Observer-based event-triggered tracking consensus of non-ideal general linear multi-agent systems

In this paper, the leader-following consensus problem of general linear multi-agent systems without direct access to real-time state is investigated. A novel observer-based event-triggered tracking consensus control scheme is proposed. In the control scheme, a distributed observer is designed to estimate the relative full states, which are used in tracking consensus protocol to achieve overall consensus. And an event-triggered mechanism with estimated state-dependent event condition is adopted to update the control signals so as to reduce unnecessary data communication. Based on the Lyapunov theorem and graph theory, the proposed event-triggered control scheme is proved to implement the tracking consensus when real-time state cannot direct obtain. Moreover, such scheme can exclude Zeno-behavior. Finally, numerical simulations illustrate the effectiveness of the theoretical results.     

Robust cooperative output regulation of heterogeneous uncertain linear multi-agent systems by intermittent communication

In this paper, we study the robust cooperative output regulation problem of heterogeneous linear multi-agent systems with system uncertainties and directed communication topology. A robust distributed event-triggered control scheme is proposed based on the internal model principle. To avoid continuous monitoring of measurement errors for the event-triggering condition, a novel self-triggered control scheme is further proposed. Moreover, by introducing a fixed timer in the triggering mechanisms, Zeno behavior can be excluded for each agent. An example is finally provided to demonstrate the effectiveness of the proposed self-triggered control scheme.     

Barrier Lyapunov function-based decentralized adaptive neural control for uncertain high-order stochastic nonlinear interconnected systems with output constraints

Decentralized adaptive neural backstepping control scheme is developed for uncertain high-order stochastic nonlinear systems with unknown interconnected nonlinearity and output constraints. For the control of high-order nonlinear interconnected systems, it is assumed that nonlinear system functions are unknown. It is for the first time to control stochastic nonlinear high-order systems with output constraints. Firstly, by constructing barrier Lyapunov functions, output constraints are handled. Secondly, at each recursive step, only one adaptive parameter is updated to overcome over-parameterization problems, and RBF neural networks are used to identify unknown nonlinear functions so that the difficulties caused by completely unknown system functions and stochastic disturbances are tackled. Finally, based on the Lyapunov stability method, the decentralized adaptive control scheme via neural networks approximator is proposed, ultimately reducing the number of learning parameters. It is shown that the designed controller can guarantee all the signals of the resulting closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB), and the tracking errors for each subsystem are driven to a small neighborhood of zero. The simulation studies are performed to verify the effectiveness of the proposed control strategy.     

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.     

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.     

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.     

Observer-based exponential stabilization for time-delay systems via augmented weighted integral inequality

In this paper, we design observer-based feedback control for a class of linear systems. The novelty of the paper comes from the consideration of an augmented weighted based integral inequality involving quadratic functions with an exponential term which is less conservative than the celebrated weighted integral inequality employed in the context of time-delay systems. By using appropriately chosen Lyapunov–Krasovskii functional (LKF), together with the derived integral inequality, a new sufficient condition for exponential stability in terms of linear matrix inequalities (LMIs) is proposed for the delayed linear systems with state feedback control. Finally, the applicability and superiority of the proposed theoretical results over the existing ones are analyzed in virtue of numerical examples.     

Average-consensus tracking of multi-agent systems with additional interconnecting agents

Average-consensus tracking problem is investigated for first-order multi-agent systems composed of valid agents and additional interconnecting agents. Valid agents have constant reference inputs, while additional interconnecting agents do not have reference inputs. Average-consensus tracking algorithms are proposed for the agents converging to the average value of constant reference inputs of valid agents. Under symmetric and connected topology, consensus conditions are obtained for the agents without and with communication delay, respectively, by using generalized Nyquist criterion. Numerical examples illustrate the correctness of theoretical results.     

Leader-following consensus of multi-agent systems with limited data rate

This paper investigates the leader-following consensus problem of time-invariant linear multi-agent systems with limited data rate. Based on the idea of assigning a priority level for each agent of the concerned multi-agent system, a novel distributed control law has been proposed. The proposed control law has two distinctive advantages. That is, it is fully distributed in the sense that it does not rely on the eigenvalues of the Laplace matrix associated with the topology. Moreover, the required data rate is independent of the number of agents and remains small even if the number of the agents in multi-agent systems is large. An example is finally given to illustrate the effectiveness of the proposed controller.     

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.     

Event-triggered consensus of nonlinear multi-agent systems with stochastic switching topology

This paper is concerned with a leader-follower consensus problem for networked Lipschitz nonlinear multi-agent systems. An event-triggered consensus controller is developed with the consideration of discontinuous state feedback. To further enhance the robustness of the proposed controller, modeling uncertainty and switching topology are also considered in the stability analysis. Meanwhile, a time-delay equivalent approach is adopted to deal with the discrete-time control problem. Particularly, a sufficient condition for the stochastic stabilization of the networked multi-agent systems is proposed based on the Lyapunov functional method. Furthermore, an optimization algorithm is developed to derive the parameters of the controller. Finally, numerical simulation is conducted to demonstrate the effectiveness of the proposed control algorithm.     

Output feedback stabilization of high-order nonlinear systems with polynomial nonlinearity

In this paper, the problem of output feedback stabilization for high-order nonlinear systems with more general low-order and high-order nonlinearities multiplied by a polynomial-type output-dependent growth rate is studied. By constructing the novel Lyapunov function and observer, based on the homogeneous domination and adding a power integrator methods, an output feedback controller is developed to guarantee that the equilibrium of the closed-loop system is globally uniformly asymptotically stable.     

Robust quantized consensus of discrete multi-agent systems under input saturation

In this paper, we consider the quantized consensus problem of multiple discrete-time integrator agents which suffer from input saturation. As agents transmit state information through communication networks with limited bandwidth, the states of agents have to be quantized into a finite number of bits before transmission. To handle this quantized consensus problem, we introduce an internal time-varying saturation function into the controllers of all agents and ensure that the range of the state of each agent can be known in advance by its neighboring agents. Based on such shared state range information, we construct a quantized consensus protocol which implements a finite-bit quantization strategy to all states of agents and can guarantee the achievement of the asymptotic consensus under any given input saturation threshold. Such desired consensus can be guaranteed at as low bit rate as 1 bit per time step for each agent. Moreover, we can place an upper bound on the convergence rate of the consensus error of agents. We further improve that quantized consensus protocol to a robust version whose parameters are determined with only an upper bound on the number of agents and does not require any more global information of the inter-agent network. Simulations are done to confirm the effectiveness of our quantized consensus protocols.     

Formation control and collision avoidance for a class of multi-agent systems

In this paper, a control scheme is proposed for a group of elliptical agents to achieve a predefined formation. The agents are assumed to have the same dynamics, and communication among the agents are limited. The desired formation is realized based on the reference formation and the mapping decision. In the control design, searching algorithms for both cases of minimum distance and tangents are established for each agent and its neighbors. In order to avoid collision, an optimal path planning algorithm based on collision angles, and a self-center-based rotation algorithm are also proposed. Moreover, randomized method is used to provide the optimal mapping decision for the underlying system. Two examples and analyses are presented to demonstrate the effectiveness and potential of the new control scheme.     

Robust multi-tracking of heterogeneous multi-agent systems with uncertain nonlinearities and disturbances

A robust multi-tracking problem is solved for heterogeneous multi-agent systems with uncertain nonlinearities and disturbances. The nonlinear function satisfies a Lipschitz condition with a time-varying gain, the integral of which is bounded by a linear function. A distributed impulsive protocol is proposed, where the position data and velocity data of desired trajectories are needed only at sampling instants. Based on the system decomposition technique, the error dynamic system of achieving multi-tracking is decomposed into two impulsive dynamic systems with vanishing perturbation and nonvanishing perturbation, respectively. Constructing a nominal model, then the multi-tracking problem is converted into the stability of impulsive dynamic system with nonvanishing perturbation under some conditions. It is proved that the proposed impulsive protocol is robust enough to solve the multi-tracking problem. Numerical examples are presented to illustrate the effectiveness of our theoretical results.     

Adaptive control of output feedback nonlinear systems with unmodeled dynamics and output constraint

This paper is concerned with the adaptive control problem of a class of output feedback nonlinear systems with unmodeled dynamics and output constraint. Two dynamic surface control design approaches based on integral barrier Lyapunov function are proposed to design controller ensuring both desired tracking performance and constraint satisfaction. The radial basis function neural networks are utilized to approximate unknown nonlinear continuous functions. K-filters and dynamic signal are introduced to estimate the unmeasured states and deal with the dynamic uncertainties, respectively. By theoretical analysis, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded, while the output constraint is never violated. Simulation results demonstrate the effectiveness of the proposed approaches.     

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 stabilization control for high-order nonlinear time-delay systems with its application

This paper investigates the state-feedback stabilization problem in the smooth case for a class of high-order nonlinear systems with time delays. By generalizing a novel radial basis function neural network (RBF NN) approximation approach to high-order nonlinear systems, we successfully remove the power order restriction and the growth conditions on system nonlinearities. It should be pointed out that the knowledge of NN nodes and weights does not need to be known a priori and operate on-line, and the adaptive parameter is only one. Furthermore, without imposing any growth assumptions on system nonlinearities, we construct a smooth adaptive state-feedback controller which guarantees the closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB). Finally, we apply the proposed scheme to a single-link robot system and a numerical example to demonstrate the effectiveness of the controller.     

Leaderless consensus of multi-agent systems via an event-triggered strategy under stochastic sampling

This paper investigates mean square leaderless consensus of networked nonlinear multi-agent systems. An efficient distributed event-triggered mechanism based on stochastic sampling is introduced to reduce the communication cost and controller updates. The stochastic sampling interval randomly switches between two given values. Mean square consensus criteria for multi-agent systems with strongly connected networks or networks containing directed spanning trees are derived, respectively. Moreover, the case with a special event-triggered weighting matrix and the case without even-triggered strategies are also discussed. Finally, an example is given to verify the theoretical results.     

Reliable consensus control for semi-Markov jump multi-agent systems: A leader-following strategy

This paper is devoted to the reliable leader-following consensus realization for a class of nonlinear multi-agent systems. The parameters of every agent are assumed to encounter sudden changes, which are governed by a semi-Markov process. A control protocol which possesses the performance of resisting actuator faults is employed for ensuring the reliable leader-following consensus and an analysis result is established by using the Lyapunov–Krasovskii functional method. Then an easy-to-implement condition is proposed for the issue of leader-following reliable consensus realization. If the condition is satisfied, the desired controller gain can be obtained via the numerical solutions of a set of linear matrix inequalities. At last, the feasibility of the proposed scheme is well explained by an illustrated example.