Consensus Of Uncertain Multi-agent Systems Research Articles

Adaptive Consensus of Uncertain Multi-Agent Systems with Unified Prescribed Performance

Adaptive Consensus of Uncertain Multi-Agent Systems with Unified Prescribed Performance

A Continuous Neural Network Adaptive Controller for Consensus of Uncertain Multi-Agent Systems

A Continuous Neural Network Adaptive Controller for Consensus of Uncertain Multi-Agent Systems

Consensus of Uncertain Multiagent Systems Under Granular Differentiability Concept

In this paper, the problem of consensus of linear multi-agent systems with both uncertain dynamics and uncertain switching topology is investigated. Uncertainties are considered as granular fuzzy numbers whicharerepresentedvia horizontalmembership functions (HMFs) and Relative Distance Measurement (RDM) arithmetic. It is first proved that there exists a crisp solution to a fuzzyLinear Matrix Inequality(LMI) problem. This proof creates a bridge such that multidimensional RDM arithmetic that has been devoted to linear functions so far could be entered into some problems with nonlinear functions. Then an algorithm is proposed for the consensus of the multi-agent systems with uncertainty. Here, by proving the existence of a crisp solution for fuzzy LMI, we are able to prove that the proposed algorithm can ensure achieving consensus. Furthermore, the gain coefficients obtained for this fuzzy system are crisp numbers and can be applied to real systems in practical applications. Finally, the final value of consensus is calculated as a fuzzy number to present a better understanding of the effect of uncertaintyon the final value of consensus. In addition, the efficiency of the proposed algorithm is shown in a simulation example.

Neuroadaptive Impulsive Control on Consensus of Uncertain Multiagent Systems Using Continuous and Sampled Information.

This article considers the consensus problem of uncertain multiagent systems, which is addressed by neuroadaptive impulsive control schemes. The proposed control schemes indicate that the communication among agents only occurs impulsively, while the dynamics uncertainty is addressed by adaptive schemes using neural networks. Based on such approaches, two specific control schemes are designed. One is that with impulsive feedback, the control scheme uses continuous-time information, which implies that the adaptive process is continuous over time. Another is that by adopting sampled information, the update of all systems, including the feedbacks on agents, the update of neural networks, and the estimation for uncertainty, can be executed only at impulsive instants. The latter case can reduce the energy cost for communication and control, but extra assistant systems are required. The estimation and consensus prove to be achieved with errors if some conditions are fulfilled. Numerical simulations, including a practical system example, are presented.

Adaptive consensus for uncertain multi-agent systems with stochastic measurement noises

This paper addresses asymptotic consensus for multi-agent systems with the measurement of neighbor information interfered by stochastic noises. Notably, intractable parametric uncertainties are allowed in the agent dynamics, which, coupling with inherent nonlinearities, firmly ask for distributed adaptive compensation. To limit the influence scope of measurement noises on adaptive mechanism, the distributed protocol design is separated into two aspects: (i)Reference consensus based on relative information. Local dynamic generators, providing certain reference signals, are constructed by exploiting the relative information multiplying a subtle time-varying gain. With the measurement noises attenuated via the time-varying gain, all the generators are guaranteed to evolve for all time and reach consensus in the almost sure sense. (ii)Agent tracking based on individual estimate. Utilizing individual information, local adaptive estimates are proposed for the agent uncertainties while not involving the noise measurements. In this way, a distributed adaptive protocol is designed to make each agent state track the corresponding reference signal while preventing the inherent nonlinearities from incurring finite-time explosion, and furthermore, to enable all the agents to reach average consensus in the almost sure sense.

Adaptive Control of Second-Order Safety-Critical Multiagent Systems With Nonlinear Dynamics

In this article, we propose a distributed adaptive control architecture for leader-following consensus of uncertain multiagent systems with second-order nonlinear dynamics. A nonlinear reference model system captures an ideal behavior of the agents for the leader-following consensus problem. We design a modified nonlinear reference model system and propose a distributed model reference adaptive control architecture to suppress the effects of system uncertainties without a strict knowledge of their magnitude and rate upper bounds. Consequently, each agent evolves within a (possibly different) prescribed distance from the corresponding modified reference system trajectories. Based on an input-to-state stability analysis, it is shown that the trajectories of the modified reference model system can get arbitrarily close to the trajectories of the ideal reference model system. As a result, the trajectories of the agents evolve within a user-specified prescribed distance from their ideal system trajectories, satisfying the safety constraints. The key feature of the presented control architecture in this article is the elimination of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> tuning process for the adaptation rate that is conventionally required in model reference adaptive control systems to ensure safety. An illustrative numerical example finally demonstrates the efficacy of the proposed distributed adaptive control architecture.

Consensus of Time-Varying Interval Uncertain Multiagent Systems via Reduced-Order Neighborhood Interval Observer

This work focuses on a multiagent system (MAS) with time-varying interval uncertainty in the system matrix, where multiple agents interact through an undirected topology graph and only the bounding matrices on the uncertainty in the system matrix are known. A reduced-order interval observer (IO), which is named the reduced-order neighborhood interval observer (NIO), is designed to estimate the relative state of each agent and those of its neighbors. It is shown that the reduced-order IO can guarantee the consensus of the uncertain multiagent system. Finally, simulation examples are proposed to verify the theoretical findings.

A Unified Framework for Adaptive Leaderless Consensus of Uncertain Multiagent Systems Under Directed Graphs

Due to the nonsymmetric property of the associated Laplacian matrix and the existence of uncertainties in the agent dynamics, the leaderless consensus problem of uncertain multiagent systems under general directed graphs is challenging. Motivated by the classical model reference adaptive control, in this article, we propose a simple yet efficient scheme, called the model reference adaptive consensus, by arranging each agent a reference output to track, where the output is generated by a linear reference model with the relative state measurements as input. We consider two typical agent dynamics, namely, the general linear dynamics with matching uncertainties and the second-order dynamics with extended matching uncertainties. Different linear reference models are designed for the above uncertain agent dynamics. For the first one, dynamical consensus is achieved under a fixed directed graph containing a directed spanning tree. For the latter one, position consensus is achieved under switching uniformly jointly connected graphs. In the proposed algorithms, only the relative states are interacted among the agents and there is no requirement on the communication of virtual signals.

Neural-Network-Based Fully Distributed Adaptive Consensus for a Class of Uncertain Multiagent Systems

In this article, we revisit the problem of distributed neuroadaptive consensus for uncertain multiagent systems (MASs) in the presence of unmodeled nonlinearities as well as unknown disturbances. Robust consensus controllers comprising a linear feedback term, a discontinuous feedback term, and a neural network approximation term are constructed, where in each term, the weight part is endowed with some dynamical changing law. The asymptotic convergence of the consensus errors is theoretically proved based on the graph theory, nonsmooth analysis, and Barbalat's lemma. Both leaderless consensus and leader-follower tracking problems are considered before the results are further extended to containment problem in the presence of multileaders. A dramatic feature of the proposed method, in comparison with related works, is the fully distributed fashion of the information, requiring neither the underlying Laplacian eigenvalues nor the input upper bounds of the leaders (if exist). Several numerical examples are presented to testify the theoretical results.

Fixed-time consensus for uncertain multi-agent systems with actuator faults

This paper addresses the fixed-time consensus tracking problem for multi-agent Euler-Lagrange systems in the presence of model uncertainties, external disturbances, and actuator faults. Firstly, a new fixed-time terminal sliding surface is proposed to eliminate the singularity. Secondly, a distributed model-free fixed-time sliding mode control is designed to solve the consensus tracking problem for agents with Euler-Lagrange dynamics. It is proved that the proposed control scheme can ensure that the tracking errors converge to an arbitrary small bound centered on zero within fixed time and then go to zero asymptotically. Simulation and experiments are conducted to verify the effectiveness of the proposed approach.

Consensus of uncertain multi-agent systems with input delay and disturbances

In this paper, the problem of robust consensus for multi-agent systems affected by external disturbances is discussed. A novel consensus control is developed by using a feedback controller based on disturbance rejection and Smith predictor scheme. Specifically, the disturbance rejection performance of the uncertain multi-agent systems is improved according to the estimation of equivalent-input-disturbance and the effect of time delay in the control system is reduced via Smith predictor scheme by shifting the delay outside the feedback loop. Furthermore, by combining Lyapunov theory, matrix inequality techniques and properties of Kronecker product, a robust feedback controller for each agent is designed such that the desired consensus of the uncertain multi-agent systems affected by external disturbances can be ensured. Finally, to illustrate the validity of the designed control scheme, two numerical examples with simulation results are provided.

Finite-time leaderless consensus of uncertain multi-agent systems against time-varying actuator faults

Abstract This paper addresses the finite-time leaderless consensus problem for a class of continuous-time multi-agent systems subject to linear fractional transformation uncertain parameters using an observer-based fault-tolerant controller. Here, it is considered that the network of the system is described by an undirected graph subject to fixed topology and the aforementioned controller is impacted by time-varying actuator faults. Then, the desired consensus protocols are proposed in such a way that the effects of possible uncertainties and actuator faults are compensated efficiently within a prescribed finite-time period. More precisely, the leaderless consensus analysis is carried out in the framework of Lyapunov-Krasovskii functional and the required conditions for the existence of proposed fault-tolerant controller are derived in terms of linear matrix inequalities. Moreover, the proposed consensus design parameters can be computed by solving a set of linear matrix inequality constraints. Finally, two examples including a formation flying satellites model are provided to show the efficiency and usefulness of the proposed control scheme.

A Descriptor Approach to Robust Leader-Following Output Consensus of Uncertain Multi-Agent Systems With Delay

In this technical note, a descriptor approach to leader-following output consensus of multi-agent systems with both stationary and dynamic leaders is given in the presence of transmission delay and model uncertainty. The proposed method can deal with stable and unstable agents described by general linear models. To this end, a new proportional-derivative-integral (PID) consensus protocol for the closed-loop multi-agent system is proposed under a directed graph. Applying this consensus protocol to the multi-agent system leads to a time-delay closed-loop equation of neutral type. To deal with the resulting neutral system, a descriptor model transformation is used to derive delay-dependent sufficient conditions for the existence of the consensus protocol in terms of certain linear matrix inequalities (LMI). The application of the proposed method is illustrated in a teleoperation system. Simulation results are given to show the effectiveness of the proposed approach.

Robust consensus for uncertain multi-agent systems with discrete-time dynamics

This paper investigates robust consensus for multi-agent systems with discrete-time dynamics affected by uncertainty. In particular, the paper considers multi-agent systems with single and double integrators, where the weighted adjacency matrix is a polynomial function of uncertain parameters constrained into a semialgebraic set. Firstly, necessary and sufficient conditions are provided for robust consensus based on the existence of a Lyapunov function polynomially dependent on the uncertainty. In particular, an upper bound on the degree required for achieving necessity is provided. Secondly, a necessary and sufficient condition is provided for robust consensus with single integrator and nonnegative weighted adjacency matrices based on the zeros of a polynomial. Lastly, it is shown how these conditions can be investigated through convex programming by exploiting linear matrix inequalities and sums of squares of polynomials. Some numerical examples illustrate the proposed results. Copyright © 2013 John Wiley & Sons, Ltd.

Mean Square Consensus for Uncertain Multiagent Systems with Noises and Delays

This paper investigates the consensus problem in mean square for uncertain multiagent systems with stochastic measurement noises and symmetric or asymmetric time-varying delays. By combining the tools of stochastic analysis, algebraic graph theory, and matrix theory, we analyze the convergence of a class of distributed stochastic approximation type protocols with time-varying consensus gains. Numerical examples are also given to illustrate the theoretical results.