Consensus of Euler-Lagrange systems networked by sampled-data information with probabilistic time delays

Role of Integral Control for Enlarging Second-Order Delay Consensus Margin Under PID Protocols: None

Proportional, integral, and derivative (PID) feedback control, as a popular control law, plays a central role in industrial processes and traditional control applications. In the context of multiagent systems, one may also wonder what the fundamental capability and limitation of PID control may be. This article attempts to provide an answer from the viewpoint of consensus robustness against uncertain delay. We consider robust consensus of second-order unstable agents under PID feedback protocols, subject to a constant but unknown time delay over an undirected graph. The issue concerns the so-called delay consensus margin (DCM), which is the largest delay range within which robust consensus can be achieved. The specific problem under study investigates the role of integral control on the robust consensus, seeking to understand whether integral control can be employed to enhance consensus robustness. Our result shows that there is none; that is, in a PID protocol, the integral control action has no improving effect on the DCM, and that PID and proportional-derivative (PD) protocols achieve the same DCM. As a byproduct of this finding, the DCM under PID and PD protocols is found to be computable by solving a quasiconcave, albeit nonsmooth, unimodal optimization problem.

Fully Distributed Optimal Position Control of Networked Uncertain Euler-Lagrange Systems Under Unbalanced Digraphs

The distributed optimal position control problem, which aims to cooperatively drive the networked uncertain nonlinear Euler-Lagrange (EL) systems to an optimal position that minimizes a global cost function, is investigated in this article. In the case without constraints for the positions, a fully distributed optimal position control protocol is first presented by applying adaptive parameter estimation and gain tuning techniques. As the environmental constraints for the positions are considered, we further provide an enhanced optimal control scheme by applying the ϵ -exact penalty function method. Different from the existing optimal control schemes of networked EL systems, the proposed adaptive control schemes have two merits. First, they are fully distributed in the sense without requiring any global information. Second, the control schemes are designed under the general unbalanced directed communication graphs. The simulations are performed to verify the obtained results.

Formation-containment control of multi-agent systems with communication delays

This paper designs formation-containment control algorithms for a class of second-order nonlinear multi-agent systems governed by Euler-Lagrange dynamics with communication delays. The formation-containment problem consists of leader agents' formation control and follower agents' containment control. Firstly, to make the leaders form a desired formation and move collectively with a constant velocity, a coordinated formation control algorithm is designed and the variable-gain technique is used to eliminate the effect of communication delays on the leaders' formation control. Secondly, considering that only the leaders have access to the desired moving velocity, we propose distributed velocity estimators for followers in which the communication delays also exist in the followers' information interaction. By using the estimated velocity information, coordinated containment control laws are designed for the followers to drive them asymptotically converge to the convex hull spanned by all leaders. Furthermore, to increase the system robustness against uncertainties and external disturbances, the adaptive updating laws are designed for all agents. Finally, simulations are given to demonstrate these obtained results.

Coordinated motions of multiple robotic manipulators with matrix-weighted network

This paper addresses coordinated problem of uncertain robotic manipulators with matrix-weighted network. Given interconnections between agents are weighted by nonnegative definite matrices, we present a sufficient and necessary condition about zero eigenvalues of matrix-weighted Laplacian and types of coordinated behaviors for multiple agents. Based on the condition, two novel control schemes are proposed for the networked robots by introducing matrix-weighted network. We employ the decomposition approach and Lyapunov-like approach to show coordinated motions of the networked system, and demonstrate that the proposed controls are capable of ensuring the robotic agents reach complete/cluster consensus and complete/cluster synchronization. Finally, some numerical examples and simulations demonstrate the obtained theoretical results.

Resilient Cooperative Control for Networked Lagrangian Systems Against DoS Attacks

In this article, we study the distributed resilient cooperative control problem for directed networked Lagrangian systems under denial-of-service (DoS) attacks. The DoS attacks will block the communication channels between the agents. Compared with the existing methods for the linear networked systems, the considered nonlinear networked Lagrangian systems with asymmetric channels under DoS attacks are more challenging and still not well explored. In order to solve this problem, a novel resilient cooperative control scheme is proposed by using the sampling control approach. Sufficient conditions are first derived in the absence of DoS attacks according to a multidimensional small-gain scheme. Then, in the presence of DoS attacks, the proposed resilient scheme works in a switching manner. Inspired by multidimensional small-gain techniques, the Lyapunov approach is used to analyze the closed-loop system, which enables us to establish sufficient stability conditions for the control gains in terms of the duration and frequency of the DoS attacks.

Model-Independent Formation Tracking of Multiple Euler-Lagrange Systems via Bounded Inputs

This article addresses two kinds of formation tracking problems, namely: 1) the practical formation tracking (PFT) problem and 2) the zero-error formation tracking (ZEFT) problem for multiple Euler-Lagrange systems with input disturbances and unknown models. In these problems, the bounded input constraint, which can be possibly caused by actuator saturation and power limitations, is taken into consideration. Then, the two classes of model-independent distributed control approaches, in which the prior information (i.e., the structures and features) of the system model is not used, are proposed correspondingly. Based on the nonsmooth analysis and Lyapunov stability theory, several novel criteria for achieving PFT and ZEFT of multiple Euler-Lagrange systems are derived. Finally, numerical simulations and comparisons are presented to verify the validity and effectiveness of the proposed control approaches.

Passivity-based filtering for networked semi-Markov robotic manipulators with mode-dependent quantization and event-triggered communication

In this article, the networked filtering problem for a class of robotic manipulators with semi-Markov type parameters is investigated under the passivity framework. In particular, the mode-dependent quantization and event-triggered communication scheme are both proposed for increasing the network transmission efficiency. Sufficient stability conditions are first derived by choosing mode-dependent Lyapunov–Krasovskii functionals. Then, the mode-dependent filter gains and the event-triggering parameters are further designed with the help of matrix convex optimization. In the end, a simulation example is provided such that the effectiveness of the proposed filtering method can be well demonstrated.

Neural network-based model predictive tracking control of an uncertain robotic manipulator with input constraints

This paper proposes a neural network-based model predictive control (MPC) method for robotic manipulators with model uncertainty and input constraints. In the presented NN-based MPC structure, two groups of radial basis function neural networks (RBFNNs) are considered for online model estimation and effective optimization. The first group of RBFNNs is introduced as a predictive model for the robotic system with online learning strategies for handling the system uncertainty and improving the model estimation accuracy. The second one is developed for solving the optimization problem. By taking into account an actor-critic scheme with different weights and the same activation function, adaptive learning strategies are established for balancing between optimal tracking performance and predictive system stability. In addition, aiming at guaranteeing the input constraints, a nonquadratic cost function is adopted for the NN-based MPC. The ultimately uniformly boundedness (UUB) of all variables is verified through the Lyapunov approach. Simulation studies are conducted to explain the effectiveness of the proposed method.

Hierarchical Controller-Estimator for Coordination of Networked Euler-Lagrange Systems

This paper proposes several hierarchical controller-estimator algorithms (HCEAs) to solve the coordination problem of networked Euler-Lagrange systems (NELSs) with sampled-data interactions and switching interaction topologies, where the cases with both discontinuous and continuous signals are successfully addressed in a unified framework. The HCEAs comprise two main layers (i.e., a control layer and an estimator layer) and one optional layer (i.e., a filter layer), in which the coordination problem is tackled in the main layers and the transient response can be optionally smoothed in the filter layer. For stabilizing the corresponding cascade closed-loop systems, several sufficient conditions on the upper bound of the aperiodic sampling intervals and the lower bound of the control parameters are established. In addition, the HCEAs are extended to address the task-space coordination problem of networked heterogeneous robotic systems, which shows the versatility of the HCEAs. Finally, comparison studies and simulation results are provided to demonstrate the effectiveness, significance, and advantages of the presented algorithms.

Adaptive Output Regulation of Heterogeneous Multiagent Systems Under Markovian Switching Topologies

This paper investigates the adaptive output regulation problem for heterogeneous linear multiagent systems under randomly switching communication topologies. The switching mechanism is governed by a time-homogeneous Markov process, whose states correspond to all possible communication topologies among agents. A novel distributed adaptive cooperative controller is presented, where the dynamic compensators are utilized to estimate the exogenous signal for all the agents in mean square sense. The distributed control law is based upon the local information of agents, without using the global information of the communication topologies. Finally, illustrative examples are put forward to demonstrate the effectiveness of the given control scheme.

Fully Distributed Adaptive Consensus Control of a Class of High-Order Nonlinear Systems With a Directed Topology and Unknown Control Directions

In this paper, we investigate the adaptive consensus control for a class of high-order nonlinear systems with different unknown control directions where communications among the agents are represented by a directed graph. Based on backstepping technique, a fully distributed adaptive control approach is proposed without using global information of the topology. Meanwhile, a novel Nussbaum-type function is proposed to address the consensus control with unknown control directions. It is proved that boundedness of all closed-loop signals and asymptotically consensus tracking for all the agents' outputs are ensured. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme.

Cooperative Tracking of Networked Agents With a High-Dimensional Leader: Qualitative Analysis and Performance Evaluation

Cooperative consensus tracking and its -gain performance is investigated in this paper for a class of multiple agent systems (MASs) in the presence of a single high-dimensional leader. Compared with the traditional models for MASs, the inherent dynamics of the leader are allowed to be different with those of the followers in the present framework, which is thus much more favorable in various practical applications. A new kind of distributed controllers associated with a reduced-order state observer are designed for each follower to track the high-dimensional leader under directed switching topology. With the help of -matrix theory and stability analysis methods of switched systems, some efficient criteria are derived for cooperative consensus tracking of MASs without any external disturbance under directed switching topology. Theoretical analysis is further extended to the case of consensus tracking for MASs subject to unknown external disturbances by showing that, a finite -gain performance for tracking errors against external disturbances can be ensured if some suitable conditions are satisfied. At last, the synthesis issue of designing an observer-based controller to achieve a prescribed -gain performance for consensus tracking is studied by using tools from control theory, where the underlying topology is assumed to be undirected and fixed. The effectiveness of theoretical results is verified by performing numerical simulations.

Consensus for Linear Multiagent Systems With Time-Varying Delays: A Frequency Domain Perspective

This paper investigates the consensus problem for multiagent systems with time-varying delays. The bounded delays can be arbitrarily fast time-varying. The communication topology is assumed to be undirected and fixed. With general linear dynamics under average state feedback protocols, the consensus problem is then transformed into the robust control problem. Further, sufficient frequency domain criteria are established in terms of small gain theorem by analyzing the delay dependent gains for both continuous-time and discrete-time systems. The controller synthesis problems can be solved by applying the frequency domain design methods. Numerical examples are demonstrated to verify the effectiveness of the proposed approaches.

Distributed Bounds on the Algebraic Connectivity of Graphs With Application to Agent Networks

This paper establishes several bounds on the algebraic connectivity and spectral radius of graphs. Before deriving these bounds, a directed graph with a leader node is first investigated, for which some bounds on the spectral radius and the smallest real part of all the eigenvalues of M = L + D are obtained using the properties of M-matrix and non-negative matrix under a mild assumption, where L is the Laplacian matrix of the graph and D = diag{d1, d2, ..., dN} with di > 0 if node i can access the information of the leader node and 0 otherwise. Subsequently, by virtue of the results on directed graphs, the bounds on the algebraic connectivity and spectral radius of an undirected connected graph are provided. Besides establishing these bounds, another important feature is that all these bounds are distributed in the sense of only knowing the information of edge weights' bounds and the number of nodes in a graph, without using any information of inherent structures of the graph. Therefore, these bounds can be in some sense applied to agent networks for reducing the conservatism where control gains in control protocols depend on the eigenvalues of matrices M or L, which are global information. Also some examples are provided for corroborating the feasibility of the theoretical results.

Distributed Position-Based Consensus of Second-Order Multiagent Systems With Continuous/Intermittent Communication

This paper considers the position-based consensus in a network of agents with double-integrator dynamics and directed topology. Two types of distributed observer algorithms are proposed to solve the consensus problem by utilizing continuous and intermittent position measurements, respectively, where each observer does not interact with any other observers. For the case of continuous communication between network agents, some convergence conditions are derived for reaching consensus in the network with a single constant delay or multiple time-varying delays on the basis of the eigenvalue analysis and the descriptor method. When the network agents can only obtain intermittent position data from local neighbors at discrete time instants, the consensus in the network without time delay or with nonuniform delays is investigated by using the Wirtinger's inequality and the delayed-input approach. Numerical examples are given to illustrate the theoretical analysis.

Sampled-Data-Based Consensus and $L_{2}$ -Gain Analysis for Heterogeneous Multiagent Systems

This paper is concerned with the sampled-data-based consensus problem of heterogeneous multiagent systems under directed graph topology with communication failure. The heterogeneous multiagent system consists of first-order and second-order integrators. Consensus of the heterogeneous multiagent system may not be guaranteed if the communication failure always happens. However, if the frequency and the length of the communication failure satisfy certain conditions, consensus of the considered system can be reached. In particular, we introduce the concepts of communication failure frequency and communication failure length. Then, with the help of the switching technique and the Lyapunov stability theory, sufficient conditions are derived in terms of linear matrix inequalities, which guarantees that the heterogeneous multiagent system not only achieves consensus but also maintains a desired L₂ -gain performance. A simulation example is given to show the effectiveness of the proposed method in this paper.

Consensus and Stability Analysis of Networked Multiagent Predictive Control Systems

This paper is concerned with the consensus and stability problem of multiagent control systems via networks with communication delays and data loss. A networked multiagent predictive control scheme is proposed to achieve output consensus and also compensate for the communication delays and data loss actively. The necessary and sufficient conditions of achieving both consensus and stability of the closed-loop networked multiagent control systems are derived. An important result that is obtained is that the consensus and stability of closed-loop networked multiagent predictive control systems are not related to the communication delays and data loss. An example illustrates the performance of the networked multiagent predictive control scheme.

A PD-Like Protocol With a Time Delay to Average Consensus Control for Multi-Agent Systems Under an Arbitrarily Fast Switching Topology

This paper is concerned with the problem of average consensus control for multi-agent systems with linear and Lipschitz nonlinear dynamics under a switching topology. First, a proportional and derivative-like consensus algorithm for linear cases with a time delay is designed to address such a problem. By a system transformation, such a problem is converted to the stability problem of a switched delay system. The stability analysis is performed based on a proposed Lyapunov-Krasoversusii functional including a triple-integral term and sufficient conditions are obtained to guarantee the average consensus for multi-agent systems under arbitrary switching. Second, extensions to the Lipschitz nonlinear cases are further presented. Finally, numerical examples are given to illustrate the effectiveness of the results.

On Neighbor Information Utilization in Distributed Receding Horizon Control for Consensus-Seeking

This paper investigates the issue on how to utilize neighbor information in the distributed receding horizon control (RHC)-based consensus problem for first-order multiagent systems. The distributed RHC-based consensus problem is first formulated in a general framework in terms of using neighbor information. Based on the framework, a sufficient condition on utilizing neighbor information to ensure consensus is developed for the finite horizon case. For the infinite horizon case, a necessary and sufficient condition is proposed, and the best way of using neighbor information to achieve fastest convergence rate is also presented. It is shown that: 1) the way of utilizing neighbor information plays an important role in reaching consensus; 2) the parameter that ensures consensus is related with the network topology; and 3) the best convergence rate in consensus can be attained if the neighbor information is appropriately utilized. Simulation studies verify the proposed theoretical results.

Guaranteed cost design for model-based cyber-physical assembly: a convex optimization approach

Purpose

The purpose of this paper is to propose a guaranteed cost control design procedure for model-based cyber–physical assembly (CPA) systems. To reflect the cyber–physical environment, the network-induced delays and disturbances are introduced in the mathematical model.

Design/methodology/approach

Based on the linear matrix inequality approach, the guaranteed cost controller is designed such that the guaranteed cost can be satisfied and the corresponding convex optimization algorithm is provided. Moreover, H-infinity theory is used to deal with the disturbance with the given H-infinity attenuation level.

Findings

By constructing appropriate Lyapunov–Krasovskii functionals, delay-dependent sufficient conditions are established in terms of linear matrix inequalities and the controller design procedure is given.

Originality/value

A simplified CPA model is given based on which the designed controller can allow us to control the closed-loop CPA systems with the guaranteed cost.