, we study the robust global containment control problem for second-order multiagent systems with bounded input disturbances subject to input saturation under general directed communication graphs. Two types of distributed controllers based on novel sliding mode control ideas are respectively proposed to solve the globally asymptotic containment problem for multiagent systems with static leaders and the practical containment problem for the case with dynamic leaders subject to unknown control inputs. One distinctive feature of the proposed controllers is that only local velocity measurements, relative position, and velocity measurements are involved in designing the controllers, which thus effectively reduces the information transmission burden among the agents for real-time implementation. Another favorable property of the designed controllers is that the global information such as the spectrum of the graph Laplacian matrix is not required in designing these controllers under general directed communication graphs. Simulations on containment control of multiple quadrotors are performed to illustrate the effectiveness of the proposed containment controllers.

Fixed-Time Bipartite Consensus Tracking of Fractional-Order Multi-Agent Systems With a Dynamic Leader

This brief considers the fixed-time bipartite consensus tracking problem of a fractional-order multiagent system (FOMAS) with a dynamic leader in a general directed signed network. Firstly, by introducing a neighborhood-based variable, the FOMAS is transformed into an integer-order MAS. Then, a distributed protocol with heterogeneous coupling gains is proposed to ensure that the fixed-time bipartite consensus tracking can be achieved within a settling time. The upper bound of the settling time can be estimated explicitly, which is irrelevant to any initial conditions. Finally, the effectiveness of the proposed distributed protocol is illustrated by numerical simulation.

Containment control of high‐order multi‐agent systems with heterogeneous uncertainties, dynamic leaders, and time delay

AbstractThis paper deals with containment control of multi‐agent systems where high‐order canonical controllable linear systems with heterogeneous uncertainties are considered as the agents' dynamics. The leaders are dynamic with polynomial‐type trajectories. In this paper, the control protocol is smooth and it is constructed from a flexible combination of local state feedback controller and a PI‐type protocol. Utilizing this protocol, containment without suffering from chattering phenomena and consideration of any bound on the agents' states is achieved. In addition, the flexibility of this protocol helps the designer to reduce or even discard the inter‐agent communication. Recalling the significant effects of time delay on the performance and stability of multi‐agent systems, in this paper input time delay is also considered. Following a Lyapunov‐Krasovskii stability approach, two linear matrix inequalities (LMIs) are derived, and then solving the LMIs' gains of the protocol are attained such that asymptotic stability of the multi‐agent system under switching graph topology is guaranteed. Finally, the feasibility of the LMIs and the validity of the theoretical results are demonstrated through some numerical examples.

Coordinated Tracking Control With Asynchronous Edge-Based Event-Triggered Communications

This paper studies the distributed event-triggered tracking control problem of general linear multiagent systems with a dynamic leader, whose control input might be nonzero and unknown. The existence of the leader's unknown input renders the network heterogeneous and largely increases the difficulty of designing distributed event-based protocols. To solve this problem, we establish a novel asynchronous edge-based event-triggered mechanism, under which communication is not required from the leader to its out-neighbors (informed followers) or by the edge, unless the embedded triggering functions are triggered. Using this mechanism, we design a static asynchronous edge-based event-triggered protocol and an adaptive one, both of which guarantee the achievement of the leader–follower consensus and the exclusion of the Zeno behavior. Note that the adaptive event-based protocol is fully distributed, requiring no global information of the network topology, such as the network's scale, the smallest nonzero eigenvalue of the Laplacian matrix, and the upper bound of the leader's control input.

Leader–Following Consensus of Multiple Uncertain Euler–Lagrange Systems With Unknown Dynamic Leader

In this paper, we consider the leader–following consensus problem of uncertain Euler–Lagrange multi-agent systems. In comparison with existing results, the leader system is used to formulate both the reference trajectory and external disturbances, and the dynamics of the leader system contains unknown parameters. The current setting makes our problem formulation more realistic while at the same time, it poses significant technical challenges to the solvability of the problem. Inspired by the robust control approach and the adaptive control approach, we propose a novel adaptive distributed control law. It is shown that by the proposed control law, consensus of multiple uncertain Euler–Lagrange systems can be achieved in spite of unknown dynamic leader systems. Our main result is demonstrated by its exemplary application to cooperative control of a group of two-link robot arms.

Adaptive Fuzzy Containment Control of Nonlinear Strict-Feedback Systems With Full State Constraints

In this paper, the distributed adaptive fuzzy containment control problem is investigated for a class of uncertain nonlinear systems guided by multiple dynamic leaders. Each follower is modeled by nonlinear strict-feedback systems subject to full state constraints. The function approximation technique using fuzzy logic systems is utilized to identify the unknown nonlinearities of each follower. Both the state feedback containment control and the observer-based output feedback containment control are constructed by combining distributed sliding-mode estimators with adaptive fuzzy backstepping control. To prevent constraint violation, multiple barrier Lyapunov functions associated with error surfaces are introduced in the control design. It is proven that uniformly ultimately bounded containment control is achieved without violating full state constraints under the condition that for each follower, there exists at least one leader that has a directed path to that follower. Simulation studies are performed to show the effectiveness of the proposed theoretical results.

On Constructing Multiple Lyapunov Functions for Tracking Control of Multiple Agents With Switching Topologies

Distributed consensus tracking for linear multiagent systems (MASs) with directed switching topologies and a dynamic leader is investigated in this paper. By fully considering the special feature of Laplacian matrices for topology candidates, several new classes of multiple Lyapunov functions (MLFs) are constructed in this paper for leader-following MASs with, respectively, an autonomous leader and a nonautonomous leader. Under the condition that each possible topology graph contains a spanning tree rooted at the leader node, some efficient criteria for achieving consensus tracking in the considered MASs are provided. Specifically, it is proven that consensus tracking in the closed-loop MASs can be ensured if the average dwell time for switching among different topologies is larger than a derived positive quantity and the control parameters in tracking protocols are appropriately designed. It is further theoretically shown that the present Lyapunov inequality based criteria for consensus tracking with an autonomous leader are much less conservative than the existing ones derived by the $M$ -matrix theory. The results are then extended to the case where the topology graph only frequently contains a directed spanning tree as the MASs evolve over time. At last, numerical simulations are performed to illustrate the effectiveness of the analytical analysis and the advantages of the proposed MLFs.

Velocity-Observer-Based Distributed Finite-Time Attitude Tracking Control for Multiple Uncertain Rigid Spacecraft

This article addresses the distributed finite-time attitude tracking control problem for a group of uncertain rigid spacecraft in the presence of unavailable angular velocity under the directed topology condition. First, a finite-time adaptive neural network observer is proposed for each follower to estimate its own unavailable angular velocity. Unlike existing velocity-observer-based design methods, the proposed one does not need the exact knowledge of the system model, and works well for the systems with both vanishing and nonvanishing uncertainties. Further, another finite-time observer is provided to obtain the precise angular velocity information of the dynamic leader in a distributed manner. Based on these two observers and adding a power integrator technique, a continuous distributed finite-time control scheme with only attitude measurements is finally established. A rigorous theoretical proof shows that the entire finite-time stability of the combined observer–controller closed-loop system is ensured. Simulation results illustrate the benefits and effectiveness of the developed control scheme.

Fully Distributed Resilience for Adaptive Exponential Synchronization of Heterogeneous Multiagent Systems Against Actuator Faults

Cooperative control of multiagent systems (MAS) on communication networks has received a great deal of attention, mostly for the case of homogeneous agents, which all have the same dynamics. An advantage of cooperative synchronization mechanisms is their local distributed nature, which makes them scalable to large networks. However, most existing design mechanisms require some global information, such as the leader's dynamics or global graph information, so that the control protocols are technically not fully distributed. Moreover, the distributed nature of the control protocols makes them susceptible to faults or uncertainties. In this paper, we study heterogeneous MAS, where all agents may have different dynamics. We provide adaptive resilience mechanisms for rejecting actuator faults, and guarantee exponential convergence of synchronization errors, whereas most existing results on actuator faults guarantee only boundedness of errors. Finally, we provide algorithms that are fully distributed, requiring no knowledge of either the leader's dynamics or of graph properties.