Consensus Controller Design Research Articles

Leader-following consensus for a class of high-order nonlinear multi-agent systems

The finite-time leader-following consensus problem is addressed for a class of high-order multi-agent systems with uncertain nonlinear dynamics. Each follower node is modeled by lower-triangular system. By using recursive method, we develop the finite-time consensus control design scheme. Based on finite-time Lyapunov stability theorem and matrix theory, we prove that the finite-time consensus of high-order uncertain nonlinear multi-agent systems is guaranteed by non-lipschitz continuous control laws. Simulation results are given to illustrate the effectiveness of the theoretical results.

Robust consensus control of uncertain multi‐agent systems with input delay: a model reduction method

SummaryThis paper addresses the robust consensus control design for input‐delayed multi‐agent systems subject to parametric uncertainties. To deal with the input delay, the Artstein model reduction method is employed by a state transformation. The input‐dependent integral term that remains in the transformed system, owing to the model uncertainties, is judiciously analysed. By carefully exploring certain features of the Laplacian matrix, sufficient conditions for the global consensus under directed communication topology are identified using Lyapunov–Krasovskii functionals in the time domain. The proposed control only relies on relative state information of the subsystems via network connections. The effectiveness and robustness of the proposed control design are demonstrated through a numerical simulation example. Copyright © 2016 John Wiley & Sons, Ltd.

Simultaneous fault detection and consensus control design for a network of multi-agent systems

The problem of simultaneous fault detection and consensus control (SFDCC) of linear continuous-time multi-agent systems is addressed in this paper. A mixed H∞/H− formulation of the SFDCC problem is presented and distributed detection filters are designed using only relative output information among the agents. With our proposed methodology, all agents reach either a state consensus or a model reference consensus while simultaneously collaborate with one another to detect the occurrence of faults in the team. Indeed, each agent not only can detect its own fault but also is capable of detecting its neighbor’s faults. It is shown that through a decomposition approach the computational complexity of solving the distributed problem is significantly reduced as compared to an optimal centralized solution. The extended linear matrix inequalities (LMIs) are used to reduce the conservativeness of the SFDCC results by introducing additional matrix variables to eliminate the couplings of Lyapunov matrices with the system matrices. It is shown that under a special condition on the network topology the faulty agent can be isolated in the team. Simulation results corresponding to a team of autonomous unmanned underwater vehicles (AUVs) demonstrate and illustrate the effectiveness and capabilities of our proposed design methodology.

Stochastic consensus control with finite frequency specification for Markov jump networks

SummaryA stochastic finite frequency consensus protocol for directed networks with Markov jump topologies and external disturbances is proposed in this paper. By introducing the frequency band information into consensus control design, the disagreement dynamics of interconnected networks asymptotically converge to zero with an improved level of disturbance attenuation in the specific frequency band. In addition, the new model transformation approach is presented by exploring certain features of Laplacian matrix in real Jordan form, which leads to more generality of the designed protocol. A numerical example validates the potential of the developed results. Copyright © 2015 John Wiley & Sons, Ltd.

Vibration suppression of distributed parameter flexible structures by Integral Consensus Control

Integral Consensus Control (ICC) is proposed and implemented in this paper for the first time, as a novel approach for vibration control in distributed parameter flexible structures. The ICC consists of multiple parallel first-order lossy integrators, with the goal of targeting all major participating resonant modes in the oscillation of the structure. The vibration control design is taken to a different level, by integrating the concept of consensus control design into the new dynamics. Each control patch on the flexible structure is considered as a node of a network, and a communication topology with consensus control terms are augmented in the controller design dynamics. The result is an effective vibration controller, which is also robust to failures and inconsistencies in the control system. A cantilever is used as a sample flexible structure to investigate the control method. Multi-agent representation of the system, state estimator dynamics and the ICC model are designed for the structure. Extensive numerical simulations have been conducted to show the suppression performance of the ICC under different input disturbances. A comparative study is presented to show the advantage of the decentralized design over the conventional centralized approach. The new consensus control design provides new possibilities to vibration control problems, where an effective, robust and synchronized suppression is needed.

Consensus Control of a Class of Lipschitz Nonlinear Systems With Input Delay

This paper deals with the consensus control design for Lipschitz nonlinear multi-agent systems with input delay. The Artstein-Kwon-Pearson reduction method is employed to deal with the input delay and the integral term that remains in the transformed system is analyzed by using Krasovskii functional. Upon exploring certain features of the Laplacian matrix, sufficient conditions for global stability of the consensus control are identified using Lyapunov method in the time domain. The proposed control only uses relative state information of the agents. The effectiveness of the proposed control design is demonstrated through a simulation study.

Robust consensus controller design for heterogeneous multi-UAV systems

In this paper, distributed consensus tracking control for heterogeneous multi-uav systems with nonlinearities and uncertainty is considered. It is assumed that the leaders output is time-varying and unmanned aerial vehicles have different nonlinear uncertain dynamics. A distributed robust consensus protocol is designed to restrain the effect of nonlinear uncertainties on the multi-UAV systems and guarantee the consensus tracking between the followers and the leader. The designed robust consensus protocol includes a nominal virtual controller and a robust virtual compensator. The nominal virtual controller is first designed to get desired consensus tracking property for the nominal disturbance-free subsystem, and then the robust virtual compensator is designed to restrain the effect of the uncertainties. From the Lyapunov stability theorem, it is shown that the consensus tracking errors can be made as small as desired with expect converge rate. Finally, an example is presented to illustrate the theoretical results.

A sub-optimal consensus design for multi-agent systems based on hierarchical LQR

This paper presents a new and systematic procedure to design sub-optimal hierarchical feedback controllers for the leader–follower consensus problem in homogeneous multi-agent systems. First, the given multi-agent system is treated as a two-layer hierarchical system where the agents perform local actions in the lower layer and interact with others in the upper layer to achieve some global goals. Then the consensus controller design is formulated as a hierarchical state feedback control problem. Employing LQR approach with an appropriately selected performance index, an optimal hierarchical state feedback controller is derived which includes two terms namely local and global terms. Consequently, by removing the local term, the remaining global term is proved to make the multi-agent system consensus which results in a sub-optimal hierarchical consensus controller. Finally, some numerical examples are introduced to illustrate the effectiveness of the proposed method.

Controller design for consensus of non-uniform rank systems with switching topology and relative output measurements

This paper studies the design problem of a controller to achieve an asymptotic consensus for a class of non-uniform rank linear systems. The interconnection topology for the N non-uniform rank systems is assumed to be modeled by a time-varying graph that switches in a finite set of connected and undirected graphs and has a non-vanishing dwell time. Under these conditions, we propose a controller for the asymptotic consensus of the N systems and provide a closed formula for an agreed trajectory that in fact indicates the attainment of average consensus. The controller is implemented through the backstepping and high-gain observer techniques, and uses only relative output measurements from the neighboring systems for the purpose of feedback. The idea behind this implementation is that the output feedback controller implemented in this way can make the norm of the state of the closed-loop system arbitrary small within any given dwell time, even for non-uniform rank systems.

Consensus control design for multi-agent systems using relative output feedback

This paper studies the consensus problem of multi-agent systems in which all agents are modeled by a general linear system. The authors consider the case where only the relative output feedback between the neighboring agents can be measured. To solve the consensus problem, the authors first construct a static relative output feedback control under some mild constraints on the system model. Then the authors use an observer based approach to design a dynamic relative output feedback control. If the adjacent graph of the system is undirected and connected or directed with a spanning tree, with the proposed control laws, the consensus can be achieved. The authors note that with the observer based approach, some information exchange between the agents is needed unless the associated adjacent graph is completely connected.

Consensus Output Regulation of a Class of Heterogeneous Nonlinear Systems

This technical note deals with consensus output regulation of network connected multi-agent systems. Every agent or subsystem is a nonlinear system in the output feedback form with relative degree one, but subsystems may have different dynamics in terms of different nonlinear functions and even different system orders. The subsystem dynamics are influenced by state variables generated from an exosystem. The outputs of the subsystems are required to follow a desired trajectory which is a function of the exosystem state. Only some subsystems have access to the desired trajectory, and the other subsystems will have to rely on the exchange of information through the network. In this technical note, a consensus control design is proposed to ensure that the outputs of all the subsystems converge to the same desired output trajectory by exploiting the internal model design strategy. The proposed control design only uses the relative outputs of the subsystems, and does not require the estimation of subsystem state variables.

타카기-수게노 퍼지모델 기반 다개체 시스템의 상태일치를 위한 제어기 설계

본 논문은 연속시간에서의 타카키-수게노 퍼지모델 기반 다개체 시스템의 상태일치를 위한 제어기 설계 기법을 제안한다. 그래프 이론을 통해 각 개체간의 정보를 교환하는 네트워크를 표현한다. 제어기 설계 조건은 선형 행렬 부등식의 형태로 유도되며, 수치적 예제를 통해 제안된 방법의 효율성을 증명한다. This paper addresses a state consensus controller design technique of Takagi-Sugeno fuzzy model-based multi-agent systems in a continuous-time domain. We express the interconnection topology among the agents through graph theory. The design condition is represented in terms of linear matrix inequalities. Numerical example is provided to demonstrate the effectiveness of the proposed method.

Robust Consensus Controller Design for Nonlinear Relative Degree Two Multi-Agent Systems With Communication Constraints

Robust static output-feedback controllers are designed that achieve consensus in networks of heterogeneous agents modeled as nonlinear systems of relative degree two. Both ideal communication networks and networks with communication constraints are considered, e.g., with limited communication range or heterogeneous communication delays. All design conditions that are presented are scalable to large and heterogeneous networks because the controller parameters depend only on the dynamics of the corresponding agent and its neighbors, but not on other agents in the network.

Output Consensus Controller Design for Nonlinear Relative Degree One Multi-Agent Systems with Delays*

Abstract Simple design conditions are presented for decentralized output feedback controllers that achieve output consensus between nonlinear, relative degree one Multi-Agent Systems (MAS) with stable zero dynamics. It is shown that consensus is achieved even if the exchange of information between the agents suffers from time-varying communication delays and switching communication topologies. In this way the assumptions both on the network topology and the delays are minimal. The proofs are based on an invariance principle for Lyapunov-Razumikhin functions, which has been recently used to prove consensus between single integrator MAS.