Cooperative Robust Output Regulation Problem Research Articles

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.

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.

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.

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.

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.

Internal model approach to cooperative robust output regulation for linear uncertain time‐delay multiagent systems

SummaryIn this paper, we study the cooperative robust output regulation problem for linear uncertain multiagent systems with both communication delay and input delay by the distributed internal model approach. The problem includes the leader‐following consensus problem of linear multiagent systems with time delay as a special case. We first generalize the internal model design method to systems with both communication delay and input delay. Then, under a set of standard assumptions, we have obtained the solution to the problem via both the state feedback control law and the output feedback control law. In contrast to the existing results, our results apply to general linear uncertain multiagent systems, accommodate a large class of leader signals, and achieve asymptotic tracking and disturbance rejection at the same time.

Event-triggered cooperative robust practical output regulation for a class of linear multi-agent systems

In this paper, we consider the event-triggered cooperative robust practical output regulation problem for a class of linear minimum-phase multi-agent systems. We first convert our problem into the cooperative robust practical stabilization problem of a well defined augmented system based on the distributed internal model approach. Then, we design a distributed event-triggered output feedback control law together with a distributed output-based event-triggered mechanism to stabilize the augmented system, which leads to the solvability of the cooperative robust practical output regulation problem of the original plant. Our distributed control law can be directly implemented in a digital platform provided that the distributed triggering mechanism can monitor the continuous-time output information from neighboring agents.

Cooperative robust output regulation problem for discrete‐time linear time‐delay multi‐agent systems

SummaryIn this paper, we study the cooperative robust output regulation problem for discrete‐time linear multi‐agent systems with both communication and input delays by a distributed internal model approach. We first introduce the distributed internal model for discrete‐time multi‐agent systems with both communication and input delays. Then, we define the so‐called auxiliary system and auxiliary augmented system. Finally, we solve our problem by showing, under some standard assumptions, that if a distributed state feedback control or a distributed output feedback control solves the robust output regulation problem of the auxiliary system, then the same control law solves the cooperative robust output regulation problem of the original multi‐agent systems.

Output Feedback Cooperative Control for Linear Uncertain Multi-Agent Systems With Nonidentical Relative Degrees

In this technical note, we present an output feedback control for the cooperative robust output regulation problem of a class of heterogeneous minimum phase linear uncertain multi-agent systems with the arbitrary large plant uncertainty and the arbitrary nonidentical relative degrees. To estimate the system state, we propose a novel distributed observer that contains two distinct parts, where the first part is of the distributed form to estimate the regulated error, while the second part is a modified version of the standard reduced-order high-gain observer by replacing the regulated error with its estimation given in the first part. Our design significantly extends some current literatures in that it strictly removes the assumption of the identical relative degree, and hence applies to a much larger class of linear multi-agent systems.

Cooperative output regulation for a class of nonlinear multi-agent systems with arbitrarily large uncertainty

This paper studies the cooperative global robust output regulation problem for the nonlinear multi-agent systems in output feedback form with relative degree $r=2$ subject to arbitrarily large uncertainty. The robust control method alone cannot handle arbitrarily large uncertainty. By combining the robust and adaptive high gain technique, we develop a recursive procedure to construct a distributed output feedback control law to deal with the problem. The theoretical result of this paper is applied to the leader-following consensus problem of a family of hyper-chaotic Lorenz systems.

Cooperative robust output regulation of a class of heterogeneous linear uncertain multi-agent systems

SUMMARY The cooperative output regulation of a linear multi-agent system can be viewed as a generalization of the leader-following consensus problem and was studied recently for the case where the system uncertain parameters vary in a sufficiently small neighborhood of their nominal value. This case was handled by the internal model design which converts the problem into a simultaneous eigenvalue placement problem of an augmented multi-agent system. In this paper, we further consider the cooperative robust output regulation problem for a class of minimum phase linear multi-agent systems in the sense that the controller allows the system uncertain parameters to vary in an arbitrarily prescribed compact subset. For this purpose, we introduce a new type of internal model that allows the cooperative robust output regulation problem of the given plant to be converted into a robust stabilization problem of an augmented multi-agent system. We then solve our problem by combining a simultaneous high-gain state feedback control technique and a distributed high-gain observer technique. A special case of our result leads to the solution of the leader-following robust consensus problem for a class of uncertain multi-agent systems. Copyright © 2013 John Wiley & Sons, Ltd.