Consensus control via iterative learning for distributed parameter models multi-agent systems with time-delay

Most of the available results of iterative learning control (ILC) are that solve the consensus problem of lumped parameter models multi-agent systems. This paper considers the consensus control problem of distributed parameter models multi-agent systems with time-delay. By using the knowledge between neighboring agents, considering time-delay problem in the multi-agent systems, a distributed P-type iterative learning control protocol is proposed. The consensus error between any two agents in the sense of L² norm can converge to zero after enough iterations based on proposed ILC law. And then we extend these conclusions to Lipschitz nonlinear case. Finally, the simulation result shows the effectiveness of the control method.     

Adaptive iterative learning protocol design for nonlinear multi-agent systems with unknown control direction

This paper investigates a new adaptive iterative learning control protocol design for uncertain nonlinear multi-agent systems with unknown gain signs. Based on Nussbaum gain, adaptive iterative learning control protocols are designed for each follower agent and the adaptive laws depend on the information available from the agents in the neighbourhood. The proper protocols guarantee each follower agent track the leader perfectly on the finite time interval and the Nussbaum-type item can seek control direction adaptively. Furthermore, the formation problem is studied as an extension. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method in this article.     

Iterative learning control for fractional-order multi-agent systems

In this paper, we apply iterative learning control to both linear and nonlinear fractional-order multi-agent systems to solve consensus tacking problem. Both fixed and iteration-varying communicating graphs are addressed in this paper. For linear systems, a PD^α-type update law with initial state learning mechanism is introduced by virtue of the memory property of fractional-order derivative. For nonlinear systems, a D^α-type update law with forgetting factor and initial state learning is designed. Sufficient conditions for both linear and nonlinear systems are established to guarantee all agents achieving the asymptotic output consensus. Simulation examples are provided to verify the proposed schemes.     

P-type iterative learning control algorithm for a class of linear singular impulsive systems

This paper is focused on the iterative learning control problem for linear singular impulsive systems. For the purpose of tracking the desired output trajectory, a P-type iterative learning control algorithm is investigated for such system. Based on the fundamental property of singular impulsive systems and the restricted equivalent transformation theory of singular systems, the convergence conditions of the tracking errors for the system are obtained in the sense of λ norm. Finally, the validation of the algorithm is confirmed by a numerical example.     

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.     

Consensus for heterogeneous networked multi-agent systems with switching topology and time-varying delays

This paper investigates consensus problem for heterogeneous discrete linear time-invariant (LTI) multi-agent systems subjected to time-varying network communication delays and switching topology. A new two-stage consensus protocol is proposed based on stochastic, indecomposable and aperiodic (SIA) matrix and pseudo predictive scheme. With pseudo predictive scheme the network delay is compromised. Consensus analysis based on seminorm is provided. Results give conditions for such systems with periodic switching topology and time-varying delays to reach consensus. Highlights of the paper include: the protocol can be implemented in a distributed manner; the pseudo predictive approach requires less computation and communication; the verification of consensus convergence does not require the global information about the communication topology; the protocol allows delay to be time-varying, topology to dynamically and asymmetrically switch and system mode to be unstable. Numerical and practical examples demonstrate the effectiveness of the theoretical results.     

Quantized consensus in second-order multi-agent systems via event-trigger control with sampled data

This paper addresses the quantized consensus problem of second-order multi-agent systems (MASs) where the topology has a directed spanning tree. An event-trigger control protocol (ETCP) is proposed by designing a combined threshold. The combined threshold not only reduces more event triggers than the state-dependent threshold, but also is more practical than the time-dependent threshold. For further reducing computation resources and transmission cost, the sampled data, self-trigger scheme and data quantization are employed together. Under the proposed ETCP, the sufficient condition is derived to guarantee the quantized consensus of second-order MASs. Finally, the comparison experiments are conducted to demonstrate the superiority of ETCP based on the combined threshold.     

Analysis of iterative learning control for one-sided Lipschitz nonlinear singular systems

This paper deals with the problem of iterative learning control for a class of singular systems with one-sided Lipschitz nonlinearity. In order to track the given desired trajectory, a closed-loop D-type learning algorithm is proposed for such nonlinear singular systems. Then the convergence result is derived by utilizing the one-sided Lipschitz and quadratically inner-bounded conditions. In this work, the main contribution is to apply the iterative learning approach to one-sided Lipschitz singular systems, while most researches are focus on the Lipschitz systems. It is shown that the algorithm can guarantee the system output converges to the desired trajectory on the whole time interval. Finally, the effectiveness of the presented algorithm is verified by a numerical example.     

Leader-following fixed-time quantized consensus of multi-agent systems via impulsive control

In this paper, we mainly tend to consider distributed leader-following fixed-time quantized consensus problem of nonlinear multi-agent systems via impulsive control. An appropriate quantized criterion and some novel control protocols are proposed in order to solve the problem. The protocols proposed integrates the two control strategies from the point of view of reducing communication costs and constraints, which are quantized control and impulsive control. The fixed-time quantized consensus of multi-agent is analyzed in terms of algebraic graph theory, Lyapunov theory and comparison system theory, average impulsive interval. The results show that if some sufficient conditions are met, the fixed-time consensus of multi-agent systems can be guaranteed under impulsive control with quantized relative state measurements. In addition, compared with finite-time consensus, the settling-time of fixed-time quantized consensus does not depend on the initial conditions of each agent but on the parameters of the protocol. Finally, numerical simulations are exploited to illustrate the effectiveness and performance to support our theoretical analysis.     

Terminal iterative learning control for discrete-time nonlinear systems based on neural networks

The terminal iterative learning control is designed for nonlinear systems based on neural networks. A terminal output tracking error model is obtained by using a system input and output algebraic function as well as the differential mean value theorem. The radial basis function neural network is utilized to construct the input for the system. The weights are updated by optimizing an objective function and an auxiliary error is introduced to compensate the approximation error from the neural network. Both time-invariant input case and time-varying input case are discussed in the note. Strict convergence analysis of proposed algorithm is proved by the Lyapunov like method. Simulations based on train station control problem and batch reactor are provided to demonstrate the effectiveness of the proposed algorithms.     

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.     

Bipartite output consensus for heterogeneous linear multi-agent systems with fully distributed protocol

This paper addresses the problem of bipartite output consensus of heterogeneous multi-agent systems over signed graphs. First, under the assumption that the sub-graph describing the communication topology among the agents is connected, a fully distributed protocol is provided to make the heterogeneous agents achieve bipartite output consensus. Then for the case that the topology graph has a directed spanning tree, a novel adaptive consensus protocol is designed, which also avoids using any global information. Each of these two protocols consists of a solution pair of the regulation equation and a homogeneous compensator. Numerical simulations show the effectiveness of the proposed approach.     

Event-triggered tracking control for couple-group multi-agent systems

This paper mainly investigates the event-triggered tracking control for couple-group multi-agent systems in a disturbance environment, where the topology of the agents is switching. Consensus protocol is designed for the case that some agents reach a consistent value, while the other agents reach another consistent value. Then, event-triggered control laws are designed to reduce the frequency of individual actuation updating for discrete-time agent dynamics. Moreover, by applying the Lyapunov function method, a sufficient condition of couple-group consensus is established in terms of a matrix inequality when the communication topology is switching. Finally, simulation examples are given to demonstrate the effectiveness of the proposed methods.     

Consensus disturbance rejection for Lipschitz nonlinear multi-agent systems with input delay: A DOBC approach

In this paper, a new predictor-based consensus disturbance rejection method is proposed for high-order multi-agent systems with Lipschitz nonlinearity and input delay. First, a distributed disturbance observer for consensus control is developed for each agent to estimate the disturbance under the delay constraint. Based on the conventional predictor feedback approach, a non-ideal predictor based control scheme is constructed for each agent by utilizing the estimate of the disturbance and the prediction of the relative state information. Then, rigorous analysis is carried out to ensure that the extra terms associated with disturbances and nonlinear functions are properly considered. Sufficient conditions for the consensus of the multi-agent systems with disturbance rejection are derived based on the analysis in the framework of Lyapunov–Krasovskii functionals. A simulation example is included to demonstrate the performance of the proposed control scheme.     

Specified-time bearing-based formation control of multi-agent systems via a dynamic gain approach

In this paper, the specified-time bearing-based formation control problem is investigated via a dynamic gain approach. Both the leader-follower and leaderless cases for single- and double-integral multi-agent systems are considered with bearing measurement, respectively. By considering the communication graph as bearing rigid, distributed bearing-based controllers with a time-varying gain are designed. By using time transformation method and Lyapunov stability theory, the close-loop systems under the proposed protocols can achieve the target formation within the specified time. Comparing with some existing results, the proposed approaches can make multi-agent systems converge to the desired formation within any preset time without dependence on the initial conditions or system parameters. Finally, some simulations and experiments are presented to demonstrate the effectiveness of the proposed algorithms.     

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.     

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.     

Finite-time consensus of linear multi-agent system via distributed event-triggered strategy

In this paper, we mainly investigate the finite-time consensus problem of general linear multi-agent systems. The paper proposed a suitable event-triggered control strategy. The strategy has some desirable properties including: distributed, independent, and asynchronous. It is theoretical demonstrated that the multi-agent system can achieve consensus in a certain time regardless of the initial condition under this event-triggered control scheme. In addition, without finding singular triggering problem, we prove the feasibility of this proposed event-triggered control protocol. Finally, we put forward some simulation graphs for the sake of showing the availability of our conclusions.     

Dissipative consensus problems for multi-agent networks via sliding mode control

In this paper, dissipative consensus problems are discussed for multi-agent networks. Firstly, sufficient conditions are proposed to ensure $(Q,S,R)?$dissipative consensus for multi-agent networks with external disturbances. Then, by designing an integral-type sliding surface function, a controller is obtained and the corresponding sufficient conditions are given to guarantee $(Q,S,R)?$dissipative consensus for multi-agent networks with external disturbances. Moreover, the sliding mode control law is formulated such that multi-agent networks drive onto the predefined surface in finite time. Finally, an example is given to illustrate the effectiveness of the obtained 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.