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.     

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.     

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.     

Adaptive distributed synchronization of heterogeneous multi-Agent systems over directed graphs with time-Varying edge weights

Time-varying edge weights represent dynamical interactions between any two nodes in multi-agent systems (MASs). In this paper, we consider a synchronization problem for heterogeneous MASs over directed graphs with time-varying edge weights from a control-theoretic perspective. We seek for an adaptive control protocol that drives the synchronization error in the presence of time-varying edge weights to converge in terms of asymptotic stability. We propose a class of observer networks for estimating leaders and output regulation equation solvers built on directed graphs with time-varying edge weights. Finally, we use a simulation study to verify the effectiveness of the proposed protocol.     

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.     

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.     

Event-triggered adaptive control of multi-agent systems with saturated input and partial state constraints

In this paper, we study the consensus tracking control problem of a class of strict-feedback multi-agent systems (MASs) with uncertain nonlinear dynamics, input saturation, output and partial state constraints (PSCs) which are assumed to be time-varying. An adaptive distributed control scheme is proposed for consensus achievement via output feedback and event-triggered strategy in directed networks containing a spanning tree. To handle saturated control inputs, a linear form of the control input is adopted by transforming the saturation function. The radial basis function neural network (RBFNN) is applied to approximate the uncertain nonlinear dynamics. Since the system outputs are the only available data, a high-gain adaptive observer based on RBFNN is constructed to estimate the unmeasurable states. To ensure that the constraints of system outputs and partial states are never violated, a barrier Lyapunov function (BLF) with time-varying boundary function is constructed. Event-triggered control (ETC) strategy is applied to save communication resources. By using backstepping design method, the proposed distributed controller can guarantee the boundedness of all system signals, consensus tracking with a bounded error and avoidance of Zeno behavior. Finally, the correctness of the theoretical results is verified by computer simulation.     

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.     

Robust time-varying output formation tracking for heterogeneous multi-agent systems with adaptive event-triggered mechanism

This paper investigates the time-varying output formation tracking problem of heterogeneous multi-agent systems subjected to model uncertainties and external disturbances via adaptive event-triggered mechanism. Firstly, an adaptive distributed event-triggered observer is constructed to acquire the leader’s state and a time-varying formation output tracking controller utilizing sliding mode method is proposed to deal with the model uncertainties and external disturbances can be addressed. Secondly, an algorithm is given to claim the design procedures of the event-triggered based controller and asymptotic convergence of the controller is proved based on Lyapunov theory. Thirdly, Zeno-behavior is proved to be excluded strictly. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.     

Formation consensus for discrete-time heterogeneous multi-agent systems with link failures and actuator/sensor faults

In this paper, a distributed control protocol is presented for discrete-time heterogeneous multi-agent systems in order to achieve formation consensus against link failures and actuator/sensor faults under fixed and switching topologies. A model equivalent method is proposed to deal with the heterogeneous system consists of arbitrary order systems with different parameters. Based on graph theory and Lyapunov theory, stability conditions to solve formation consensus problem are developed for the underlying heterogeneous systems with communication link failures. In order to tolerate actuator/sensor faults, a distributed adaptive controller is proposed based on fault compensation. The desired control is designed by linear matrix inequality approach together with cone complementarity linearisation algorithm. After applying the new control scheme to heterogeneous systems under the directed topologies with link failures and faults, the resulting closed-loop heterogeneous system is validated to be stable. The effectiveness of the new formation consensus control strategy and its robustness are verified by simulations.     

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.     

Distributed adaptive output-feedback tracking control of non-affine multi-agent systems with prescribed performance

This paper addresses the distributed adaptive output-feedback tracking control problem of uncertain multi-agent systems in non-affine pure-feedback form under a directed communication topology. Since the control input is implicit for each non-affine agent, we introduce an auxiliary first-order dynamics to circumvent the difficulty in control protocol design and avoid the algebraic loop problem in control inputs and the unknown control gain problem. A decentralized input-driven observer is applied to reconstruct state information of each agent, which makes the design and synthesis extremely simplified. Based on the dynamic surface control technique and neural network approximators, a distributed output-feedback control protocol with prescribed tracking performance is derived. Compared with the existing results, the restrictive assumptions on the partial derivative of non-affine functions are removed. Moreover, it is proved that the output tracking errors always stay in a prescribed performance bound. The simulation results are provided to demonstrate the effectiveness of the proposed method.     

Consensus of linear multi-agent systems based on full-order observer

This paper considers distributed consensus problem of multi-agent systems consisting of general linear dynamics with a time-invariant communication topology. A distributed full-order observer type consensus protocol based on relative output measurements of neighbor agents is proposed. It is found that the consensus problem of linear multi-agent systems with a directed communication topology having a spanning tree can be solved if and only if all subsystems are asymptotically stable. Some necessary and sufficient conditions are obtained for ensuring consensus in multi-agent systems. The design technique is based on algebraic graph theory, Riccati inequality and linear control theory. Finally, simulation example is given to illustrate the effectiveness of the theoretical results.     

Synchronous control of multiple electrohydraulic actuators under distributed switching topologies with lumped uncertainty

A leader-following synchronous control is proposed in multiple electrohydraulic actuators (MEHAs) under distributed switching topologies to guarantee the follower electrohydraulic actuators (EHAs) tracking the leader motion. Each EHA has a 3-orders nonlinear dynamics with lumped uncertainties involving uncertain hydraulic parameters and unknown external load. Then a quasi-synchronization controller together with a high-gain disturbance observer is designed by Lyapunov techniques to guarantee the synchronous errors asymptotically convergence to a zero neighborhood. Finally, the effectiveness of the proposed quasi-synchronous controller is verified by both simulation and experimental bench such that the finite EHA nodes achieve leader-following synchronous motion under distributed switching topologies.     

Distributed data driven control for multi-agent consensus with unknown system dynamics

This study investigates the consensus tracking problem for unknown multi-agent systems (MASs) with time-varying communication topology by using the methods of data-driven control and model predictive control. Under the proposed distributed iterative protocol, sufficient conditions for reducing tracking error are analyzed for both time invariable and time varying desired trajectories. The main feature of the proposed protocol is that the dynamics of the multi-agent systems are not required to be known and only local input-output data are utilized for each agent. Numerical simulations are presented to illustrate the effectiveness of the derived consensus conditions.     

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.     

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.     

Fully distributed observer-based tracking control for Lur’e systems with event-triggered communication

This paper investigates the problem of cooperative tracking for Lur’e systems under directed spanning tree topology. First, a control protocol is proposed to achieve cooperative tracking consensus by a distributed observer, which utilizes only the states of neighboring agents based on the event-triggering conditions with mixed node and edge. Then, an improved tracking protocol is developed by considering the case that only the outputs of neighbors can be obtained. With the aid of adaptive updating parameters, the two protocols do not utilize the minimum eigenvalue of Laplacian matrix, and can deal with the nonlinear dynamics of Lur’e systems in a fully distributed manner. Moreover, with the Lyapunov analysis framework, the tracking errors can be proved to converge to zero in both cases. Zeno behavior is excluded from the event-triggering conditions containing states and outputs of neighbors. Finally, the effectiveness of the proposed protocols is verified by two numerical simulations.     

Distributed tracking control of second-order multi-agent systems with sampled data

This paper studies the leader–follower consensus problem of second-order multi-agent dynamical systems with fixed and stochastic switching topologies in a sampled-data setting. A distributed linear consensus protocol is designed to track an active leader, where the current position information of neighbor agents and self-velocity data are utilized. A necessary and sufficient condition is established under fixed and directed topology for reaching consensus, which depends on the sampling period and control gain parameters. A sufficient condition is obtained under the Markov switching topology case. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results.