Robust Cooperative Output Regulation Problem Research Articles

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

This paper investigates the robust cooperative output regulation problem for a class of heterogeneous uncertain linear multi-agent systems with an unknown exosystem via event-triggered control (ETC). By utilizing the internal model approach and the adaptive control technique, a distributed adaptive internal model is constructed for each agent. Then, based on this internal model, a fully distributed ETC strategy composed of a distributed event-triggered adaptive output feedback control law and a distributed dynamic event-triggering mechanism is proposed, in which each agent updates its control input at its own triggering time instants. It is shown that under the proposed ETC strategy, the robust cooperative output regulation problem can be solved without requiring either the global information associated with the communication topology or the bounds of the uncertain or unknown parameters in each agent and the exosystem. A numerical example is provided to illustrate the effectiveness of the proposed control strategy.

Robust Cooperative Output Regulation for Networks of Hyperbolic PIDE–ODE Systems

In this paper the robust cooperative output regulation problem for multi-agent systems (MAS) with general heterodirectional hyperbolic PIDE-ODE agents is considered. This setup also covers networks of ODEs with arbitrarily long input and output delays. The output of the agents can be defined at all boundaries, in-domain and may depend on the ODE state, while disturbances act on the agents in-domain, at the boundaries, the output and the ODE. The communication network is described by a constant digraph and if its Laplacian is reducible, then heterogeneous agents are permitted also in the nominal case. The solution is based on the cooperative internal model principle, which requires to include a diffusively driven internal model in the controller. The corresponding state feedback regulator design starts with a local backstepping stabilization of the coupled hyperbolic PIDE-ODE systems. It is shown that the remaining simultaneous stabilization of the MAS can be traced back to the simultaneous stabilization of the finite-dimensional cooperative internal model. Solvability conditions in terms of the network topology and the agents transfer behavior are presented. The new design method is applied to the formation control of a platoon of uncertain heavy ropes carrying loads to verify its applicability. Simulations confirm the synchronization performance achieved by the resulting networked controller.

Robust cooperative output regulation for heterogeneous nonlinear multi-agent systems with an unknown exosystem subject to jointly connected switching networks

This paper investigates the robust cooperative output regulation problem for heterogeneous lower triangular nonlinear multi-agent systems with an unknown exosystem over jointly connected switching networks. The problem has been studied for the exactly known exosystem over switching networks. However, the existing result for the unknown exosystem is still limited to the static networks. To ensure that all followers acquire the reference trajectory generated by the unknown exosystem through the jointly connected switching networks, by combining a set of auxiliary filtering variables and fixed-time stability theory, an adaptive distributed observer is designed. On the basis of the adaptive distributed observer and the distributed internal model approach, we propose a distributed controller under several standard assumptions to solve the problem. Compared with the similar work subject to the static networks, the controller in this paper is applicable to the more general communication network while weakening the assumptions of the controlled system.

A Lyapunov Approach to Robust Cooperative Output Regulation of Multiagent Systems Under Infinite Communication Delays

This article investigates the robust cooperative output regulation problem of heterogeneous uncertain linear multiagent systems with switching topologies and infinite distributed communication delays. A novel distributed observer is proposed for each agent to estimate the state of the so-called exosystem by taking consideration of both switching topologies and infinite distributed communication delays. A distributed output feedback controller is then developed based on the internal model principle and the estimated state without using the prior knowledge of communication delays. It is shown via the newly developed Lyapunov-like method that the robust cooperative output regulation problem can be solved under some mild assumptions. Finally, a numerical example is given to demonstrate the effectiveness of the proposed controller.

Robust cooperative output regulation of linear uncertain multi-agent systems by distributed event-triggered dynamic feedback control

In this paper, distributed state and output feedback control law based on the dynamic event-triggered mechanism are proposed to solve the robust cooperative output regulation problem for a class of general linear uncertain multi-agent systems (MASs) subject to external disturbances. The discrete-time control law proposed for each agent is equivalent to a discrete one and thus directly implementable in the digital platform. Our design can handle parametric uncertainties, reject external disturbances and track a dynamic leader while excluding the Zeno phenomenon by providing the existence of a lower bound for inter-event times of each agent, the efficiency of which is illustrated by a numerical example.

Robust Cooperative Output Regulation for a Network of Parabolic PDE Systems

This article considers the robust cooperative output regulation for a network of parabolic PDE systems. The solution to this problem is obtained by extending the cooperative internal model principle from finite to infinite dimensions. For a time-invariant digraph describing the communication topology, a two-step backstepping approach is presented to systematically design cooperative state feedback regulators. This allows to solve both the leader–follower and the leaderless output synchronization problem in the presence of disturbances and model uncertainty for a finite-dimensional leader. Solvability conditions of the robust cooperative output regulation problem are presented in terms of the communication graph and the agent transfer behavior. The results of this article are demonstrated for a network consisting of four uncertain parabolic agents with and without a finite-dimensional leader in the presence of disturbances.

Robust Cooperative Output Regulation of Heterogeneous Uncertain Linear Multiagent Systems With Unbounded Distributed Transmission Delays

This article studies the robust cooperative output regulation problem of heterogeneous uncertain linear multiagent systems under unbounded distributed transmission delays. A novel distributed observer is first proposed to estimate the state of an exosystem in the presence of unbounded distributed transmission delays. Then, two novel distributed controllers, one based on state feedback and the other based on output feedback, are further developed without any prior knowledge of the unbounded transmission delays. It is shown that the resulting closed-loop multiagent systems can achieve robust cooperative output regulation. It is also shown that the better transient performance is achieved with our proposed controllers in contrast to many existing low-gain controllers, which are proposed to deal with both bounded and unbounded transmission delays. Our results can be directly applied to solve cooperative output regulation problems of multiagent systems with bounded distributed or constant transmission delays. Furthermore, our results can also be directly applied to solve leader–following consensus problems of multiagent systems with unbounded distributed, bounded distributed, or constant transmission delays. Finally, a simulation example is provided to illustrate the effectiveness of the proposed controllers.

Robust bipartite output regulation of linear uncertain multi-agent systems

In this paper, we study the robust bipartite output regulation problem for a class of linear uncertain multi-agent systems. After formulating the problem, we extend the concept of the virtual regulated output from the unsigned digraph to the signed digraph. Based on the virtual regulated output, we can define a so-called distributed internal model and form a so-called ancillary augmented system. We then show that, under some standard conditions, the problem can be converted into the distributed stabilisation problem of the ancillary augmented system, thus leading to the solvability of the problem. A special case of our result where the digraph is unsigned recovers the solution of the robust cooperative output regulation problem for the same class of linear uncertain multi-agent systems.

Robust Cooperative Output Regulation of Heterogeneous Uncertain Linear Multiagent Systems With Time-Varying Communication Topologies

This article investigates the robust cooperative output regulation problem for heterogeneous uncertain linear multiagent systems, with time-varying communication topologies. Suppose that the considered systems are detectable by all measurements, rather than the conventional regulated output alone. Under this weaker detectability condition, a new distributed regulator via partial state feedback is first established with the addition of an integrator to the input channel. This is then extended to obtain the practical cooperative output regulation via measurement feedback with the employment of an extended high-gain observer.

Robust cooperative output regulation of multi-agent systems via adaptive event-triggered control

This paper investigates the robust cooperative output regulation problem of uncertain linear multi-agent systems with additive disturbances via the celebrated internal model principle. Two novel distributed controllers are designed based on the adaptive control strategy and the event-triggered transmission scheme, where the adaptive control strategy is utilized to avoid the requirement for a priori knowledge of the minimal nonzero eigenvalue of the Laplacian matrix associated with the communication topology, and the event-triggered transmission scheme is utilized to reduce the frequency of data transmission. It is shown that the proposed control schemes achieve robust cooperative output regulation asymptotically and Zeno behavior is excluded. Finally, a simulation example is presented to illustrate the effectiveness of the proposed controllers.

Robust cooperative output regulation of uncertain linear multi-agent systems not detectable by regulated output

This paper considers the robust cooperative output regulation problem via measurement feedback for a class of linear multi-agent systems, which is not detectable by regulated output. To solve it, necessarily additional measurement is assumed to be available, and the normal form defined on the additional measurement is utilized. Under mild assumptions on the communication network and the zero dynamics, a novel distributed measurement feedback controller can be established, consisting of the distributed dynamical compensator, internal model and possibly asymptotic observer, such that all regulated errors can globally exponentially converge to zero. Only regulated output of each agent needs to be transmitted to its neighbors, while neither the plant state nor the controller state is required to be exchanged with its neighbors.

Robust cooperative output regulation under exosystem detectability constraint

ABSTRACTThis paper revisits the robust cooperative output regulation problem for a class of linear uncertain multi-agent systems. In particular, it is assumed here that the agents in the system can only access incomplete measurements of the exosystem, and the local regulated error signals are not available to the agents to be used in control. Under these assumptions, the agents in the system cannot independently reconstruct the exosystem dynamics, or rely on their own local measurements to achieve the objectives of the output regulation problem. The solution to the regulation problem proposed in this paper is a distributed dynamic control law that reconstructs the exosystem states, given a mild collective detectability assumption. Furthermore, the proposed distributed control law incorporates an internal model of the exosystem to allow for uncertain dynamics of the multi-agent system. A numerical example is offered to illustrate the effectiveness of the proposed control solution.

Robust cooperative output regulation of heterogeneous uncertain linear multi-agent systems by intermittent communication

In this paper, we study the robust cooperative output regulation problem of heterogeneous linear multi-agent systems with system uncertainties and directed communication topology. A robust distributed event-triggered control scheme is proposed based on the internal model principle. To avoid continuous monitoring of measurement errors for the event-triggering condition, a novel self-triggered control scheme is further proposed. Moreover, by introducing a fixed timer in the triggering mechanisms, Zeno behavior can be excluded for each agent. An example is finally provided to demonstrate the effectiveness of the proposed self-triggered control scheme.

Robust cooperative output regulation of heterogeneous Lur'e networks

SummaryIn this paper, we study robust cooperative output regulation problems for a directed network of Lur'e systems that consist of a nominal linear dynamics with an unknown static nonlinearity around it through negative feedback. We assume that the linear part of each agent is identical, but the nonlinearities are allowed to be different for distinct agents. In this sense, the network is heterogeneous. As is common in the context of Lur'e systems, the unknown nonlinearities are assumed to be sector bounded within one given sector. The interconnection graph among these agents is assumed to contain a directed spanning tree. Similar to classical output regulation problems, there is a virtual exosystem generating a reference signal in which all the agents are required to track cooperatively. Our designed distributed dynamic state/output feedback protocol makes a copy of the reference signal at each agent asymptotically, and then the robust cooperative output regulation problem becomes a robust tracking problem that can be handled by each agent via local information. It turns out that our cooperative protocols are fully distributed. Sufficient conditions on the existence of output synchronization protocols are given along with some discussions on these conditions. Finally, two simulation examples illustrate our design. Copyright © 2016 John Wiley & Sons, Ltd.

Distributed adaptive controllers for cooperative output regulation of heterogeneous agents over directed graphs

This paper considers the cooperative output regulation problem for linear multi-agent systems with a directed communication graph, heterogeneous linear subsystems, and an exosystem whose output is available to only a subset of subsystems. Both the cases with nominal and uncertain linear subsystems are studied. For the case with nominal linear subsystems, a distributed adaptive observer-based controller is designed, where the distributed adaptive observer is implemented for the subsystems to estimate the exogenous signal. For the case with uncertain linear subsystems, the proposed distributed observer and the internal model principle are combined to solve the robust cooperative output regulation problem. Compared with the existing works, one main contribution of this paper is that the proposed control schemes can be designed and implemented by each subsystem in a fully distributed fashion for a class of directed graphs.

Robust cooperative output regulation problem for non-linear multi-agent systems

In this study, the author considers a robust cooperative output regulation problem for a class of uncertain non-linear multi-agent systems. The dynamics of each agent can be represented by a non-linear system with unknown parameters. It is assumed that only some of the agents are able to access the exosystem, and thus the problem has to be solved by cooperation among different agents. An internal model-based control strategy is proposed such that, regardless of small parameter perturbations of the agent and control law, the objective of asymptotic tracking and disturbance rejection can be achieved by the control law. Moreover, this method does not require each agent to have identical dynamics.