Distributed H ∞ consensus of multi-agent systems: a performance region-based approach

This article addresses the distributed H _∞ consensus problem of multi-agent systems with general linear node dynamics using relative output measurements. The notion of H _∞ consensus performance region is first introduced and then analysed as a basis for the protocol design. A new kind of distributed observer-type H _∞ protocols is further proposed. Theoretical analysis indicates that the distributed H _∞ consensus problem can be solved if and only if the coupling strength of the protocol belongs to the H _∞ performance region of the closed-loop network. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.     

Leader-following consensus of multiple uncertain Euler–Lagrange systems under switching network topology

In recent years, the leader-following consensus problem for multiple uncertain Euler–Lagrange systems has been studied under some restrictive assumptions on the network topology. In this paper, we further study the same problem under switching network topology. We propose a distributed adaptive control law that can solve the problem under a switching network satisfying jointly connected condition. Under this condition, our results do not require the network to be undirected and allow the network to be disconnected at any time instant. Moreover, by introducing an exosystem to generate various reference signals, our control law can handle a class of reference signals such as sinusoidal signals with arbitrary amplitudes and initial phases or ramp signals with arbitrary slopes.     

Leader–follower consensus of linear multi-agent systems with unknown external disturbances

This paper addresses the leader–follower consensus tracking problem for multi-agent systems with identical general linear dynamics and unknown external disturbances. First, a distributed extended state observer is proposed, where both the local states and disturbance of each agent are estimated simultaneously by using the relative output information between neighbors. Then a consensus algorithm is proposed for each agent based on the relative estimated states between neighbors and its own disturbance estimate. It is shown that, with the proposed observer-based consensus algorithm, the leader–follower consensus problem can be solved. Finally, we present a simulation example to demonstrate the effectiveness of the proposed algorithm.     

Distributed H∞ consensus control for nonlinear multi-agent systems under switching topologies via relative output feedback

Neural Computing and Applications - For a class of nonlinear multi-agent systems under switching topologies with disturbances, we propose a distributed H∞ consensus control protocol based on...     

Event-triggered H∞ consensus control for input-constrained multi-agent systems via reinforcement learning

This article presents an event-triggered H∞ consensus control scheme using reinforcement learning (RL) for nonlinear second-order multi-agent systems (MASs) with control constraints. First, considering control constraints, the constrained H∞ consensus problem is transformed into a multi-player zero-sum game with non-quadratic performance functions. Then, an event-triggered control method is presented to conserve communication resources and a new triggering condition is developed for each agent to make the triggering threshold independent of the disturbance attenuation level. To derive the optimal controller that can minimize the cost function in the case of worst disturbance, a constrained Hamilton–Jacobi–Bellman (HJB) equation is defined. Since it is difficult to solve analytically due to its strongly non-linearity, reinforcement learning (RL) is implemented to obtain the optimal controller. In specific, the optimal performance function and the worst-case disturbance are approximated by a time-triggered critic network; meanwhile, the optimal controller is approximated by event-triggered actor network. After that, Lyapunov analysis is utilized to prove the uniformly ultimately bounded (UUB) stability of the system and that the network weight errors are UUB. Finally, a simulation example is utilized to demonstrate the effectiveness of the control strategy provided.     

H ∞ consensus control of multi-agent systems with switching topology: a dynamic output feedback protocol

This article is devoted to the consensus control for switching networks of multiple agents with linear coupling dynamics and subject to external disturbances, which is transformed into an H _∞ control problem by defining an appropriate controlled output. On this basis, a distributed dynamic output feedback protocol is proposed with an undetermined system matrix, and a condition in terms of linear matrix inequalities (LMIs) is derived to ensure consensus of the multi-agent system with a prescribed H _∞ level. Furthermore, system matrix of the protocol is designed by solving two LMIs. A numerical example is included to illustrate the effectiveness of the proposed consensus protocol.     

On H ∞-consensus filtering for multi-agent systems

This article investigates the H _∞-consensus filtering problem for multi-agent systems. The purpose of the problem addressed herein is to design decentralised full-order filters such that the filtering error dynamics achieve consensus and the prescribed noise attenuation level in H _∞ sense. Based on the state decomposition and the Lyapunov function method, sufficient conditions expressed in terms of linear matrix inequalities are derived for existence of such filters. Finally, a simulation example is utilised to demonstrate the usefulness of the developed theoretical results.     

Robust H ∞ consensus control concerning second-order multi-agent systems with time-varying delays on dynamic topologies

Robust H _∞ consensus control for second-order multi-agent systems is addressed. Considering the delayed directed networks with disturbances and uncertainty parameters on dynamic topologies, the consensus protocols are proposed and analysed. By constructing the common Lyapunov–Krasovkii functional, applying the Lyapunov–Krasovkii theory and integral inequality approach, the sufficient condition of consensus protocol convergence is derived, guaranteeing robust H _∞ consensus for given second-order multi-agent systems. Finally, numerical examples are provided to demonstrate the effectiveness of the main results.     

H∞ and H2 control of multi-agent systems with transient performance improvement

In this paper, the H_∞ consensus control and H₂ robust control synthesised with transient performance problems are investigated for a group of autonomous agents with linear or linearised dynamics. Based on the relative information between neighbouring agents and a subset of absolute information of the agents, distributed controllers are proposed for both H_∞ and H₂ cases. Compared with the existing protocols, the one presented in this article focuses on improving the transient performance of the consensus problem. By using the tools from matrix analysis and robust control theory, conditions for the existence of controllers to those problems under an undirected communication topology are provided. Then, it is shown that the H₂ performance limit of uncertain systems under a distributed controller equals the minimum H_∞ consensus index synthesised with transient performance of a single agent by using a state feedback controller, independent of the communication topology. Finally, a simulation example as an application in Raptor-90 helicopter is proposed to illustrate the effectiveness of the theoretical results.     

An output formation consensus control for leader–follower networked multi-agent systems under communication constraints and switching topologies

In this paper, the formation consensus problem for a class of leader–follower networked multi-agent systems under communication constraints and switching topologies is investigated. A networked predictive control scheme is proposed to achieve stability and output formation consensus with the switching topology, capable of compensating for data loss and time delays in the network. By equating the whole closed-loop networked multi-agent system with the proposed control scheme to the corresponding switched system, the sufficient and necessary condition of output formation consensus and stability for agents is given. Finally, using three-degree-of-freedom air-bearing spacecraft simulators as the control objects, the proposed scheme is demonstrated to be able to actively compensate for the communication constraints through numerical simulations, and it is also verified to have a good control performance by further realizing the formation task of the simulators through practical experiments.     

Mixed H2 /H∞ control under variance constraints

Dual problems, which we call output and input variance constrained H₂ /H_∞ controls, are considered. In these problems, we seek control-laws that satisfy mixed H₂ /H_∞ performance criteria, under multiple variance constraints on either outputs or inputs of time-invariant multivariable systems. The approach taken is to convert the problems into non-linear programming with both equality and inequality constraints. For both problems, the Kuhn-Tucker optimality condition is employed to obtain a first-order necessary condition for a regular point that minimizes an upper bound on the quadratic performance for the given H_∞ constraint. A second-order necessary condition and sufficiency for the strict local minimizer of the upper bound are investigated. Efficient algorithms for synthesizing the desired controllers are proposed.     

Improved H ∞ analysis of Markovian jumping stochastic systems with time-varying delays

This article investigates the problems of H _∞ analysis for Markovian jump stochastic systems with both nonlinear disturbance and time-varying delays. By virtue of the delay partition approach, the improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian jump stochastic systems are obtained in terms of linear matrix inequalities (LMIs). The proposed approach involves neither free weighting matrices nor any model transformation, and it is shown that the new criteria have the capability of providing less conservative results than the state-of-the-art. Two numerical simulations are conducted to demonstrate the effectiveness of the proposed method in comparison with existing methods.     

Consensus control of nonlinear leader–follower multi-agent systems with actuating disturbances

This paper studies a semi-global asymptotic consensus problem of nonlinear multi-agent systems with local actuating disturbances. For a modest nonlinear scenario, a consensus protocol is proposed based on a viable two-layer network. The consensus problem is treated as distributed output regulation, which is resolved by a joint decomposition of the zero-error constraint inputs and a configuration of a flexible internal model network. An illustrative example is also given to show the efficiency of the two-layer networked design.     

Robust H ∞ fuzzy control of nonlinear systems with multiple time delays

A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and R_k of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H ^∞ control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach.     

Robust L 2 − L ∞ consensus control for uncertain high-order multi-agent systems with time-delay

This article studies that the robust consensus problem for high-order multi-agent systems with time-delay, which are subjected to external disturbances and communication uncertainties. An approach based on the weighting matrix is introduced to meet the requirement that the peak value of controlled output is often required into a certain range. Then, a dynamic model of high-order multi-agent systems is established. Using a feedback controller and interactions from the neighbours including uncertainties, a linear control protocol is proposed for the systems with networks under fixed or switching topologies. Sufficient conditions in terms of linear matrix inequalities are derived to make all the agents reach robust consensus with the prescribed L ₂???L _∞ performance. A numerical simulation is provided to demonstrate the effectiveness of the proposed protocol.     

Prescribed-time leader-following consensus of linear multi-agent systems by bounded linear time-varying protocols

This paper considers the prescribed-time leader-following consensus problem of input-constrained linear multi-agent systems under generally directed communication topology in two cases:the Laplacian matrix related to the entire communication topology between agents is either known or unknown.In particular,the consensus problem for the former case is solved by a novel bounded linear time-varying(LTV) protocol,where the feedback gain is formulated by the parametric Lyapunov equation and the knowle...     

Leader–follower fixed-time consensus of multi-agent systems with high-order integrator dynamics

The leader–follower fixed-time consensus of high-order multi-agent systems with external disturbances is investigated in this paper. A novel sliding manifold is designed to ensure that the tracking errors converge to zero in a fixed-time during the sliding motion. Then, a distributed control law is designed based on Lyapunov technique to drive the system states to the sliding manifold in finite-time independent of initial conditions. Finally, the efficiency of the proposed method is illustrated by numerical simulations.