Robust Output Regulation Problem Research Articles

Robust cooperative output regulation of heterogeneous Lur'e networks

SummaryIn this paper, we study robust cooperative output regulation problems for a directed network of Lur'e systems that consist of a nominal linear dynamics with an unknown static nonlinearity around it through negative feedback. We assume that the linear part of each agent is identical, but the nonlinearities are allowed to be different for distinct agents. In this sense, the network is heterogeneous. As is common in the context of Lur'e systems, the unknown nonlinearities are assumed to be sector bounded within one given sector. The interconnection graph among these agents is assumed to contain a directed spanning tree. Similar to classical output regulation problems, there is a virtual exosystem generating a reference signal in which all the agents are required to track cooperatively. Our designed distributed dynamic state/output feedback protocol makes a copy of the reference signal at each agent asymptotically, and then the robust cooperative output regulation problem becomes a robust tracking problem that can be handled by each agent via local information. It turns out that our cooperative protocols are fully distributed. Sufficient conditions on the existence of output synchronization protocols are given along with some discussions on these conditions. Finally, two simulation examples illustrate our design. Copyright © 2016 John Wiley & Sons, Ltd.

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.

Tracking of piezoelectric actuators with hysteresis: A nonlinear robust output regulation approach

SummaryHysteretic characteristics commonly exist in piezoelectric actuators (PEAs) and degrade the positioning accuracy particularly in the case of low‐frequency trajectory tracking. A PEA with hysteretic characteristics is usually difficult to precisely control because the unmeasurable hysteretic force is typically generated by a complicated nonlinear dynamic model. This task can be theoretically formulated as a robust output regulation problem with a specific nonlinear and non‐autonomous exosystem. In this paper, the theoretical problem is first solved within a novel internal model architecture. With the proposed controller, the PEA is able to asymptotically track a desired reference trajectory with the robustness to plant uncertainties. The effectiveness of the design is verified by extensive experiments. Copyright © 2016 John Wiley & Sons, Ltd.

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.

Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

ABSTRACTMost of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.

Backstepping Design of Robust Output Feedback Regulators for Boundary Controlled Parabolic PDEs

In this article a backstepping-based solution of the robust output regulation problem for boundary controlled parabolic PDEs with spatially varying parameters is presented. This is achieved by stabilizing the plant extended with a finite-dimensional internal model of the exogenous signals. For the resulting PDE-ODE system with spatially varying parameters a systematic backstepping-based compensator design method is developed. The robustness of the achieved output regulation is verified for non-destabilizing model uncertainties. An uncertain parabolic system illustrates the results of the article.

Output regulation of output feedback systems with unknown exosystem and unknown high-frequency gain sign

This paper discusses the global robust output regulation problem for a class of nonlinear output feedback systems. It is assumed that the exosystem and the high-frequency gain sign are unknown and that the unknown parameters can be arbitrarily large. To solve this problem, two major challenges are to be overcome. First, the concurrence of the unknown exosystem and the unknown high-frequency gain sign cannot be handled merely by designing estimators for the two unknown parameters respectively. Second, the conventional extended matching design approach cannot be directly implemented, owing to the arbitrarily large unknown parameters. To cope with these difficulties, a new estimator is developed, and the extended matching design approach is modified to obtain a suitable update law for the estimator. The effectiveness of the proposed adaptive controller is illustrated by an example.

Global robust output regulation of multivariable systems with nonlinear exosystem

Summary It is well known that multi-input, multi-output nature of nonlinear system and generalized exosystem have posed some challenges to output regulation theory. Recently, the global robust output regulation problem for a class of multivariable nonlinear system subject to a linear neutrally stable exosystem has been studied. It has been shown that a linear internal model-based state feedback control law can lead to the solution of previous problem. In this paper, we will further study the global robust output regulation problem of the system subject to a nonlinear exosystem. By utilizing nonlinear internal model design and decomposing the multi-input control problem into several single-input control problems, we will solve the problem by recursive control law design. The theoretical result is applied to the non-harmonic load torque disturbance rejection problem of a surface-mounted permanent magnet synchronous motor. Copyright © 2016 John Wiley & Sons, Ltd.

Distributed adaptive controllers for cooperative output regulation of heterogeneous agents over directed graphs

This paper considers the cooperative output regulation problem for linear multi-agent systems with a directed communication graph, heterogeneous linear subsystems, and an exosystem whose output is available to only a subset of subsystems. Both the cases with nominal and uncertain linear subsystems are studied. For the case with nominal linear subsystems, a distributed adaptive observer-based controller is designed, where the distributed adaptive observer is implemented for the subsystems to estimate the exogenous signal. For the case with uncertain linear subsystems, the proposed distributed observer and the internal model principle are combined to solve the robust cooperative output regulation problem. Compared with the existing works, one main contribution of this paper is that the proposed control schemes can be designed and implemented by each subsystem in a fully distributed fashion for a class of directed graphs.

An adaptive regulation problem and its application

This paper studies an adaptive regulation problem for the modified FitzHugh-Nagumo neuron model under external electrical stimulation. We first present the solution of the global robust output regulation problem for output feedback system with an uncertain exosystem which models the external electrical stimulation with unknown frequency and amplitude. Then, we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output regulation problem for the modified FitzHugh-Nagumo neuron model are all satisfied. Then, we apply the obtained output regulation result to constructing an output feedback control law for the modified FitzHugh-Nagumo neuron model to achieve global stability of the closed-loop system in the presence of uncertain parameters and external stimulus. An example is given to show that the proposed algorithm can completely reject the external electrical stimulation.

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.

Robust Perturbed Output Regulation and Synchronization of Nonlinear Heterogeneous Multiagents

The conventional robust output regulation problem aims to achieve reference tracking and disturbance rejection in the presence of system uncertainties while the references and disturbances are generated by an autonomous exosystem. When the exosystem is perturbed by an external event, a novel robust perturbed output regulation problem is formulated and solved in this paper. The formulation arises from a class of synchronization problem of multiple agents. With the aid of a new reference model-based control framework, the proposed solution to the robust perturbed output regulation problem leads to a decentralized control algorithm for synchronization of multiple agents of nonlinear heterogeneous dynamics.

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.

Robust output regulation of linear time-delay systems: A state predictor approach

Summary This paper considers the robust output regulation problem for linear systems in the presence of state, input, and output delays. First, a state feedback control law is constructed from a state predictor, recently developed for systems with state and input delays. Necessary and sufficient conditions for the existence of a solution to the regulator equations are presented. Next, an error feedback control law for the output regulation problem is constructed by means of an error-based state predictor. Finally, the proposed error feedback solution is extended to solve the output regulation problem in the presence of model uncertainty. Numerical examples demonstrate the effectiveness of the proposed predictor-based solutions. Copyright © 2015 John Wiley & Sons, Ltd.

Cooperative robust output regulation for heterogeneous second-order discrete-time multi-agent systems

This paper considers the cooperative robust output regulation for second-order discrete-time multi-agent systems. Each agent could access the information with its neighbors under the directed network topology. A distributed dynamic state feedback control law is designed. A stability region is given for the discrete-time multi-agent systems, and internal model method is used for the robust output regulation problem. At last, numerical simulation is utilized to show the effectiveness of the obtained results.

Robust output regulation problem for linear time-delay systems

In this paper, we study the robust output regulation problem for linear systems with input time-delay. By extending the internal model design method to linear time-delay systems, we have established solvability conditions for the problem by both dynamic state feedback control and dynamic output feedback control. The advantages of internal model approach over the feedforward design approach are that it can handle perturbations of the uncertain parameters in the plant and the control law, and it does not need to solve the regulator equations.

Constraint robust adaptive stabilization for a class of lower triangular systems with unknown control direction

This paper studies the constrained robust adaptive stabilization problem for a class of lower triangular systems with unknown control direction. A robust adaptive feedback control law for the systems is proposed by incorporating the technique of Barrier Lyapunov Function with Nussbaum gain. Such a controlled system arises from the study of the constrained robust output regulation problem for a class of output feedback systems with the unknown control direction and a nonlinear exosystem. An application of the constrained robust adaptive stabilization design leads to the solution of the constrained robust output regulation problem in the sense that the output tracking error is constrained within the prescribed barrier limit while asymptotically approaching to zero and the closed loop signals are all bounded for all the time. A numerical example is provided to illustrate the performance of the proposed control.

Output regulation for heterogeneous linear multi-agent systems based on distributed internal model compensator

This article considers robust output regulation of uncertain heterogeneous multi-agent systems in the case that all the agents have non-identical nominal dynamics. The directed communication graph contains a spanning tree and the exosystem is as its root. Since not all the agents can access the information of the exosystem, the distributed compensator is used for the unaccessible part. The dynamic state feedback control law and dynamic output feedback control law are proposed under this topological structure. Then we give a novel compact form and a general global method to solve the robust output regulation problem based on internal model principle. Finally, some examples are presented to illustrate the effectiveness of our results.