Cooperative Global Robust Output Regulation Research Articles

Practical output regulation for nonlinear multiagent systems with event‐triggered control protocol under directed switching networks

SummaryIn this paper, the event‐triggered‐based cooperative global robust practical output regulation problem is studied for nonlinear multiagent systems with directed switching networks. Firstly, the considered problem can be resolved with a prerequisite where the problem is solvable by an input‐to‐state stabilizing controller with measurement feedback. Specifically, the considered problem can be converted into a stabilization one for the so‐called augmented system through the canonical internal model construction. Then by combining the multiple Lyapunov functions (MLF) with the average dwell time (ADT) method, it is demonstrated that this stabilization problem can be solved by output feedback with measurement disturbances, which indicates a solution to the initial problem. At last, a suitable event‐triggering mechanism is proposed to save communication resources and reduce computational burden among all the agents. Finally, a group of FitzHugh‐Nagumo multiagent systems is provided to verify our theoretical results.

Cooperative Global Robust Practical Output Regulation of Nonlinear Lower Triangular Multiagent Systems via Event-Triggered Control.

In this article, the problem of cooperative global robust practical output regulation is examined for uncertain nonlinear multiagent systems in a lower triangular form via event-triggered control. The problem is dealt with in three steps. At the first step, a decentralized internal model is constructed based on the lower triangular form such that the regulation issue is translated to a stabilization one. Next, a nonlinear decentralized state-feedback controller is designed to achieve input-to-state stabilization with the sampling error as the input. In the third step, a simple event-triggering mechanism is embedded in the controller to achieve an event-based controller redesign. An illustrative example is presented to verify the theoretical results.

Cooperative Adaptive Output Regulation for Lower Triangular Nonlinear Multi-Agent Systems Subject to Jointly Connected Switching Networks.

The cooperative global robust output regulation problem for multi-agent systems is a generalization of the leader-following consensus problem. The problem has been studied for various multi-agent systems over connected static networks and for some special classes of nonlinear multi-agent systems over jointly connected switching networks. In this paper, we further consider the same problem for a class of heterogeneous lower triangular nonlinear multi-agent systems over jointly connected switching networks. This class of systems is quite general in that it contains inverse dynamics, is of any order, and its subsystems can have different relative degrees. We will integrate the adaptive distributed observer and the distributed internal model approach to come up with a recursive approach to deal with our problem. We will also apply our approach to a leader-following consensus problem for a group of hyperchaotic Lorenz systems.

Constructive Nonlinear Internal Models for Global Robust Output Regulation and Application

This technical note focuses on an internal model construction approach. Several novel types of parameterized nonlinear internal models with certain output are proposed to be useful for achieving nonadaptive control based global robust output regulation with uncertain exosystems. That is, the globally stabilizing control for the augmented system can be done independent of adaptive stabilization control law. We also solve a cooperative global robust output regulation problem as an interesting application of the proposed internal models. In this way, we note that the hurdles can be circumvented arising in the same problem if the canonical linear internal model were used.

Cooperative global robust output regulation for a class of nonlinear multi-agent systems by distributed event-triggered control

This paper studies the event-triggered cooperative global robust output regulation problem for a class of nonlinear multi-agent systems via a distributed internal model design. We show that our problem can be solved practically in the sense that the ultimate bound of the tracking error can be made arbitrarily small by adjusting a design parameter in the proposed event-triggered mechanism. Our result offers a few new features. First, our control law is robust against both external disturbances and parameter uncertainties, which are allowed to belong to some arbitrarily large prescribed compact sets. Second, the nonlinear functions in our system do not need to satisfy the global Lipschitz condition. Thus our systems are general enough to include some benchmark nonlinear systems that cannot be handled by existing approaches. Finally, our control law is a specific distributed output-based event-triggered control law, which lends itself to a direct digital implementation.

A nonlinear internal model design for heterogeneous second-order multi-agent systems with unknown leader

This paper focuses on robust nonlinear coordination of heterogeneous uncertain second-order multi-agent systems subject to directed communication topologies. We develop a nonlinear internal model principle based approach for the problem in a framework of cooperative global robust output regulation, independent of the a priori of the leader dynamics information except its order. As a major consequence, this study assures, by means of establishing a strict-Lyapunov function for the closed-loop system, not only a specified exponential convergence rate but also tolerable bounds of unmodeled disturbances. Hence, the former guarantees an appealing performance and the latter an important robustness property.

Event-Triggered Cooperative Global Robust Practical Output Regulation for Second-Order Uncertain Nonlinear Multiagent Systems.

In this paper, we study the cooperative global robust practical output regulation problem for a class of second-order uncertain nonlinear multiagent systems via a distributed event-triggered state feedback control strategy. Compared with the existing work, one of the main challenges is that we need to design two distributed internal models to learn both the desired steady-state state and steady-state input for each agent. Moreover, to obtain a directly implementable digital control law, the two distributed internal models of each agent only depend on the sampled states of the neighboring agents and itself. As a result, the resulting augmented system is more complicated, and the control law needs to be recursively designed. To overcome the difficulty, we propose a novel distributed event-triggered control law and a novel distributed event-triggered mechanism to deal with our problem. By adjusting a design parameter in the proposed event-triggered mechanism, we show that the Zeno behavior does not happen and the ultimate bound of the tracking error can be made arbitrarily small. Our design will be illustrated by two examples.

Cooperative global robust group output regulation for multi-agent systems with heterogeneous uncertain second-order nonlinear dynamics

In this paper, we study the global robust group output regulation problem for multi-agent systems with heterogeneous uncertain second-order nonlinear dynamics. The intelligence factor is introduced to construct a designed graph matrix which overcomes the communication influence between multiple coupled subnetworks with different exosystems. In terms of internal model principle, the global robust group output regulation problem is converted into the global robust dynamic stability problem of the so-called augmented multi-agent system. Further, the augmented multi-agent system is globally stabilized via a distributed state feedback control law. A special case of the main result of this paper leads to the solution of the global robust multi-tracking control problem for nonlinear multi-agent networks. A simulation is performed to illustrate the effectiveness of the theoretical results.

Cooperative Global Robust Output Regulation for Nonlinear Output Feedback Multiagent Systems Under Directed Switching Networks

In this paper, we study the cooperative global robust output regulation problem for nonlinear multiagent systems in output feedback form with any relative degree subject to directed switching networks. Through the augmentation by a distributed internal model and a distributed observer of the given system, we first convert the original problem into the global robust stabilization problem of the so-called extended augmented system, which is a multi-input-coupled switched system. Then, we establish a few technical lemmas to lay the foundation for constructing a switching control law and the corresponding multiple Lyapunov functions for the switched system. Then, we present the solvability conditions of our problem via the multiple Lyapunov functions and average dwell time method. The main result will be applied to the leader-following synchronization problem for a group of hyperchaotic Lorenz multiagent systems with a directed switching network.

Cooperative Adaptive Output Regulation for Second-Order Nonlinear Multiagent Systems With Jointly Connected Switching Networks.

This paper studies the cooperative global robust output regulation problem for a class of heterogeneous second-order nonlinear uncertain multiagent systems with jointly connected switching networks. The main contributions consist of the following three aspects. First, we generalize the result of the adaptive distributed observer from undirected jointly connected switching networks to directed jointly connected switching networks. Second, by performing a new coordinate and input transformation, we convert our problem into the cooperative global robust stabilization problem of a more complex augmented system via the distributed internal model principle. Third, we solve the stabilization problem by a distributed state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of Van der Pol oscillators.

Cooperative Global Robust Output Regulation for a Class of Nonlinear Multi-Agent Systems With a Nonlinear Leader

In this technical note, we study the cooperative global robust output regulation problem for the unity relative degree nonlinear multi-agent system in normal form with a nonlinear leader system. The same problem was studied recently under the assumptions that the system contains only polynomial nonlinearities, the leader system is linear and the communication network is undirected. By employing a distributed nonlinear internal model, we will construct a control law that accommodates non-polynomial nonlinearities, nonlinear leader systems, and directed communication networks. Our result will be illustrated by an example with the well known Van der Pol oscillator as the leader system.

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 Global Robust Output Regulation for Nonlinear Uncertain Multi-Agent Systems in Lower Triangular Form

In this paper, we study the cooperative global robust output regulation problem for a class of lower triangular nonlinear uncertain multi-agent systems. We first introduce a type of distributed internal model to convert the cooperative global robust output regulation problem into a global robust stabilization problem of a so-called augmented multi-agent system which is in the block lower triangular form. We then further show that, under a set of standard assumptions, the augmented multi-agent system can be globally stabilized via a distributed state feedback control law by developing a block backstepping technique. A special case of the main result of this paper leads to the solution of the leader-following global robust consensus problem for a class of nonlinear uncertain multi-agent systems.

Cooperative Global Robust Output Regulation for a Class of Nonlinear Multi-Agent Systems With Switching Network

This technical note studies the cooperative global robust output regulation problem for a class of nonlinear multi-agent systems with switching network by a distributed output feedback control law. We first convert the problem via the internal model approach to a global robust stabilization problem of an augmented system. Then, using average dwell time method, we present a set of solvability conditions for the latter problem by a distributed switched output feedback control law, thus leading to the solution of the original problem. Our approach is illustrated by a family of Lorenz systems subject to a harmonic exosystem.

Cooperative Global Output Regulation for a Class of Nonlinear Multi-Agent Systems

In this technical note, we consider the cooperative global robust output regulation problem for nonlinear multi-agent systems in output feedback form by distributed output feedback control. The main result can be summarized as follows: if the information of the leader can reach every follower through a path and the communication flows among the followers are bidirectional, then the problem can be solved by a distributed output feedback control law if the global robust output regulation problem for each subsystem can be solved by an output feedback control law.