Non-identical Dynamics Research Articles

Distributed adaptive control for distance‐based formation and flocking control of multi‐agent systems

In this study, a distributed adaptive control strategy for distance-based formation and flocking control of multi-agent system with parametric uncertainty is proposed. A 3-agent leader–first-follower system is considered first. The agents are supposed to have non-identical dynamics, whereas with similar structure. By introducing two new variables that involve distance error and velocity error and utilising them in the controller design, global convergence of all agents to the desired formation and to the velocity of the leader is established. Finally, the three-agent case is inductively extended to N-agent case. The stability and the effectiveness of the proposed control strategy are analysed in theory and demonstrated through simulation results, respectively.

Disturbance attenuation of complex dynamical systems through interaction topology design

Control of complex systems has been extensively investigated over the past decades. Most of the investigations concern the collective dynamical property of synchronization, while the issue of disturbance attenuation of complex systems is not widely considered. This is particularly true for the problem of simultaneous disturbance attenuation for all agents with (all) non-identical nodes dynamics. Methodologically, for both synchronization and disturbance attenuation, approaches can be taken by either feedback compensation, or properly designed switching signals. The concept of disturbance attenuation through topology design has not been recognized. This note aims to develop this idea. Straightforward yet interesting results are obtained. Numerical examples are illustrated to verify the claims while related design issues are also discussed.

An adaptive approach to longitudinal platooning with heterogeneous vehicle saturations

Adaptive CACC strategies have been recently proposed to stabilize a platoon with non-identical and uncertain vehicle dynamics (heterogeneous platoon). This work proposes a method to augment such strategies with a mechanism coping with saturation constraints (i.e. engine constraints). In fact, in a platoon of heterogeneous vehicles, engine constraints might lead to loss of cohesiveness. The proposed mechanism is based on making the reference dynamics (i.e the dynamics to which the platoon should homogenize) ‘not too demanding’, by applying a properly designed saturation action. Such saturation action will allow all vehicles in the platoon not to hit their engine bounds. Cohesiveness will then be achieved at the price of losing some performance, which is in line with the state of art studies on this topic. Simulations on a platoon of 5 vehicles are conducted to validate the theoretical analysis.

Output Synchronization and <inline-formula> <tex-math notation="LaTeX">$L_{2}$ </tex-math> </inline-formula>-Gain Analysis for Network Systems

A novel control strategy for the output synchronization and ${L_{2}}$ analysis of network systems is presented in this paper. Nodes in the heterogeneous network have nonidentical dynamics. The designed distributed controller contains reference generator to copy the dynamics of the target trajectory and robust regulator (RG) to achieve synchronization purpose. All RGs adopt the network communication channels to exchange system information. The distributed control law is calculated on static output feedback and ensure outputs of RGs converges to the target trajectory. Meanwhile, each nonidentical node tracks its RG with ${L_{2}}$ performance index. The controller design strategy is presented in the obtained necessary and sufficient conditions. Finally, the effectiveness of the controller design strategy is demonstrated by a numerical example.

Event-triggered group consensus for multi-agent systems subject to input saturation

This paper investigates group consensus for leaderless multi-agent systems with non-identical dynamics. The consensus protocol is put forward in the form of the distributed event-triggered control subject to saturation, which depends on information from neighboring agents at event-triggered instants. In order to exclude the Zeno behavior and save resources, the given event-triggered condition is detected only at discrete sampling times, where the sampling intervals can be variable. Based on the graph theory, Lyapunov–Krasovskii functional method and by adopting the free-weighting matrix technique, some sufficient group consensus criteria in terms of linear matrix inequalities are derived. Furthermore, optimization problems aiming at maximizing the event-triggered parameter and the consensus region are proposed. Finally, numerical simulations illustrate the effectiveness of the theoretical results.

Output synchronization control for a class of complex dynamical networks with non-identical dynamics

This paper is concerned with the output synchronization control problem for a class of complex dynamical networks (CDNs) with non-identical dynamics. An output feedback control protocol consisting of a feedforward control law and a feedback control law is developed to achieve the output synchronization. More specifically, the feedforward control law is designed to compensate the coupling dynamics of the CDNs, and the feedback control law is designed by solving an algebraic Riccati equation (ARE), which is established by defining a modified quadratic performance index. It is shown that the output feedback control protocol solves the output synchronization control problem, and the graph theory is used to construct a global Lyapunov function, based on which a rigorous asymptotic convergence analysis of output synchronization errors is conducted. Finally, a simulation example is given to verify the effectiveness of the theoretical results.

Adaptive surrounding control for linear multi-agent systems with unknown disturbance

This paper deals with the surrounding control problem of multi-agent systems with linear non-identical dynamics for each agent. In these dynamics, a non-identical time-varying term is considered for each agent. It is assumed that, there exist unknown parameter vectors in time-varying terms of the followers. First, an estimator is introduced to estimate the geometric center of the leaders and then, an adaptive law is proposed to compensate the unknown parameter vector of the followers. Using Lyapunov stability theory, the stability of the system with the proposed control law is studied. Finally, a simulation example is given to show the effectiveness of theoretical results.

Robust output tracking for heterogeneous double-integrator dynamics with external disturbance

ABSTRACTThis paper studies the robust output tracking for heterogeneous double-integrator dynamics with external disturbance. It is assumed that there exist interactions among agents and their neighbours. All the agents have non-identical dynamics with others, and all the system matrices are unknown. A state feedback control protocol with only neighbours information is proposed based on a distributed compensator for non-identical dynamics and an internal-model compensator for the unknown parts. By the algebraic graph theory and matrix theory, sufficient conditions are given to guarantee that all the outputs of the agents converge to the reference output as time tends to infinity. Finally, two numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Model-Matching type-methods and Stability of Networks consisting of non-Identical Dynamic Agents

Many recent approaches of distributed control over networks of dynamical agents rely on the assumption of identical agent dynamics. In this paper we propose a systematic method for removing this assumption, leading to a general approach for distributed-control stabilization of networks of non-identical dynamics. Local agents are assumed to share a minimal set of structural properties, such as input dimension, state dimension and controllability indices, which are generically satisfied for parametric families of systems. Our approach relies on the solution of certain model-matching type problems using local state-feedback and input matrix transformations which map the agent dynamics to a target system, selected to minimize the joint control effort of the local feedback-control schemes. By adapting a well-established distributed LQR control design methodology to our framework, the stabilization problem for a network of non-identical dynamical agents is solved. The applicability of our approach is illustrated via a simple UAV formation control problem.

Cluster synchronization of coupled systems with nonidentical linear dynamics

SummaryThis paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly correlated if static couplings are used for all individual systems. In this paper, a dynamic coupling structure, which incorporates a global weighting factor and a vanishing auxiliary control variable, is proposed for each agent and is shown to be a feasible solution. Lower bounds on the global and local weighting factors are derived under the condition that every interaction subgraph associated with each cluster admits a directed spanning tree. The spanning tree requirement is further shown to be a necessary condition when the clusters connect acyclically with each other. Simulations for two applications, cluster heading alignment of nonidentical ships and cluster phase synchronization of nonidentical harmonic oscillators, illustrate essential parts of the derived theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.

Coupling strength versus coupling impact in nonidentical bidirectionally coupled dynamics.

The understanding of interacting dynamics is important for the characterization of real-world networks. In general, real-world networks are heterogeneous in the sense that each node of the network is a dynamics with different properties. For coupled nonidentical dynamics symmetric interactions are not straightforwardly defined from the coupling strength values. Thus, a challenging issue is whether we can define a symmetric interaction in this asymmetric setting. To address this problem we introduce the notion of the coupling impact. The coupling impact considers not only the coupling strength but also the energy of the individual dynamics, which is conveyed via the coupling. To illustrate this concept, we follow a data-driven approach by analyzing signals from pairs of coupled model dynamics using two different connectivity measures. We find that the coupling impact, but not the coupling strength, correctly detects a symmetric interaction between pairs of coupled dynamics regardless of their degree of asymmetry. Therefore, this approach allows us to reveal the real impact that one dynamics has on the other and hence to define symmetric interactions in pairs of nonidentical dynamics.

Fully distributed adaptive consensus control for a class of nonlinear systems of directed topology

In this paper, we investigate the problem of consensus tracking of a desired trajectory for a class of nonlinear systems consisting of multiple nonlinear subsystems with intrinsic mismatched unknown parameters. The subsystems are allowed to have non-identical dynamics with similar structures and the same yet arbitrary system order. Suppose that the communications among the subsystems can be represented by a directed graph. A fully distributed adaptive control approach based on a backstepping technique that is different from most of the existing results is proposed, which does not use global information as a parameter of the topology. It is proved that boundedness of all closed-loop signals and asymptotic consensus tracking for all the subsystems’ outputs are ensured. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve a formation control problem for multiple underactuated ships.

Finite-time consensus of a leader-following multi-agent network with non-identical nonlinear dynamics and time-varying topologies

In this paper, the finite-time consensus of a leader-following multi-agent network with non-identical nonlinear dynamics and time-varying topologies is investigated. All the agents, especially the leaders, have non-identical and nonlinear dynamics. According to the algebraic graph theory, Lyapunov stability theory and Kronecker product, a control strategy strategy is established to guarantee the finite-time consensus of multi-agent network with multiple leaders. Furthermore, several numerical simulations illustrate the effectiveness and feasibility of the proposed method.

Hierarchical Decomposition Based Consensus Tracking for Uncertain Interconnected Systems via Distributed Adaptive Output Feedback Control

In this note, distributed adaptive controllers are developed for output consensus tracking of multiple linear systems with unknown parameters, uncertain subsystem interconnections and external disturbances. The subsystems are allowed to have non-identical dynamics and the same yet arbitrary order. It is assumed that only part of subsystems can have direct access to the time-varying trajectory information and the subsystem states are unmeasurable for local feedback control. In our design, the directed graph representing the information transmission status among subsystems is preprocessed by splitting it into a hierarchical structure. Then local adaptive controllers of subsystems in different layers can be computed in a sequential order and the difficulty on deriving mutually dependent local controls in previous consensus works are successfully overcome. In each subsystem, additional estimates are introduced to account for the unknown parameters and states in its neighbors' dynamics. Besides, only the information of local outputs and inputs need be collected from the neighboring subsystems. Certain robust terms are added in distributed adaptive laws to mitigate the effects of uncertain subsystem interactions and disturbances. It is proved that with our scheme, all closed-loop signals can be ensured bounded when the strengths of uncertain subsystem interconnections are sufficiently weak. The tracking errors for the entire group of subsystems will converge to a compact set and the transient tracking error performance can be adjusted by appropriately choosing design parameters.

Adaptive Leader-Following Consensus of Multi-Agent Systems with Unknown Nonlinear Dynamics

This paper deals with the leader-following consensus of multi-agent systems with matched nonlinear dynamics. Compared with previous works, the major difficulty here is caused by the simultaneous existence of nonidentical agent dynamics and unknown system parameters, which are more practical in real-world applications. To tackle this difficulty, a distributed adaptive control law for each follower is proposed based on algebraic graph theory and algebraic Riccati equation. By a Lyapunov function method, we show that the designed control law guarantees that each follower asymptotically converges to the leader under connected communication graphs. A simulation example demonstrates the effectiveness of the proposed scheme.

Synchronization of nonlinear heterogeneous cooperative systems using input–output feedback linearization

In this paper, input–output feedback linearization is used to design distributed controls for multi-agent systems with nonlinear and heterogeneous non-identical dynamics. Using feedback linearization, the nonlinear and heterogeneous dynamics of agents are transformed to identical linear dynamics and non-identical internal dynamics. Based on the dependence of agent outputs on agent inputs, feedback linearization may lead to a first-order or high-order tracking synchronization problem. The controller for each agent is designed to be fully distributed such that each agent only requires its own information and the information of its neighbors. The effectiveness of the proposed control protocols are verified by simulation on a microgrid test system.

Output regulation for heterogeneous linear multi-agent systems based on distributed internal model compensator

This article considers robust output regulation of uncertain heterogeneous multi-agent systems in the case that all the agents have non-identical nominal dynamics. The directed communication graph contains a spanning tree and the exosystem is as its root. Since not all the agents can access the information of the exosystem, the distributed compensator is used for the unaccessible part. The dynamic state feedback control law and dynamic output feedback control law are proposed under this topological structure. Then we give a novel compact form and a general global method to solve the robust output regulation problem based on internal model principle. Finally, some examples are presented to illustrate the effectiveness of our results.

Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots

In this paper, we investigate the output consensus problem of tracking a desired trajectory for a class of systems consisting of multiple nonlinear subsystems with intrinsic mismatched unknown parameters. The subsystems are allowed to have non-identical dynamics, whereas with similar structures and the same yet arbitrary system order. And the communication status among the subsystems can be represented by a directed graph. Different from the traditional centralized tracking control problem, only a subset of the subsystems can obtain the desired trajectory information directly. A distributed adaptive control approach based on backstepping technique is proposed. By introducing the estimates to account for the parametric uncertainties of the desired trajectory and its neighbors’ dynamics into the local controller of each subsystem, information exchanges of online parameter estimates and local synchronization errors among linked subsystems can be avoided. It is proved that the boundedness of all closed-loop signals and the asymptotically consensus tracking for all the subsystems’ outputs are ensured. A numerical example is illustrated to show the effectiveness of the proposed control scheme. Moreover, the design strategy is successfully applied to solve a formation control problem for multiple nonholonomic mobile robots.

Cooperative Phenomena in Networks of Oscillators With Non-Identical Interactions and Dynamics

The incipience of synchrony in a diverse population of phase oscillators with non-identical interactions is an intriguing phenomenon. We study frequency synchronization of such oscillators composing networks with arbitrary topology in the context of the Kuramoto model and we show that its synchronization manifold is exponentially stable when the coupling has certain properties. Several example systems with periodic linear, cubic and sinusoidal coupling functions were examined, some including frustration and external fields. The numerical results confirmed the analytic findings and revealed some other interesting occurrences, like phase clustering in a synchronized network of strongly coupled oscillators. We also analyze the effects of the topology by considering random weighted networks.

Towards a theory for diffusive coupling functions allowing persistent synchronization

We study synchronization properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we characterize a class of coupling functions that allows for uniformly stable synchronization in connected complex networks—in the sense that there is an open neighbourhood of the initial conditions that is uniformly attracted towards synchronization. Moreover, this stable synchronization persists under perturbations to non-identical node dynamics. We illustrate the theory with numerical examples and conclude with a discussion on embedding these results in a more general framework of spectral dichotomies.