Containment control of heterogeneous fractional-order multi-agent systems

Fractional-order calculus has been studied deeply because many networked systems can only be described with fractional-order dynamics in complex environments. When different agents of networked systems show diverse individual features, fractional-order dynamics with heterogeneous characters will be used to illustrate the multi-agent systems (MAS). Based on the distinguishing behaviors of agents, a compounded fractional-order multi-agent systems(FOMAS) is presented with diverse dynamical equations. Suppose multiple leader agents existing in FOMAS, containment consensus control of FOMAS with directed weighted topologies is studied. By applying frequency domain analysis theory of the fractional-order operator, an upper bound of delays is obtained to ensure containment controls of heterogenous FOMAS with communication delays. The consensus results of delayed fractional-order dynamics in this paper can be expanded to the integer-order models. Finally, the results are verified by simulation examples.     

Sliding-mode consensus algorithms for disturbed second-order multi-agent systems

In this paper, both leaderless and leader-follower consensus problems for a class of disturbed second-order multi-agent systems are studied. Based on integral sliding-mode control, sliding-mode consensus protocols are proposed for leaderless and leader-follower multi-agent systems with disturbances, respectively. Firstly, for leaderless second-order multi-agent systems, a sliding-mode consensus protocol is proposed to make the agents achieve asymptotic consensus. Secondly, for leader-follower second-order multi-agent systems, a finite-time sliding-mode consensus protocol is designed to make the agents achieve consensus in finite time. Both kinds of consensus protocols inherit the anti-disturbance performance and robustness of sliding-mode control and require less communication information. Finally, two numerical simulations are given for leaderless and leader-follower second-order multi-agent systems to validate the efficiency of the proposed consensus protocols.     

Fractional-order follower observer design for tracking consensus in second-order leader multi-agent systems: Periodic sampled-based event-triggered control

This paper investigates the tracking consensus problem for the second-order leader systems by designing fractional-order observer, where a periodic sampled-based data event-triggered control is employed. In order to track the position information of leader, observers for followers are designed by fractional-order system, where only the relative position information is available. Furthermore, in the process of observers design, a sampled-based event-triggered strategy is proposed so that observers use the event-triggered sampled-data, to reduce the overall load of the network. In our proposed event-triggered strategy, the event detection only works at every sampling time instant which determines whether the sampled-data should be discarded or used. Under this control strategy, the Zeno-behavior is absolutely excluded since the minimum of inter-event times is inherently lower bounded by one sampling period. It is found that the followers can track state of the leader if fractional-order observers are appropriately designed and relevant parameters are properly selected. By using the generalized Nyquist stability criterion, a necessary and sufficient condition for the observer tracking consensus of the second-order leader systems is derived. The results show that the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix, and fractional-order α of observer play a vital role in reaching consensus.     

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.     

Distributed fault detection for nonlinear multi-agent systems under fixed-time observer

This paper mainly investigates the fault detection problem for nonlinear multi-agent systems with actuator faults. For fault detection, a fixed-time observer is proposed by employing auxiliary variable received from neighbor agents. Then, with the aid of the observer, a residual vector is introduced by the auxiliary variable to detect the faults occurring on any followers, and each observer can estimate the whole state of followers. Moreover, the convergence time is dependent on the parameters of the designed observer and independent of initial condition of system state. Finally, the theoretical result is verified by a simulation example.     

Static group synchronization of second-order multi-agent systems via pinning control

This paper investigates the expected static group synchronization problem of the second-order multi-agent systems via pinning control. For directed communication topology with spanning tree, based on Gershgorin disk theorem and the matrix property, a static pinning control protocol with fixed gains is first introduced and some sufficient and necessary static group synchronization criteria are also established. It is worth mentioning that a rigorous proof is also given that only one pinning node is needed to guarantee static group synchronization, which could be inferred that our protocol might be more economical and effective in large scale of multi-agent systems. Then, for weakly connected directed communication topology with nodes of zero in-degree, an adaptive pinning control applied to the node with zero in-degree is also proposed to achieve static group synchronization. Finally, the efficiency of the proposed protocols is verified by two simulation examples.     

Adaptive fault-tolerant control for a class of nonlinear multi-agent systems with actuator faults

This paper considers the distributed adaptive fault-tolerant control problem for linear multi-agent systems with matched unknown nonlinear functions and actuator bias faults. By using fuzzy logic systems to approximate the unknown nonlinear function and constructing a local observer to estimate the states, an effective distributed adaptive fault-tolerant controller is developed. Furthermore, different from the traditional method to estimate the weight matrix, only the weight vector needs to be estimated by exchanging the order of weight vectors and fuzzy basis functions in the fuzzy logic systems. In contrast to the existing results, the assumption that the dimensions of input vector and output vector are equal is removed. In addition, it is proved that the proposed control protocol guarantees all signals in the closed-loop systems are bounded and all agents converge to the leader with bounded residual errors. Finally, simulation examples are given to illustrate the effectiveness of the proposed method.     

Event-triggered decentralized output-feedback control for interconnected nonlinear systems with input quantization

In this paper, the event-triggered decentralized control problem for interconnected nonlinear systems with input quantization is investigated. A state observer is constructed to estimate the unmeasurable states, and the state-dependent interconnections are accommodated by presenting some smooth functions. Then by employing backstepping technique and neural networks (NNs) approximation capability, a novel decentralized output feedback control strategy and an event-triggered mechanism are designed simultaneously. It is proved through Lyapunov theory that the closed-loop system is stable and the tracking property of all subsystems is guaranteed. Finally, the effectiveness of the proposed scheme is illustrated by an example.     

Novel event-triggered filter design for nonlinear networked control systems

This paper investigates the problem of event-triggered filter design for nonlinear networked control systems (NCSs) in the framework of interval type-2 (IT2) fuzzy systems. A novel IT2 fuzzy filter for ensuring asymptotic stability and H_∞ performance of filtering error system is proposed, where the premise variables are different from those of the fuzzy model. Attention is focused on solving the problem of event-triggered filter design subject to parameter uncertainties, data quantization, and communication delay in a unified frame. It is shown that the proposed event-triggered filter design communication mechanism for IT2 fuzzy NCSs has the advantage of the existing event-triggered approaches to reduce the utilization of limited network resources and provides flexibility in balancing the tracking error and the utilization of network resources. Finally, simulation example is given to validate the advantages of the presented results.     

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.     

Containment control of fractional-order multi-agent systems with time-varying delays

In this paper, containment control problems of networked fractional-order multi-agent systems with time-varying delays are studied. The normalized directed graphs are employed to characterize the communication topologies. Two sampled-data based containment control protocols are proposed, which can overcome the time-varying delays and switching topologies. It is interestingly found that the decays of the closed-loop systems correspond to the Mittag-Leffler function and its approximation, which are the extensions of the exponential function and its approximation, respectively. Based on the algebraic graph theory, the properties of row-stochastic matrix, and the relation between the topologies and the matrices, some conditions for containment control are established. For the fixed topology, a necessary and sufficient condition is obtained; and for the switching topology, a sufficient condition is provided. Finally, the theoretical results are illustrated by several numerical simulations.     

Impulsive control for passivity and exponential synchronization of coupled neural networks with multiple weights

This paper investigates the passivity and synchronization problems for two classes of multiple weighted coupled neural networks (MWCNNs) with or without time delays. Firstly, by utilizing an impulsive control strategy and some inequality techniques, several passivity criteria for MWCNNs with diverse dimensions of output and input are established. Then, based on the Lyapunov functional, some sufficient conditions to ensure the synchronization of MWCNNs via impulsive control are derived. In addition, combined with the comparison principle and the impulsive delay differential inequality, the global exponential synchronization of MWCNNs with time-varying delays is considered under impulsive control. Finally, two numerical examples illustrate the effectiveness of the obtained results.     

Viable immersion and invariance control for a class of nonlinear systems and its application to aero-engines

This paper presents a novel approach to stabilize a class of nonlinear systems with state constraints. The motivation behind this study is the need to develop a stabilizing state feedback controller that does not require the knowledge of Lyapunov function and can regulate the states to the equilibrium while meeting the constraints. By using an integration of two relatively new tools: immersion and invariance (I&I) theory and viability theory, a sufficient condition for stability and stabilizability of a general nonlinear affine system with state constraints is derived; Then, the related results are exploited to stabilize a class of nonlinear system in feedback form and with state constraints represented by inequalities and the viable I&I stabilizing state feedback controller is obtained constructively. Further, an application to a nonlinear aero-engine model with the temperature constraint is given to illustrate the applicability and the effectiveness of the proposed method. Finally, a comparative simulation is presented, highlighting the advantages of the viable I&I controller.     

Leaderless and leader-following consensus of linear multi-agent systems with distributed event-triggered estimators

This paper considers the event-triggered leaderless and leader-following consensus problems for linear multi-agent systems. By introducing event-triggered estimators, two novel control schemes are proposed. Different from the existing event-triggered controllers, which rely on the Fiedler eigenvalue of Laplacian matrix, the developed controllers only use the information from neighboring agents. Meanwhile, the adaptive trigger parameters are designed in the event-triggered mechanisms to improve the self-regulation ability of the event-triggered estimators. In addition, the leaderless consensus and the leader-following consensus can be achieved under the corresponding control protocols. Finally, two simulation examples are given to illustrate the validity of the proposed control protocols.     

Sampled observer-based adaptive output feedback fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the sampled outputs-based adaptive fault-tolerant control problem for a class of strict-feedback uncertain nonlinear systems, where the nonlinear functions are allowed to include the unmeasured system states. Within the framework, a sampled output observer is introduced to jointly estimate the system states and parameters. By combining the estimated states and the supervisory switching strategy, an adaptive fault-tolerant controller is designed to achieve the desirable tracking performance. By using Lyapunov stability theory, it is proved that all the signals of the closed-loop systems are bounded and the tracking error converges to an adjustable neighbourhood of the origin eventually both in the fault free and faulty cases. Especially, if the outputs are available all the time, the proposed output feedback fault-tolerant control method can ensure the tracking error satisfy the prescribed performance bounds regardless of the faults. Finally, two examples are used to illustrate the effectiveness of the proposed method.     

Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data

This paper deals with the leader-following consensus problem of multi-agent systems with the consideration that each agent can only transmit its position state to the neighbors at irregular discrete sampling times. In the proposed algorithm, a continuous-discrete time observer is designed for the continuous estimation of both position and velocity from the discrete position information of the neighbors. These estimated states are then used for designing a continuous control law which solves the leader-following consensus problem. Moreover, the dynamics of the leader is not fixed and can be controlled through an external input. The stability analysis has been carried out by employing the Lyapunov approach which provides sufficient conditions to tune the parameters according to the maximum allowable sampling period. The developed algorithm has been simulated and then tested on an actual multi-robot system consisting of three differential drive wheeled robots. Both simulation and hardware results validate the effectiveness of the control algorithm.     

Observer-based decentralized control of large-scale stochastic high-order feedforward systems with multi time delays

This paper investigates the problem of observer-based decentralized control for a class of large-scale stochastic high-order feedforward systems with multi time delays. By using the homogeneous domination idea and constructing the implementable observer, the decentralized output-feedback controller design scheme is firstly proposed. Then, with the aid of stochastic time delay system stability theory, the globally asymptotically stable in probability of the closed-loop system is verified by selecting an appropriate Lyapunov–Krasoviskii functional. Finally, an example is provided to demonstrate the efficiency of the proposed design method.     

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.     

A new class of fixed-time bipartite consensus protocols for multi-agent systems with antagonistic interactions

In this paper, we study the fixed-time consensus problem for multi-agent systems with structurally balanced signed graph. A new class of fixed-time nonlinear consensus protocols is designed by employing the neighbor’s information. By using Lyapunov stability method, states of all agents can be guaranteed to reach agreement in a fixed time under our presented protocols, and the consensus values are the same in modulus but different in sign. Moreover, it is shown that the settling time is not dependent on the initial conditions, and it makes a good convenience to estimate the convergence time by just knowing the graph topology and the information flow of the multi-agent systems. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed consensus protocols.     

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.