Cooperative Robust Output Regulation Research Articles

Sampled‐data cooperative semi‐global robust practical output regulation for nonlinear multi‐agent systems with an uncertain leader

AbstractThis article explores the problem of sampled‐data cooperative robust practical output regulation for nonlinear multi‐agent systems whose leader system is unknown. In this study, the nonlinearities of the follower systems are not constrained by the linear growth condition. Based on the robust control technology and the adaptive control technology, a distributed output‐based sampled‐data control protocol is developed to deal with the uncertainty of the exosystem which can belong to any large known compact set. We first perform the coordinate transformation of closed‐loop system to obtain the so‐called augmented system, and then perform the stability analysis for this system. As a result, it is proven that the steady‐state tracking errors are in any small given neighborhood of the origin. Finally, the performance of the proposed controller is validated by a numerical example.

Event‐triggered cooperative robust output regulation of minimum‐phase linear uncertain multi‐agent systems

AbstractIn this article, we investigate the event‐triggered cooperative robust output regulation problem of a class of minimum‐phase linear uncertain multi‐agent systems. In particular, we first propose a dynamic event‐triggered mechanism and an event‐triggered distributed output feedback control law. Then, by the internal model, the event‐triggered cooperative robust output regulation problem is converted into the event‐triggered cooperative robust stabilization problem of an augmented system composed of the distributed internal model and the original multi‐agent system. Next, we show that the event‐triggered cooperative robust stabilization problem can be solved by the proposed event‐triggered distributed output feedback control law together with a dynamic event‐triggered mechanism, and thus the event‐triggered cooperative robust output regulation problem is solved exactly in the sense that the tracking error of each subsystem converges to zero asymptotically while preventing the Zeno behavior from happening. Finally, we provide an example to illustrate the proposed control approach.

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.

Cooperative robust output regulation for a class of nonlinear multi-agent systems over jointly connected switching networks

In this paper, we consider the cooperative robust output regulation problem for a class of nonlinear multi-agent systems over jointly connected switching networks. First, by attaching each subsystem with an input driven filter, we obtain an extended system. Second, by integrating the distributed observer approach and the distributed internal model approach, we convert the cooperative output regulation problem of the original system into a distributed robust stabilisation problem of an augmented error system which is also a multi-agent system. Finally, we solve the original problem by stabilising the augmented error system via a distributed output feedback control law.

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.

Cooperative robust output regulation of linear uncertain multi‐agent systems: A dynamic event‐triggered approach

AbstractIn the article, the cooperative robust output regulation problem of multi‐agent systems with general linear uncertain dynamics is investigated by event‐triggered control. Recently, the similar problem is solved practically by a distributed event‐triggered control law where the tracking error of the system tends to some small neighborhood of the origin asymptotically. In comparison, we develop a distributed event‐triggered output feedback control law together with a class of dynamic event‐triggered mechanisms to solve this problem exactly. In particular, we first design a class of dynamic event‐triggered mechanisms. Then, based on the internal model principle, we propose a distributed event‐triggered output feedback control law. By rigorous proofs, we show that under the proposed distributed control law together with the dynamic event‐triggered mechanism, the cooperative robust output regulation problem is solved exactly, which means that the tracking errors of all followers converge to zero asymptotically while prohibiting the Zeno behavior. Finally, we use an example to illustrate our control approach.

Distributed output data-driven optimal robust synchronization of heterogeneous multi-agent systems

This work presents an output-feedback policy learning algorithm underlining input–output system data for distributed robust optimal synchronization of heterogeneous multi-agent systems. The output-feedback synchronization problem in the context of this work is formulated via robust output regulation and reinforcement learning modeling the interactions among agents by a zero-sum game. The proposed learning and control structure only requires the local system data for each agent and distributed output data among communicating neighbors. We utilize system-level synchysis for the continuous-time state reconstruction for the distributed learning with convergence and stability proofs under the proposed output-feedback policy for solving the zero-sum game. We further show that policy learning is assured under the proposed data criteria relating to input–output data only rather than any inter-immediate gains from policy iterations. Based on the cooperative robust output regulation, this work gains robustness after the learning is complete and establishes an output data-driven distributed optimal robust synchronization without knowing accurate system dynamics. A numerical example shows the effectiveness of the proposed learning algorithm.

Adaptive cooperative output regulation of polytopic systems via spectrum estimation: An [formula omitted] perspective

This paper focuses on the fully distributed robust cooperative output regulation of polytopic multi-agent systems. Based on the internal model principle, the problem being studied is first converted into a stabilization problem of interconnected systems without external disturbance. Next, small-gain conditions are characterized to obtain an equivalent H∞ problem, where the upper bound of the H∞ performance index is closely associated with the spectral radius of the communication topology correlation matrix. To design adaptive fully distributed control protocols in both state and output feedback settings, a finite-time observer and a topology information estimation algorithm are proposed to avoid global information. Compared with existing related works, our methods do not require global information a priori. Finally, the proposed methodology is applied to numerical and practical examples of multi-pendulum systems to demonstrate the feasibility and applicability of the theoretical results.

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.

Cooperative robust output regulation for a class of nonlinear multi-agent systems subject to a nonlinear leader system

In this paper, we study the cooperative robust output regulation problem for a class of nonlinear multi-agent systems subject to a nonlinear leader system. We first establish a result on the existence of a distributed observer for a class of nonlinear leader systems. Then, we convert the cooperative robust output regulation problem into a robust stabilization problem of an augmented system composed of the given multi-agent system and the distributed internal model. Finally, we stabilize this augmented system by a decentralized output feedback control law, which together with the distributed observer and the distributed internal model, constitutes an overall distributed output feedback control law to solve the cooperative robust output regulation problem of the given multi-agent system. An example with the well-known Van der Pol system as the leader system is used to illustrate our design.

Cooperative Semiglobal Robust Output Regulation of Non-Introspective Nonlinear Agents With Partial Normal Form and State-Dependent High-Frequency Gain

This paper investigates cooperative semig-lobal robust output regulation problem for a class of non-introspective nonlinear multiagent systems. Each agent of this class is allowed to have a partial normal form , instead of only the conventional normal form, with a state-dependent high-frequency gain. Besides, all agents are unaccessible to the controller states of their neighbors. In this setting, if the uniform detectability assumption in the sense of [25] is satisfied, then a robust distributed regulator can be designed with the employment of a distributed nonlinear internal model and a novel distributed extended lower-power high-gain observer, such that the numerical implementation problem is solved and the regulated output of each agent asymptotically converges to the desired reference input robustly with guaranteed domain attraction.

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.

Cooperative Robust Output Regulation for Second-Order Nonlinear Multiagent Systems With an Unknown Exosystem

The cooperative robust output regulation problem for a class of second-order nonlinear multiagent systems with an exactly known exosystem has been studied recently. This paper further studies the same problem for the same class of systems subject to an unknown exosystem. We first show that the problem can be converted into the adaptive stabilization problem for an augmented system composed of the given multiagent system and the distributed internal model. Due to the unknown parameters in the exosystem, the augmented system is a nonlinear multi-input system with both linearly parameterized uncertainties and norm-bounded nonlinear uncertainty. By combining the adaptive control technique and the robust control technique, we will solve our problem by a distributed adaptive robust state feedback controller.