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Stable-protocol (SP) output consensus analysis and design problems for high-order linear time-invariant swarm systems with time-varying delays are investigated. First, a dynamic output feedback consensus protocol is proposed on the basis of the observable decomposition, and a necessary and sufficient condition for SP output consensus is given, which transforms the SP output consensus problem into asymptotical stability problems of multiple lower-dimensional subsystems. Then, in terms of linear matrix inequalities (LMIs), a sufficient condition for SP output consensualisation is presented, which can guarantee the scalability of swarm systems since it includes only five LMI constrains independent of the number of agents. Furthermore, an explicit expression of the output consensus function, which is independent of the time-varying delay, is shown and the impacts of initial states of agents and consensus protocols on the output consensus function are determined, respectively. Finally, a numerical example is given to demonstrate theoretical results.

This paper studies the consensus problem of Multi-Agent Systems (MASs) with input-delay using the Model Predictive Control (MPC) approach. Due to challenges such as input delay and communication graph, the traditional MPC is not efficient for the considered systems. In this regard, a novel MPC is developed for MASs with input delay. The main advantage of this paper is to design distributed controllers based on minimizing given cost functions which result in the improvement of the transient responses. For this purpose, first, distributed observers are derived to estimate the leader's states, perfectly. Then, distributed controllers are achieved through the MPC approach. Finally, numerical and practical examples are simulated to affirm the efficiency and applicability of the presented scheme.

This paper studies the output consensus problem of heterogeneous linear stochastic multiagent systems with multiplicative noises in system parameters and measurements, where the system noise in each agent is allowed to be different. By employing stochastic output regulation theory and the stochastic Lyapunov function approach, a composite controller embedded with stochastic output regulator equations (SOREs) and a stochastic dynamic compensator is designed to achieve the mean-square output consensus of the multi-agent systems. To implement the consensus algorithm, a sufficient condition for feasible solutions of the SOREs is first established in terms of Lyapunov and Selvester equations. Then the time-varying SOREs are approximated by the Euler-Maruyama method combined with an a-posteriori partial estimation of the increments of the Brownian motion. A numerical example illustrates the theoretical results.

The distributed optimal output synchronization problem for the leaderless heterogeneous multi-agent system with a general global cost function is investigated for the first time by linear quadratic (LQ) optimal control theory. Conventional algorithms for heterogeneous systems are quite complex, requiring the design of a virtual reference generator and the solving of regulation equations. This paper presents a novel distributed asymptotically optimal controller by incorporating the design of distributed observer and feedforward controller. A general form of the distributed controller is obtained by solving an augmented algebraic Riccati equation, which is parallel to classical optimal control theory. The optimal topology is an arbitrary directed graph containing only a spanning tree. It is shown that the proposed algorithms outperform the traditional consensus methods in the convergence speed by selecting proper observer gain matrices, and eliminate the reliance on the nonzero eigenvalues of Laplacian matrix. Simulation example further demonstrates the effectiveness of the proposed scheme and a faster superlinear convergence speed than the existing algorithm.

In this paper, an adaptive neural network (NN) fault-tolerant controller is designed for the leader-following consensus control problem of a nonlinear multi-agent systems (MASs) under the complex effect of actuator fault, state time-delay, asymmetric output error constraint and the lumped uncertainty. Firstly, by using an asymmetric barrier Lyapunov function (BLF), output errors are ensured to meet the asymmetric output error constraint requirements. Then, Lyapunov–Krasovskii (L–K) functional and Young’s inequality are combined to tackle state time-delay. Radial basis function neural network (RBFNN) is employed to approximate the unknown nonlinear function. Furthermore, adaptive technique is utilized to solve actuator fault. Based on the Lyapunov stability theory, the semi-global bounded stability of closed-loop system is proved. Finally, the validity of the designed control strategy is verified by compared simulation and the application of the two-stage chemical reactors.

This paper addresses the consensus tracking problem of a class of nonlinear multi-agent systems by using observer-based control. The systems are in output-feedback form with both actuator hysteresis and external disturbances. Radial basis function neural networks are used to approximate unknown nonlinear functions. By constructing a state observer and using the backstepping technique, a distributed adaptive neural output-feedback control scheme is proposed to solve the consensus tracking problem. Approximation errors of neural networks together with external disturbances are adaptively estimated and counteracted. For a communication graph containing a spanning tree, we show that the proposed controller guarantees all signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the consensus tracking error and the observer error converge to an adjustable neighborhood of the origin. Finally, two simulation examples are provided to verify the performance of the control design.

This paper deals with the consensus output tracking problem for multi-agent systems with unknown high-frequency gain signs, in which the subsystems are connected over directed graphs. The subsystems may have different dynamics, as long as the relative degrees are the same. A new type of Nussbaum gain is first presented to tackle adaptive consensus control of network-connected systems without the knowledge of the high-frequency gains. Adaptive laws and internal models are then proposed to handle the uncertainties and unknown parameters. An integral Lyapunov function based on sufficient conditions is finally introduced to tackle the asymmetry of the Laplacian matrix of directed graphs, into which we incorporate the new Nussbaum gain and the adaptive internal model to design the controller. It is apparent that the control scheme and the adaptive laws are fully distributed, which means that only the relative information of the neighbourhood subsystems’ outputs is used, and the simulation results validate the effectiveness of the control design, whereby they guarantee the asymptotic convergence of errors to zero as well as the boundedness of the state variables.

For dealing with the energy consumption in multi-agent systems (MASs), an event-triggered (ET) methodology is promising, which relies on the activation of communication devices only when communication of data is needed. This paper explores the leaderless consensus for nonlinear MASs using an adaptive ET approach via an output feedback methodology. This adaptive ET scheme is preferred as it can adapt to the environment through setting a communication threshold. The proposed approach renders the observed states of agents by use of nonlinear observers in an output feedback control dilemma, making it more practical. Simple Luenberger observers are developed to avoid the problem of always measuring agents’ states. The strategy of adaptive ET-based control is employed to minimize resource use and information transmission. Design conditions for the observer-based adaptive ET consensus control of nonlinear MASs have been derived via a Lyapunov function, containing state estimation error, consensus error, adaptation term, and nonlinearity bounds. In contrast to the existing methods, the present approach applies a more practical output feedback schema, uses adaptive ET proficiency, and deals with nonlinear agents. An example of a formation of autonomous underwater vehicles achieving the basic consensus realization between displacement and velocity is included to illustrate the viability of the resultant approach.

This paper considers a robust consensus tracking problem of heterogeneous multi-agent systems with time-varying interconnection topologies. Based on common Lyapunov function and internal model techniques, both state and output feedback control laws are derived to solve this problem. The proposed design is robust by admitting some parameter uncertainties in the multi-agent system.