Containment control of singular heterogeneous multi-agent systems

In this paper, we first consider the containment control problem of singular heterogeneous multi-agent systems, where all the followers converge to the convex hull spanned by the leaders. To solve this problem, we propose two distributed control laws: one is based on the state feedback control framework, which is suitable for the case that the full state information of each follower is accessible; and the other is based on the output regulation framework, where each follower only can access to its output. Furthermore, the distributed observers are designed for every follower to estimate the convex combination of the leader states which is determined by the communication graph. It should be noted that our results can also regard the non-singular multi-agent systems’ containment control problem as a special case. Finally, simulation results corroborate the effectiveness of our analytical results.     

Distributed model reference adaptive containment control of heterogeneous multi-agent systems with unknown uncertainties and directed topologies

In this paper, the containment control problem of heterogeneous uncertain high-order linear Multi-Agent Systems (MASs) is addressed and solved via a novel fully-Distributed Model Reference Adaptive Control (DMRAC) approach, where each follower computes its adaptive control action on the basis of local measurements, information shared with neighbors (within the communication range) and the matching errors w.r.t. its own reference model, without requiring any previous knowledge of the global directed communication topology structure. The approach inherits the robustness of the direct model reference adaptive control (MRAC) scheme and allows all agents converging towards the convex hull spanned by leaders while fulfilling at the same time local additional performance requirements at single-agent level, such as prescribed settling time, overshoot, etc. The asymptotic stability of the whole closed-loop network is analytically derived by exploiting the Lyapunov theory and the Barbalat lemma, hence proving that each follower converges to the convex hull spanned by the leaders, as well as the boundedness of the adaptive gains. Extensive numerical analysis for heterogeneous MAS composed of stable, unstable and oscillating agent dynamics are presented to validate the theoretical framework and to confirm the effectiveness of the proposed approach.     

Distributed chattering-free containment control for multiple Euler–Lagrange systems

This paper investigates the distributed chattering-free containment control problem for multiple Euler–Lagrange systems with general disturbances under a directed topology. It is considered that only a subset of the followers could receive the information of the multiple dynamic leaders. First, by combining a linear sliding surface with a nonsingular terminal sliding manifold, a distributed chattering-free asymptotic containment control method is proposed under the assumption that the upper bounds of the general disturbances are known. Further, based on the high-order sliding mode control technique, an improved distributed chattering-free finite-time containment control algorithm is developed. Besides, adaptive laws are designed to estimate the unknown upper bounds of the general disturbances. It is demonstrated that all the followers could converge into the convex hull spanned by the leaders under both proposed control algorithms by graph theory and Lyapunov theory. Numerical simulations and comparisons are provided to show the effectiveness of both algorithms.     

Prescribed-time containment control with prescribed performance for uncertain nonlinear multi-agent systems

The existing studies on prescribed-time control cannot directly deal with nonlinear functions which don’t satisfy Lipschitz growth conditions. No results are available for prescribed-time containment control of pure-feedback UNMASs with prescribed performance. Therefore, completely unknown nonlinear function, prescribed-time tracking of system states and prescribed performance of containment errors are simultaneously considered in this paper. Fuzzy logic systems are utilized to approximate completely unknown nonlinear function. Prescribed-performance function is introduced and further incorporated into a novel speed function. Combining the proposed speed function and barrier Lyapunov function, this article presents a novel adaptive fuzzy prescribed-time containment control method which can guarantee, under prescribed performance, all followers converge to a convex formed by dynamic leaders in a prescribed time. Moreover, all tracking errors converge to predefined regions in a prescribed time. The effectiveness of the proposed prescribed-time containment control method are confirmed by strict proof and simulation.     

Time-varying output formation tracking of heterogeneous linear multi-agent systems with multiple leaders and switching topologies

This paper studies the time-varying output formation tracking problems for heterogeneous linear multi-agent systems with multiple leaders in the presence of switching directed topologies, where the agents can have different system dynamics and state dimensions. The outputs of followers are required to accomplish a given time-varying formation configuration and track the convex combination of leaders’ outputs simultaneously. Firstly, using the neighboring relative information, a distributed observer is constructed for each follower to estimate the convex combination of multiple leaders’ states under the influences of switching directed topologies. The convergence of the observer is proved based on the piecewise Lyapunov theory and the threshold for the average dwell time of the switching topologies is derived. Then, an output formation tracking protocol based on the distributed observer and an algorithm to determine the control parameters of the protocol are presented. Considering the features of heterogeneous dynamics, the time-varying formation tracking feasible constraints are provided, and a compensation input is applied to expand the feasible formation set. Sufficient conditions for the heterogeneous multi-agent systems with multiple leaders and switching directed topologies to achieve the desired time-varying output formation tracking under the designed protocol are proposed. Finally, simulation examples are given to validate the theoretical results.     

Event-triggered containment control of second-order nonlinear multi-agent systems

This paper investigates the event-triggered containment control for a class of second-order nonlinear multi-agent systems. A centralized event-triggered protocol is first designed, then the result is extended to the decentralized counterpart. By the tools from nonsmooth analysis, it is shown that the containment control objective can be achieved via the presented protocols. To avoid the Zeno behavior, the event-triggered conditions are redesigned. It is proven that all followers can asymptotically converge to the convex hull spanned by multiple leaders via the proposed strategies and the Zeno behavior can be excluded, simultaneously. Two examples are given to illustrate the feasibility of the proposed protocols.     

Output containment control of heterogeneous multi-agent systems with leaders of bounded inputs: An adaptive finite-time observer approach

In this paper, we address the problem of output containment control of general linear multi-agent systems (MASs). The MAS under consideration is comprised by multiple followers and multiple leaders, all with heterogeneous dynamics. In particular, the leaders’ dynamics are subject to heterogeneous non-zero (possibly persistent) but bounded inputs, which are not measurable for any follower agent, making the associated distributed control design problem rather challenging. A new distributed observer-based containment control protocol is proposed to overcome associated challenges. It consists of two hierarchical layers including (i) the first layer of adaptive finite-time cooperative observer responsible for estimating the convex-hull signals formed by multiple leaders’ states through inter-agent collaboration; and (ii) the second layer of distributed state-feedback controller responsible for local tracking control through a modified output regulation technique. Important novelties of the proposed protocol are that (i) it deals with MASs with not only heterogeneous followers but also heterogeneous leaders; (ii) exact output containment control performance can be achieved in the presence of unmeasurable leaders’ inputs and unknown connectivity of communication network; and (iii) associated solvability conditions are formulated as linear matrix inequalities plus linear algebraic equations, which can be tested and solved effectively via efficient semi-definite programming. The developed theoretical results are demonstrated both rigorously using Lyapunov methods and through numerical simulations.     

Distributed containment control for multiple ocean bottom flying nodes with velocity error constraint and input saturation

This paper uses the directed communication topology to investigate the finite-time error constraint containment control for multiple Ocean Bottom Flying Node (OBFN) systems with thruster faults. The OBFN is a benthic Autonomous Underwater Vehicle (AUV), which has been used to explore submarine resources. The model uncertainties, velocity error constraint, external disturbances, and thruster faults of OBFNs motivate the design of containment controller. Moreover, some followers could obtain the states of leader OBFNs. We designed the command filter and the input signal is a hyperbolic tangent function. The virtual velocity error command is generated to follow the velocity error. Then the novel velocity error constraint distributed control algorithm is developed. Furthermore, for the problem of input saturation, by designing a stable anti-saturation compensator, an improved containment algorithm is proposed. It is proved that both the proposed approaches can converge the containment errors towards zero through Lyapunov theory in finite time, which means the followers can reach the convex hull formed by leaders in finite time. Finally, simulation results demonstrate the effectiveness of the two strategies.     

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.     

Cooperative containment control in time-delayed multi-agent systems with discrete-time high-order dynamics under dynamically changing topologies

This paper addresses the containment control problem for discrete-time high-order multi-agent systems (MASs) with dynamically changing topologies and time-varying delays. By considering the influence of switching topologies, a distributed containment control protocol that only involves the agent’s own information and its neighbors’ partial information is given to make all the followers enter and keep moving in the convex hull formed by the static leaders. A novel technique is employed to transform the high-order MAS with dynamically changing topologies into a switched augmented system with nonnegative coefficient matrices, and then convert the convergence problem of the switched augmented system to a product problem of infinite time-varying row stochastic matrices. With the help of graph theory and the properties of stochastic indecomposable and aperiodic (SIA) matrices, a sufficient condition in terms of communication topologies is derived, that is, the high-order containment control with dynamically changing topologies and time-varying delays can be achieved if the union of the effective communication topologies across any time intervals with some given length contains a spanning forest rooted at the leaders. Finally, computer simulations are conducted to illustrate the efficiency of the theoretical findings.     

Adaptive resilient containment control for nonlower triangular multiagent systems with time-varying delay and sensor faults

This paper investigates the adaptive resilient containment control for nonlinear multiagent systems (MASs) with time-varying delay, unmodeled dynamics and sensor faults. To solve the coupling problem of unknown state delays and sensor faults in a nonlower triangular structure, we develop an effective method by using a new lemma and the Lyapunov-Krasovskii functional. Then, to reduce the negative impact of unknown sensor faults, a novel adaptive resilient containment control method is designed based on a distributed sliding-mode estimator, which can effectively improve the transient performance of the MASs. Moreover, by using a dynamic signal, the problem of unmodeled dynamics is solved. The proposed control scheme can not only drive all followers suffering from sensor faults to converge to the convex hull formed by the leaders but also relatively reduce the undesired chattering phenomenon. Finally, a comparative simulation example is given to illustrate the effectiveness of the proposed strategy.     

Observer-based semi-global containment of saturated multi-agent systems with uncertainties

In this article, the robust semi-global containment control for multi-agent systems affected by uncertainties, such as input additive disturbance, input saturation and dead zone is addressed. An observer-based control algorithm is designed by combining the high-gain observer approach and the low-and-high gain feedback technique. Under the assumption that all agents are asymptotically null controllable with bounded controls and each follower can access the information of at least one leader through a directed path, sufficient conditions for the semi-global output feedback containment control are provided. Finally, numerical simulations are proposed to verify the main theoretical results.     

Prescribed-time guidance scheme design for missile salvo attack

In this paper, for three-dimensional interception of multiple missiles on a maneuvering target, a prescribed-time salvo attack guidance scheme with impact angle constraints and impact time constraint is investigated. The target accelerations are estimated accurately by a prescribed-time extended state observer. With the proposed guidance scheme, it ensures the LOS angles converge to desired values within a predetermined convergence time, and achieves salvo attack at a predetermined impact time. Prescribed-time convergency is shown for the proposed observer and controllers. Finally, the validity of the proposed guidance scheme is verified through numerical simulation.     

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.     

Containment control for second-order nonlinear multi-agent systems with aperiodically intermittent position measurements

In some real systems, the intermittent communications and the inaccurate velocity measurements are usually inevitable. To overcome these two communication limitations, this article aims at investigating the containment control problem for a class of second-order multi-agent systems with inherent nonlinear dynamics and aperiodically intermittent position measurements. Under the case that the velocity information is unavailable, a distributed filter is introduced for each second-order follower. Based on the distributed filter, a novel intermittent containment control protocol without velocity measurements is designed. Some sufficient conditions are derived under the common assumption that only relative position measurements between the neighbouring agents are utilized intermittently, and these conditions ensure that the second-order nonlinear multi-agent systems can achieve containment control. Furthermore, some simpler containment conditions are obtained for multi-agent systems with double-integrator dynamics under aperiodically intermittent communications. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.     

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.     

Distributed observer-based consensus tracking for nonlinear MASs with nonuniform input delays and disturbances

In this paper, we investigate the consensus tracking problem of nonlinear MASs with nonuniform time-varying input delays and external disturbances. For each follower, the composited disturbance observer and the state observer are employed to estimate bounded composited disturbances and unmeasured states, and a distributed observer based on output-feedback is proposed to approximate the leader’s states approachably. Sequentially, the consensus tracking control is converted into a stability control problem for the nonlinear MASs with nonuniform time-varying input delays. Subsequently, a distributed controller based on the truncated prediction approach is presented, which only depends on the boundary value of time-varying input delays. The distributed controller can render each follower synchronically stable via the Lyapunov stability theory. Finally, a group of single-link manipulators is used as an example to verify the effectiveness of the theoretical results.     

Distributed consensus tracking control based on state and disturbance observations for mixed-order multi-agent mechanical systems

In this paper, we study the cooperative consensus control problem of mixed-order (also called hybrid-order) multi-agent mechanical systems (MMSs) under the condition of unmeasurable state, unknown disturbance and constrained control input. Here, the controlled mixed-order MMSs are consisted of the mechanical agents having heterogeneous nonlinear dynamics and even non-identical orders, which means that the agents can be of different types and their states to be synchronized can be not exactly the same. In order to achieve the ultimate synchronization of all mixed-order followers, we present a novel distributed adaptive tracking control protocol based on the state and disturbance observations. Wherein, a distributed state observer is used to estimate the followers’ and their neighbors’ unmeasurable states. And, a novel estimated-state-based disturbance observer (DOB) is proposed to reduce the effect of unknown lumped disturbance for the mixed-order MMSs. The proposed control protocol and observers are fully distributed and can be calculated for each follower locally. Lyapunov theory is used for proving the stability of the proposed control algorithm and the convergence of the cooperative tracking errors. A practical cooperative longitudinal landing control example of unmanned aerial vehicles (UAVs) is given to illustrate the effectiveness of the presented control protocol.     

Distributed fault-tolerant tracking control for heterogeneous nonlinear multi-agent systems under sampled intermittent communications

This paper studies the distributed fault-tolerant control (FTC) problem for heterogeneous nonlinear multi-agent systems (MASs) under sampled intermittent communications. First, in order to estimate the state of leader under sampled intermittent communications, the distributed intermittent observer for each follower is constructed. By using the tool from switching system theory, the estimation error converges to zero exponentially if the communication rate is larger than a threshold value even under the impact of sampled intermittent communications. Then, by applying model reference adaptive tracking technique, a robust FTC protocol is developed to track the distributed intermittent observer. Two algorithms are presented to choose the feedback gain of the distributed intermittent observer and the tracking feedback gain of the fault-tolerant tracking controller. It is proved that the global consensus tracking error is bounded under the developed distributed control protocol. Finally, an example with the coupled pendulums is provided to verify the efficiency of the designed method.