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In this article, we study the robust output regulation problem of linear systems by an event-triggered output feedback control law. We first summarize the solvability of the linear robust output regulation problem by the internal model design. Then, we implement this continuous-time control law by an event-triggered output feedback control law together with an output-based triggering mechanism. We show that, under almost the same solvability conditions as those for the linear robust output regulation problem, the robust output regulation problem can also be solved by an event-triggered output feedback control law without incurring Zeno phenomenon. Furthermore, we show that, it is possible to solve the robust output regulation problem practically while preventing the interevent time from approaching zero as time tends to infinity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this note, we first present a framework for designing a distributed control law to solve a cooperative control problem of nonlinear multiagent systems with a nonlinear leader system. The distributed control law is composed of a purely decentralized control law and a distributed observer for the leader system, based on the certainty equivalence principle. Then, we establish a sufficient condition to guarantee the existence of a distributed observer for a class of nonlinear autonomous systems. The framework is then applied to solve the leader-following consensus problem for a class of high-order nonlinear heterogeneous multiagent systems subject to external disturbances. Our design is illustrated by an example with the Van der Pol system as the leader system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

This note studies the global robust output regulation problem for a class of nonlinear systems by an output-based event-triggered control law. First, we convert the problem into the event-triggered global robust stabilization problem of a well-defined augmented system based on the internal model approach. Then, we design an output-based event-triggered control law together with an output-based event-triggered mechanism to solve the stabilization problem, which in turn leads to the solution to the original problem by an output-based event-triggered control law. Finally, we illustrate our approach by an example. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper studies the disturbance attenuation problem of a class of nonlinear systems in feedforward form that is subject to both dynamic uncertainty and disturbance. When the disturbance vanishes, the equilibrium of the closed-loop system is globally asymptotically stable Two versions of small gain theorem with restrictions are employed to establish the global attractiveness and local stability of the closed-loop system at the equilibrium respectively. [ABSTRACT FROM AUTHOR]

Output regulation aims to achieve, in addition to closed-loop stability, asymptotic tracking and disturbance injection for a class of reference inputs and disturbances. Thus, it poses a more challenging problem than stabilization. For over a decade, the nonlinear output regulation problem has been one of the focuses in nonlinear control research, and active research on this problem has generated many fruitful results. Nevertheless, there are two hurdles that impede the further progress of the research on the output regulation problem. The first one is the assumption that the solution or the partial solution of the regulator equations is polynomial. The second one is the lack of a systematic mechanism to handle the global robust output regulation problem. In this paper, we establish a general framework that systematically converts the robust output regulation problem for a general nonlinear system into a robust stabilization problem for an appropriately augmented system. This general framework, on one hand, relaxes the polynomial assumption, and on the other hand, offers a greater flexibility to incorporate recent new stabilization techniques, thus setting a stage for systematically tackling the robust output regulation with global stability. [ABSTRACT FROM AUTHOR]

Regulator equations arise in studying the output regulation problem for nonlinear systems. The solvability of the regulator equations is the necessary condition for that of the output regulation problem. It has been shown under various assumptions that the solvability of the regulator equations can be reduced to that of a center manifold equation defined by the zero dynamics of a composite system consisting of the plant and the exosystem. In this note, we will further show that, for a quite general class of nonlinear systems, the solvability of the regulator equations can be reduced to that of a center manifold equation if the relative degree of the composite system at the origin exists. [ABSTRACT FROM AUTHOR]

Proves that the difficulty in achieving output regulation in nonlinear systems with nonhyperbolic zero dynamics can be circumvented in some cases. Approximation method to solve the center manifold equation associated with the output regulation problem for general linear systems; Solvability of the regulator equations.

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. [ABSTRACT FROM AUTHOR]

In this technical note, we study the global disturbance rejection problem of nonlinear systems in lower triangular form with unknown exosystem via state feedback control. The problem is dealt with in two steps. In the first step, an augmented system composed of the given plant and an internal model is constructed. Owing to the presence of the unknown parameter in the exosystem, the augmented system contains both nonlinearly and linearly parameterized uncertainties. In the second step, the stabilization of the augmented system is solved by an approach integrating both robust and adaptive techniques. The solution of the stabilization problem of the augmented system in turn leads to the solution of the global disturbance rejection problem of the original system. Further, the convergence issue of an estimated unknown parameter vector is also discussed. [ABSTRACT FROM PUBLISHER]

This paper deals with an asymptotic tracking problem for the Chua's circuit. We first show that the control problem for the Chua's circuit can be formulated as the global robust output regulation problem for nonlinear systems in output feedback form. Then we show that the solvability conditions for the output regulation problem for the Chua's circuit are all satisfied. Finally, an output feedback control law is designed for the Chua's circuit. The control law enables, in the presence of large parameter variations, the output of the circuit to track a class of sinusoidal signals with arbitrary amplitudes and initial phases while maintaining the global stability of the closed-loop system. [ABSTRACT FROM AUTHOR]