Global Robust Output Regulation Problem Research Articles

Output regulation of nonlinear output feedback systems with exponential parameter convergence

This paper revisits the global robust output regulation (GROR) problem of nonlinear output feedback systems with uncertain exosystems by error output feedback control. The problem was conventionally tackled by employing a linear canonical internal model and as a result, suitable adaptive stabilization has to be done for the augmented system to achieve output regulation. Distinguished from that, a novel nonlinear internal model approach is developed in the present study that successfully converts the GROR problem into a robust non-adaptive stabilization problem for the augmented system. The feature of the new approach is two-fold. On one hand, stabilization of augmented system is disentangled from any extra adaptive control law and thus the procedure is simplified. On the other hand, it leads to explicit strict Lyapunov characterization for the closed-loop system and consequently assures exponential parameter convergence.

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.

Robust and decentralised output regulation of switched non‐linear systems with switched internal model

This study investigates the global robust output regulation problem for a class of switched non-linear systems with stabilisable and unstabilisable subsystems. First, this study proposes a new concept, namely switched internal model, as an extension of the concept of non-switched internal model, which provides a tool for solving the output regulation problem of switched non-linear systems. Also, the authors show that the problem of output regulation boils down to a global robust regulation problem of an appropriately switched augmented system via a switched internal model. Then, the global robust regulation problem under a class of switching signals with average dwell time is solved by using the average dwell time method, which leads to the solution of the problem of global robust output regulation. Further, the authors apply this type of switched internal models above to solve the global decentralised output regulation problem for a class of large-scale switched non-linear systems with stabilisable and unstabilisable subsystems. An example is provided to demonstrate the effectiveness of the proposed approach.

A class of nonlinear internal models for global robust output regulation problem

SummaryThe global robust output regulation problem of nonlinear systems in output feedback form has been studied via a linear internal model. In this paper, we study the same problem using a class of nonlinear internal models. An advantage of nonlinear internal models is that it exists even when the system contains nonpolynomial nonlinearity and the exosystem is nonlinear. Thus, the result of this paper applies to a larger class of nonlinear systems and a larger class of exosystems. Copyright © 2014 John Wiley & Sons, Ltd.

Cooperative Global Robust Output Regulation for Nonlinear Multi-Agent Systems in Output Feedback Form

In this paper, we consider the global robust output regulation problem for a class of nonlinear multi-agent systems by distributed output feedback control. We first show that the problem can be converted into the global stabilization problem of a class of multi-input, multi-output nonlinear systems called augmented system. Then, we further show that, under a set of standard assumptions, the augmented system can be globally stabilized by a distributed output feedback control law. Finally, we apply our approach to solve a leader-following synchronization problem for a group of Lorenz multi-agent systems.

Global robust output regulation control for cascaded nonlinear systems using the internal model principle

This article considers the global robust output regulation problem via output feedback for a class of cascaded nonlinear systems with input-to-state stable inverse dynamics. The system uncertainties depend not only on the measured output but also all the unmeasurable states. By introducing an internal model, the output regulation problem is converted into a stabilisation problem for an appropriately augmented system. The designed dynamic controller could achieve the global asymptotic tracking control for a class of time-varying reference signals for the system output while keeping all other closed-loop signals bounded. It is of interest to note that the developed control approach can be applied to the speed tracking control of the fan speed control system. The simulation results demonstrate its effectiveness.

Global robust output regulation of lower triangular systems with nonlinear exosystems and its application

This paper studies the global robust output regulation problem for lower triangular systems subject to nonlinear exosystems. By employing the internal model approach, this problem can be boiled down to a global robust stabilization problem of a time-varying nonlinear system in the cascade-connected form. Then, a set of sufficient conditions for the solvability of the problem is derived, and thus, leading to the solution to the global robust output regulation problem. An application of the main result of this paper is also proposed.

Speed tracking control of PM synchronous motor by internal model design

In this article, we consider a speed tracking and load torque disturbance rejection problem of PM synchronous motor by internal model design. The problem is first formulated as a global robust output regulation problem of a special class of multivariable systems. Then the output regulation problem is further converted into a global stabilisation problem of an augmented system composed of the original plant and an internal model. As the augmented system does not take any known special form, we have developed a specific tool to deal with the stabilisation problem. In particular, a generalised changing supply function technique applicable to non-input-to-state stable (ISS) systems is developed. This technique, in conjunction with a particular nonlinear internal model, leads to an effective solution to the problem.

Global robust output regulation for a class of multivariable systems

SUMMARYIn this paper, we study the global robust output regulation problem for a class of multivariable nonlinear systems. The problem is first converted into a stabilization problem of an augmented system composed of the original plant and an internal model. The augmented system is a multi‐input system containing both dynamic uncertainty and time‐varying static uncertainty. By decomposing the multi‐input control problem into several single‐input control problems, we will solve the problem by solving several single‐input control problems via a recursive approach utilizing the changing supply function technique. The theoretical result is applied to the speed tracking control and load torque disturbance rejection problem of a surface‐mounted permanent magnet synchronous motor. Copyright © 2011 John Wiley & Sons, Ltd.

New results on robust output regulation of nonlinear systems with a nonlinear exosystem

SUMMARYThe global robust output regulation problem for nonlinear plants subject to nonlinear exosystems has been a challenging problem and has not been well addressed. The main difficulty lies in finding a suitable internal model. The existing internal model for handling the nonlinear exosystem is not zero input globally asymptotically stable, and can only guarantee a local solution for the output regulation problem. In this paper, we first propose a new class of internal models, which is guaranteed to exist under the generalized immersion condition. An advantage of this internal model is that it is zero input globally asymptotically stable. This fact will greatly facilitate the global stabilization of the augmented system associated with the given plant and the internal model. Then we will further utilize this class of internal models to solve the global robust output regulation problem for output feedback systems with a nonlinear exosystem. Copyright © 2011 John Wiley & Sons, Ltd.

Output Regulation for Output Feedback Systems With iISS Inverse Dynamics

This paper develops an approach to dealing with the global robust output regulation problem for a class of nonlinear systems with integral input-to-state stable (iISS) inverse dynamics by using output feedback control. As iISS condition is strictly weaker than the ISS condition, the result of this paper applies to a larger class of nonlinear systems.

Global Robust Output Regulation of Nonlinear Systems subject to a Nonlinear Exosystem

AbstractThe global robust output regulation problem for nonlinear plants subject to nonlinear exosystems has been a challenging problem and has not been well addressed. The main difficulty lies in finding a suitable internal model. In this paper, we first propose a new class of internal models which is guaranteed to exist under the generalized immersion condition [2]. An advantage of this internal model is that it is zero input globally asymptotically stable. This fact will facilitate the global stabilization of the augmented system associated with the given plant and the internal model. Then we will further utilize this class of internal models to solve the global robust output regulation problem for output feedback systems with a nonlinear exosystem.

Global output regulation for output feedback systems with an uncertain exosystem and its application

AbstractThis paper presents the solvability conditions for the global robust output regulation problem for a class of output feedback systems with an uncertain exosystem by using output feedback control. An adaptive control technique is used to handle the unknown parameter vector in the exosystem. It is shown that this unknown parameter vector can be exactly estimated asymptotically if a controller containing a minimal internal model is employed. The effectiveness of our approach has been illustrated by an asymptotic tracking problem of a generalized fourth‐order Lorenz system. Copyright © 2009 John Wiley & Sons, Ltd.

Output Regulation Design for a Class of Nonlinear Systems With an Unknown Control Direction

This paper presents the solution of the global robust output regulation problem for a class of nonlinear systems without knowing the control direction. The class of the systems is larger than previously studied strict output feedback systems of relative degree equal to one. The result is also applied to an asymptotic tracking problem associated with the well-known Lorenz system.

Output regulation for a class of uncertain nonlinear systems with nonlinear exosystems and its application

In this paper, we consider the global robust output regulation problem for a class of uncertain nonlinear systems with nonlinear exosystems. By employing the internal model approach, we show that this problem boils down to a global robust stabilization problem of a time-varying nonlinear system in lower triangular form, the solution of which will lead to the solution of the global robust output regulation problem. An example shows the effectiveness of the proposed approach.

Global Robust Output Regulation by State Feedback for Strict Feedforward Systems

This note studies the global robust output regulation problem by state feedback for strict feedforward systems. By utilizing the general framework for tackling the output regulation problem , the output regulation problem is converted into a global robust stabilization problem for a class of feedforward systems that is subject to both time-varying static and dynamic uncertainties. Then the stabilization problem is solved by using a small gain based bottom-up recursive design procedure.

A global state feedback output regulating control for uncertain systems in strict feedback form

A family of single-input, single-output, nonlinear systems in strict feedback form with uncertain constant parameters which appear linearly and belong to a known compact set Π is considered. A global robust output regulation problem via state feedback is addressed and solved under the assumptions that the regulator equations are solvable in Π , the output equation does not depend on uncertain parameters, no modelled disturbances affect the system and the output reference signal is generated by a known exosystem whose state is bounded and available for feedback. Robust adaptive techniques are used to guarantee closed loop boundedness and to achieve, without requiring persistency of excitation, global asymptotic output regulation for a class of feedback linearizable systems which may have unbounded uncertain tracking dynamics or may not have a well-defined global relative degree.