Prescribed-time containment control of high-order nonlinear multi-agent systems based on distributed observer

This paper investigates the prescribed-time containment control problem for multi-agent systems with high-order nonlinear dynamics under a directed communication topology. Firstly, in view of the fact that only some follower agents can directly access the state information of multiple leader agents, a prescribed-time distributed observer is put forward to estimate the convex hull spanned by these leaders. Then, with the help of the distributed observer, a novel containment control method is developed for each follower based on a time-varying scaling function, so that all followers can converge to the convex hull spanned by the states of multiple leaders within a prescribed time. The comparison with the finite-time and fixed-time control methods differs in that the convergence time of the method proposed in this paper is independent of the initial conditions and control parameters and can be arbitrarily preassigned according to actual needs. Finally, an example is given to demonstrate the usefulness of the prescribed-time containment control method.     

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.     

Containment control of multi-agent systems via a disturbance observer-based approach

This paper deals with the containment control problem for multi-agent systems with exogenous disturbances. A disturbance observer-based control approach is employed to estimate the disturbances generated by an exogenous system. Consequently, distributed disturbance observer-based containment control protocols are proposed by using the state feedback control and the output feedback control, respectively. Furthermore, with the help of algebraic graph theory and Lyapunov stability theory, sufficient conditions are established to ensure that multi-agent systems with exogenous disturbances can achieve containment control via the disturbance observer-based approach. Finally, the effectiveness of our theoretical results is verified by providing numerical simulation examples.     

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.     

Aperiodically intermittent output feedback consensus control for second-order leader-following multi-agent systems based on observer

This study examines the leader-following consensus problem of a class of second-order nonlinear multi-agent systems, where the velocity information is supposed to be unmeasurable. Under the setting, this paper presents a novel aperiodically intermittent output feedback control protocol such that all followers reach consensus with the leader, in which a distributed state observer is built for each follower to observe the velocity state. Based on the Lyapunov stability theory and some matrix analysis techniques, a couple of sufficient conditions for the leader-following consensus of the nonlinear multi-agent system under study are obtained even though the velocity state is unavailable. Finally, the effectiveness of the theoretical results is verified by numerical simulation.     

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.     

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.     

Continuous-time distributed optimization with strictly pseudoconvex objective functions

In this paper, the distributed optimization problem is investigated by employing a continuous-time multi-agent system. The objective of agents is to cooperatively minimize the sum of local objective functions subject to a convex set. Unlike most of the existing works on distributed convex optimization, here we consider the case where the objective function is pseudoconvex. In order to solve this problem, we propose a continuous-time distributed project gradient algorithm. When running the presented algorithm, each agent uses only its own objective function and its own state information and the relative state information between itself and its adjacent agents to update its state value. The communication topology is represented by a time-varying digraph. Under mild assumptions on the graph and the objective function, it shows that the multi-agent system asymptotically reaches consensus and the consensus state is the solution to the optimization problem. Finally, several simulations are carried out to verify the correctness of our theoretical achievements.     

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.     

Robust distributed tracking control for linear multi-agent systems based on distributed intermediate estimator

This paper considers the distributed tracking control problem for linear multi-agent systems with disturbances and a leader whose control input is nonzero and not available to any follower. Based on the relative output measurements of neighboring agents, a novel distributed observer-based tracking protocol is proposed, where the distributed intermediate estimators are constructed to estimate the leader’s unknown control input and the states of the tracking error system simultaneously, then a distributed tracking protocol is designed based on the derived estimates. It is proved that the states of the tracking error system are uniformly ultimately bounded and an explicit tracking error bound is obtained. A simulation example of aircrafts verifies the effectiveness of the proposed method.     

Observer-based output regulation of cooperative-competitive high-order multi-agent systems

In this paper, a coopetitive output regulation problem is considered for general linear multi-agent systems with antagonistic interactions, where not all the agents have access to the state, the output, the system matrix and the output matrix of the exogenous system or exosystem. In this sense, the internal model incorporation of the system matrix of the exosystem is also only available to some agents. Thus, we propose distributed observers for each agent: (i) To estimate the state, the output, the system matrix and the output matrix, and (ii) the unavailable internal model of the exosystem. Then, a distributed dynamic output feedback controller is proposed for each agent to solve the coopetitive output regulation problem. The exponential stability of the closed-loop system is analyzed with the output regulation theory. Finally, some simulation results are presented to validate the proposed control strategy.     

Distributed secure consensus control of nonlinear multi-agent systems under sensor and actuator attacks

In this paper, we focus on an output secure consensus control issue for nonlinear multi-agent systems (MASs) under sensor and actuator attacks. Followers in an MAS are in strict-feedback form with unknown control directions and unknown dead-zone input, where both sensors and nonlinear characteristics of dead-zone in actuators are paralyzed by malicious attacks. To deal with sensor attacks, uncertain dynamics in individual follower are separated by a separation theorem, and estimation parameters are introduced for compensating and mitigating the influence from adversaries. The influence from actuator attacks are treated as a total displacement in a dead-zone nonlinearity, and an upper bound, as well as its estimation, is introduced for this displacement. The dead-zone nonlinearity, sensor attacks and unknown control gains are gathered together regarded as composite unknown control directions, and Nussbaum functions are utilized to address the issue of unknown control directions. A distributed secure consensus control strategy is thus developed recursively for each follower in the framework of surface control method. Theoretically, the stability of the closed-loop MAS is analyzed, and it is proved that the MAS achieves output consensus in spite of nonlinear dynamics and malicious attacks. Finally, theoretical results are verified via a numerical example and a group of electromechanical systems.     

Adaptive tracking control for nonlinear heterogeneous multi-agent systems with unknown dynamics

This paper is concerned with the tracking control problem for nonlinear heterogeneous multi-agent systems with a static leader, where the leader’s state is only available to a small portion of follower agents. The considered multi-agent system is composed of first- and second-order follower agents with unknown nonlinearities and unknown disturbances, and the communication graph of follower agents is fixed and directed. A robust adaptive neural network controller is designed for each follower agent. By applying the Lyapunov theory with the singular value analysis method, it is shown that all follower agents will synchronize to the leader agent with bounded residual errors. A numerical example is presented to demonstrate the effectiveness of the theoretical findings.     

Distributed control for output-constrained nonlinear multi-agent systems with completely unknown non-identical control directions

This paper studies the consensus problem for a class of nonlinear multi-agent systems with asymmetric time-varying output constraints and completely unknown non-identical control directions. Firstly, in order to deal with the problem of asymmetric time-varying output constraints, the original output-constrained multi-agent systems are transformed into new unconstrained multi-agent systems by constructing the state transformation for each agent. Secondly, the emergence of multiple Nussbaum-type function terms is avoided by introducing novel sliding-mode-esque auxiliary variables and consensus estimate variables, which allows the control directions to be completely unknown non-identical. Thirdly, a novel control strategy is proposed by combining novel variables with state transformation method for the first time, which makes the design of distributed consensus protocol more concise. Through Lyapunov stability analysis, the proposed distributed protocol ensures that the output constraints are never violated and the consensus can be achieved asymptotically. Finally, a practical simulation example is given to demonstrate the effectiveness of the proposed distributed consensus protocol.     

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 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 adaptive observer-based prescribed finite-time control of constrained multi-agent systems

This work considers a distributed adaptive output feedback control problem for nonlinear constrained multi-agent systems (MAS) in the prescribed finite time. To begin with, a state observer is constructed to estimate the unmeasurable state. Then, we develop a novel observer based distributed adaptive prescribed finite time output feedback control algorithm by incorporating the prescribed finite-time control technique into the backstepping design method. Through Lyapunov stability theory, it can be shown that all signals of MASs are bounded, the tracking errors converge to the adjustable regions around the origin within the pre-given error accuracy and settling time, and all states keep in the prescribed constraint regions. Finally, a simulation example verifies the efficacy of the obtained theoretical results.