Bipartite time-varying formation group containment control for multi-agent systems based on multi-layer network and semi-signed directed graph

The bipartite time-varying formation group containment tracking control problem of multi-agent systems with unknown input leader on semi-signed digraph is studied. In this paper, the multi-agent system is divided into three layers: the leader layer with unknown input, the formation layer with cooperative-competitive relationship, and the containment layer without competitive relationship. First, the formation members in formation layer track the state of the leader in the leader layer, to achieve bipartite time-varying formation and form two convex hull. Then, by assuming two subgroups of the containment layer exist a well-informed individual (which can receive corresponding convex hull of all the formation members of communication), respectively, the followers of the two subgroups can not only converge to respectively two convex hulls formed by formation layer, also can make the followers of the same subgroup converge to a common value, this provides a prerequisite for the formation control of the followers in the containment layer. Next, different control protocols are designed for formation layer and containment layer respectively based on neighbor information, and Lyapunov function is constructed to provide stability proof for the realization of the problem. Finally, several simulation results are given to verify the validity of the theory.     

Time-varying formation tracking for high-order multi-agent systems with switching topologies and a leader of bounded unknown input

Time-varying formation tracking problems for high-order multi-agent systems with switching topologies are investigated. Different from the previous work, the states of the followers form a predefined time-varying formation while tracking the state of the leader with bounded unknown control input. Besides, the communication topology can be switching, and the dynamics of each agent can have nonlinearities. Firstly, a nonlinear time-varying formation tracking control protocol is presented which is constructed using only local neighboring information. Secondly, an algorithm with four steps is proposed to design the time-varying formation tracking protocol, where the time-varying formation tracking feasibility condition is introduced. Thirdly, by using the Lyapunov theory, the stability of the proposed algorithm is proven. It is proved that the high-order multi-agent system with switching topologies achieves the time-varying formation tracking if the feasibility condition holds and the dwell time is larger than a positive constant. Finally, a numerical example with six followers and one leader is given to demonstrate the effectiveness of the obtained results.     

Cooperative surrounding control with collision avoidance for networked Lagrangian systems

This paper investigates the cooperative surrounding control problem for networked multi-agent systems with nonlinear Lagrangian dynamics. With the consideration of the target with constant and time-varying velocity, two cooperative surrounding control algorithms with collision avoidance are proposed, in which possible collision among agents is prevented so as to achieve a more reliable and safer performance. For the case when the target has a constant velocity, a velocity observer is designed firstly for each agent. Secondly, to handle the nonlinear dynamics and avoid collisions, the neural networks and potential functions are used for the controller design. Then, the cooperative surrounding control algorithm is proposed such that all the agents surround the target with the desired relative positions. For the case when the target has a time-varying velocity, the velocity observer is designed under the assumption that the target’s partial acceleration is known for each agent. Then, the cooperative surrounding control algorithm is proposed such that the surrounding error between the target and each agent is bounded. The main difference between these two algorithms is that the former can ensure the collision avoidance among target and agents, while the latter can do so only among agents because the target’s velocity is time-varying. The Lyapunov theory is used to prove the stability of the cooperative surrounding control algorithms. The simulation illustrates the effectiveness of the theoretical results.     

Practical time-varying output formation tracking for high-order multi-agent systems with collision avoidance,obstacle dodging and connectivity maintenance

Practical time-varying output formation tracking problems with collision avoidance, obstacle dodging and connectivity maintenance for high-order multi-agent systems are investigated, and the practical time-varying output formation tracking error is controlled within an arbitrarily small bound. The outputs of followers are designed to track the output of the leader with unknown control input while retaining the predefined time-varying formation. Uncertainties are considered in the dynamics of the followers and the leader. Firstly, distributed extended state observers are developed to estimate the uncertainties and the leader’s unknown control input. A strategy of obstacle dodging is given by designing an ideal secure position for the followers which are in the threatened area of the obstacles. By constructing collision avoidance, obstacle dodging and connectivity maintenance artificial potential functions, corresponding negative gradient terms are calculated to achieve the safety guarantee. Secondly, a practical time-varying output formation tracking protocol is proposed by using distributed extended state observers and the negative gradient terms. Additionally, an approach is presented to determine the gain parameters in the protocol. The stability of the closed-loop multi-agent system with the protocol is analyzed by using Lyapunov stability theory. Finally, a simulation experiment is provided to illustrate the effectiveness of the obtained methods.     

Affine formation control for multi-agent systems with prescribed convergence time

In this paper, the affine formation control problem for multi-agent systems with prescribed convergence time is investigated. Firstly, on the basis of a time-varying scaling function, a distributed continuous control algorithm is designed, under which a stationary affine formation of the nominal configuration is able to be achieved within a prescribed time. Secondly, to track a time-varying formation within the prescribed time, a distributed control protocol is proposed by employing a leader–follower control strategy. Furthermore, the boundary layer technique is adopted to avoid chattering effect. Finally, simulation examples are provided to demonstrated the effectiveness of the proposed design.     

一类具有动态领导者和时滞的多主体系统的一致性

研究了一类具有动态领导者并且存在时变耦合时滞的多主体系统的一致性问题．在所考虑的模型中,领导者的速度不能被精确量测．为了跟踪这样一个领导者主体,将对每个跟随者主体构造分散式状态估计器以及设计基于邻居的控制器;同时,由于耦合时滞的存在,基于邻居的控制器和状态估计器均包含了时变时滞的作用．当多主体系统的耦合拓扑是固定的或切换的有向图时,跟随者与领导者之间的跟踪误差得到了估计．特别地,可以证明,当动态领导者的速度可以被精确量测时,每一个跟随者都能够跟踪上领导者．     

Distributed adaptive fault-tolerant formation control for heterogeneous multiagent systems under switching directed topologies

This paper studies the cooperative fault-tolerant formation control problem of tracking a dynamic leader for heterogeneous multiagent systems consisting of multipile unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults under switching directed interaction topologies. Based on local neighborhood formation information, the distributed fault-tolerant formation controllers are constructed to ensure that all follower UAVs and UGVs can accomplish the demanding formation configuration in the state space and track the dynamic leader’s trajectory. By incorporating the sliding mode control and adaptive control technique, the actuator faults and unknown parameters of follower agents can be compensated. Through the theoretical analysis, it is proved that the cooperatively semiglobally uniformly ultimately boundedness of the closed-loop system is guaranteed, and the formation tracking errors converge to a small adjustable neighborhood of the origin. A simulation example is introduced to show the validity of the proposed distributed fault-tolerant formation control algorithm.     

Distributed state estimator-based consensus tracking of multi-agent systems with exogenous disturbance

The consensus tacking problem for multi-agent systems with a leader of none control input and unknown control input is studied in this paper. By virtue of the relative state information of neighboring agents, state estimator and disturbance estimator are designed for each follower to estimate the system states and exogenous disturbance, respectively. Meanwhile, a novel control protocol based on two estimators is designed to make tracking error eventually converge to zero. Furthermore, the obtained results are further extended to the leader with unknown control input. A novel state estimator with adaptive time-varying gain is proposed such that consensus tracking condition is independent of the Laplacian matrix with regard to the communication topology. Finally, two examples are presented to verify the feasibility of the proposed control protocol.     

Adaptive observer-based event-triggered finite time formation tracking for multi-agent systems with a non-cooperative leader

The event-triggered time-varying formation tracking for a class of second-order multi-agent systems (MASs) subject to a non-cooperative leader is investigated in this paper. First, in the presence of the unknown input of the leader and external disturbances, a distributed observer with adaptive parameters is put forward for followers to estimate the velocity tracking error. Then, based on the estimated tracking error and an auxiliary variable, a finite time formation controller is further constructed, which is updated depending on a pre-designed event-triggered mechanism. As a result, the desired time-varying formation configuration can be realized in finite time with less communication resource consumption. It’s noted that the constructed formation strategy doesn’t rely on any global information and thus is fully distributed. The stability of the controlled multi-agent system is proved rigorously and it’s verified that event-triggered intervals are with a positive lower bound. At last, simulations are carried out to illustrate the effectiveness of the presented algorithm.     

Two-layer distributed hybrid affine formation control of networked Euler–Lagrange systems

This paper tackles a distributed hybrid affine formation control (HAFC) problem for Euler–Lagrange multi-agent systems with modelling uncertainties using full-state feedback in both time-varying and constant formation cases. First, a novel two-layer framework is adopted to define the HAFC problem. Using the property of the affine transformation, we present the sufficient and necessary conditions of achieving the affine localizability. Because only parts of the leaders and followers can access to the desired formation information and states of the dynamic leaders, respectively, we design a distributed finite-time sliding-mode estimator to acquire the desired position, velocity, and acceleration of each agent. In the sequel, combined with the integral barrier Lyapunov functions, we propose a distributed formation control law for each leader in the first layer and a distributed affine formation control protocol for each follower in the second layer respectively with bounded velocities for all agents, meanwhile the adaptive neural networks are applied to compensate the model uncertainties. The uniform ultimate boundedness of all the tracking errors can be guaranteed by Lyapunov stability theory. Finally, corresponding simulations are carried out to verify the theoretical results and demonstrate that with the proposed control approach the agents can accurately and continuously track the given references.     

Event-triggered bipartite consensus for nonlinear multi-agent systems under switching topologies: A time-varying gain method

In this paper, the event-triggered bipartite consensus problem is investigated for nonlinear multi-agent systems under switching topologies, only part of topologies contain directed spanning tree rooted at the leader. First, a dynamic bipartite compensator is constructed based on relative output information to provide control signal. Then, the time-varying gain method is adopted to propose a compensator-based event-triggered control protocol without Zeno behavior. Notably, the control protocol proposed achieves the bipartite consensus while reducing update frequency effectively. Moreover, a low conservative switching law is designed by the topology-dependent average dwell time strategy, which fully considers the differences among topologies and provides an independent average dwell time for each topology. As an extension, the nonlinear multi-agent systems with non-zero input of leader are further studied. Finally, a practical example is presented to demonstrate the feasibility of proposed control protocol.     

New distributed adaptive protocols for uncertain nonlinear leader-follower multi-agent systems via a repetitive learning control approach

In this paper, the distributed consensus problem of leader-follower multi-agent systems with unknown time-varying coupling gains and parameter uncertainties are investigated, and the fully distributed protocols with the adaptive updating laws of periodic time-varying parameters are designed by using a repetitive learning control approach. By virtue of algebraic graph theory, Barbalat’s lemma and an appropriate Lyapunov-Krasovskii functional, it is shown that each follower agent can asymptotically track the leader even though the dynamic of the leader is unknown to any of them, i.e., the global asymptotic consensus can be achieved. At last, a simulation example is given to illustrate the feasibility and efficiency of the proposed protocols.     

Distributed bearing-based formation control of networked thrust-propelled vehicles

In this paper, the distributed bearing-based formation control problem of networked thrust-propelled vehicles (TPVs) is addressed, in which both the constant and time-varying velocity leaders are considered, respectively. By introducing a reference acceleration and adaptive control scheme for the followers, the mass knowledge is not necessary in contrast to the existing works. Based on the designed reference accelerations, distributed adaptive control laws are proposed for the networked TPVs. Then the stabilization conditions are presented and an inner-bearing prescribed formation can be achieved. Under the proposed control laws, the leader-follower formation maneuver problem for networked TPVs with system uncertainties can be solved. Finally, simulation results are provided to demonstrate the effectiveness of the proposed control laws.     

Robust finite-time cooperative formation control of UGV-UAV with model uncertainties and actuator faults

This paper investigates the finite-time cooperative formation control problem for a heterogeneous system consisting of an unmanned ground vehicle (UGV) - the leader and an unmanned aerial vehicle (UAV) - the follower. The UAV system under consideration is subject to modeling uncertainties, external disturbance as well as actuator faults simultaneously, which is associated with aerodynamic and gyroscopic effects, payload mass, and other external forces. First, a backstepping controller is developed to stabilize the leader system to track the desired trajectory. Second, a robust nonsingular fast terminal sliding mode surface is designed for UAV and finite-time position control is achieved using terminal sliding mode technique, which ensures the formation error converges to zero in finite time in the presence of actuator faults and other uncertainties. Furthermore, by combining the radial basis function neural networks (NNs) with adaptive virtual parameter technology, a novel NN-based adaptive nonsingular fast terminal sliding formation controller (NN-ANFTSMFC) is developed. By means of the proposed adaptive control strategy, both uncertainties and actuator faults can be compensated without the prior knowledges of the uncertainty bounds and fault information. By using the proposed control schemes, larger actuator faults can be tolerated while eliminating control chattering. In order to realize fast coordinated formation, the expected position trajectory of UAV is composed of the leader position information and the desired relative distance with UGV, based on local distributed theory, in the three-dimensional space. The tracking and formation controllers are proved to be stable by the Lyapunov theory and the simulation results demonstrate the effectiveness of proposed algorithms.     

Disturbance-observer-based formation-containment control for UAVs via distributed adaptive event -triggered mechanisms

In this paper, the adaptive event-triggered formation-containment control for unmanned aerial vehicles (UAVs) is investigated in the presence of multiple leaders and external disturbances. By utilizing the leader-following model, the reference leader provides the desired flight trajectory for multiple formation leaders while the followers are driven into the convex hull spanned by the formation leaders. Initially, some effective disturbance observers are designed to obtain the estimations for eliminating the negative effects of external disturbances. Secondly, in order to alleviate the network burden, a dynamic triggering law is designed for the adaptive event-triggered mechanism (AETM) and the triggering frequency is heavily related to the triggering errors. Then, by exploiting Kronecker product technique and Lyapunov stability theory, two sufficient conditions on the stability of closed-loop system are established, which can help achieve the desired formation control target. Furthermore, the controller gains and observer ones can be determined by calculating the derived linear matrix inequalities (LMIs). Finally, a simulation example is given to illustrate the feasibility of the designed control protocol.     

Leader-following consensus control of multiple nonholomomic mobile robots: An iterative learning adaptive control scheme

In this paper, the distributed iterative learning control for nonholonomic mobile robots with a time-varying reference is investigated, in which the mobile robots are with parametric uncertainties and are not fully actuated. Besides, the control gains of mobile robots are unknown. The leader is with a time-varying reference trajectory, and there is no need to assume that the time-varying reference is linearly parameterized by a set of known functions. A distributed control scheme is designed for each mobile robot based on a set of local compensatory filters designed by its neighborhood information. Stability analysis is established through a set of composite energy function. The uniform convergence of the consensus errors can be guaranteed. An example is given to show that our designed control law is effective.     

Event-triggered time-varying formation control for general linear multi-agent systems

This paper investigates event-triggered formation control problems for general linear multi-agent systems. The time-varying formation this paper studied can be described by a bounded piecewise differentiable vector-valued function. Firstly, a time-varying formation control protocol based on event-triggered scheme is constructed by the states of the neighboring agents. Each agent broadcasts its state information to neighbor nodes if the triggering condition is satisfied, and the communication load is decreased significantly. Then, an algorithm consisting of three steps is proposed to design the event-triggered formation control protocol. Moreover, it is proven that under the designed event-triggered formation protocol, the multi-agent systems can achieve the desired time-varying formation which belongs to the feasible formation set with the bounded formation error and the closed systems do not exhibit Zeno behavior. Finally, simulation results are given to demonstrate the effectiveness of the theoretical analysis.     

Stochastic model predictive control for linear systems with unbounded additive uncertainties

This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form, which are treated in analogy with robust constraints, by using the probabilistic reachable set. The first one is the time-varying tube-based stochastic model predictive control algorithm, which is designed by employing the time-varying probabilistic reachable sets as tubes. The second one is the constant tube-based stochastic model predictive control algorithm, which is developed by enforcing a constant tightened constraint in the entire prediction horizon. In addition, the soft constraints are proposed to associate with the state initialization in the algorithms to enhance the feasibility. The algorithm feasibility and closed-loop stability results are provided. The efficacy of the approaches is demonstrated by means of numerical simulations.     

Practical constrained output feedback formation control of underactuated vehicles via the autonomous dynamic logic guidance

This paper investigates the practical leader-follower formation control issue of underactuated vehicles. To achieve the waypoints-based formation navigation, the autonomous dynamic logic (ADL) guidance is proposed by incorporating the marine practice into the virtual ship-based formation guidance strategy. In the proposed guidance, only a dominant virtual leader is required for constructing the waypoints-based formation reference framework, which shows the simplicity and the practicability. As for the control part, a constrained output feedback algorithm is developed by means of the linear extended state observer (LESO). By constructing the augmented variable, the model uncertainty and unknown disturbances are integrated to be estimated and compensated together. In addition, a second-order dynamic auxiliary system is designed to handle the problem of actuator saturation, where two additional saturation compensation terms are introduced to stabilize the kinematics and the kinetics error dynamics, respectively, and the smoothness of constrained control signals can be guaranteed owing to the modification of Gaussian error function. Using the Lyapunov direct method, all signals in the closed-loop system are proved to be semi-global uniformly ultimately bounded (SGUUB). Finally, two simulation experiments, including the comparative experiment and the formation navigation experiment in the presence of simulated ocean disturbances, are carried out to illustrate the feasibility and the superiority of proposed scheme.     

Adaptive learning tracking for uncertain systems with partial structure information and varying trial lengths

This paper considers the adaptive iterative learning control (ILC) for continuous-time parametric nonlinear systems with partial structure information under iteration-varying trial length environments. In particular, two types of partial structure information are taken into account. The first type is that the parametric system uncertainty can be separated as a combination of time-invariant and time-varying part. The second type is that the parametric system uncertainty mainly contains time-invariant part, whereas the designed algorithm is expected to deal with certain unknown time-varying uncertainties. A mixing-type adaptive learning scheme and a hybrid-type differential-difference learning scheme are proposed for the two types of partial structure information cases, respectively. The convergence analysis under iteration-varying trial length environments is strictly derived based on a novel composite energy function. Illustrative simulations are provided to verify the effectiveness of the proposed schemes.