Robust Output Regulation Research Articles

Global robust practical output regulation for nonlinear systems in output feedback form by output‐based event‐triggered control

SummaryIn this paper, we study the event‐triggered global robust practical output regulation problem for a class of nonlinear systems in output feedback form with any relative degree. Our approach consists of the following three steps. First, we design an internal model and an observer to form the so‐called extended augmented system. Second, we convert the original problem into the event‐triggered global robust practical stabilization problem of the extended augmented system. Third, we design an output‐based event‐triggered control law and a Zeno‐free output‐based event‐triggered mechanism to solve the stabilization problem, which, in turn, leads to the solvability of the original problem. Finally, we apply our result to the controlled hyperchaotic Lorenz systems.

Robust cooperative output regulation of uncertain linear multi-agent systems not detectable by regulated output

This paper considers the robust cooperative output regulation problem via measurement feedback for a class of linear multi-agent systems, which is not detectable by regulated output. To solve it, necessarily additional measurement is assumed to be available, and the normal form defined on the additional measurement is utilized. Under mild assumptions on the communication network and the zero dynamics, a novel distributed measurement feedback controller can be established, consisting of the distributed dynamical compensator, internal model and possibly asymptotic observer, such that all regulated errors can globally exponentially converge to zero. Only regulated output of each agent needs to be transmitted to its neighbors, while neither the plant state nor the controller state is required to be exchanged with its neighbors.

Robust Output Regulation of Counter-Flow Heat Exchangers

We consider a partial differential equation model widely used for counter-flow heat exchangers and the related robust output regulation problem with boundary control and boundary observation. We show that the control system is an exponentially stable regular linear system, which enables us to use a specific known controller design to robustly regulate the system. The results are illustrated with numerical simulations.

Robust Output Regulation of Disturbed Systems with Uncertainties and Input Constraints

In this paper a “state-space” revised version of the consecutive compensator control approach is proposed to regulate systems with uncertainties and input constraints affected by external disturbances. As a preliminary result the redesigned controller is applied to a system coupled with unmodeled dynamics. The main result enhances this approach by implementing the internal model and back-calculation anti-windup scheme in the control law. The paper throughly addresses the stability issues and provides a numerical example illustrating the proposed approach.

Robust output regulation of Zeta converter with load/input variations: LMI approach

The output regulation of DC–DC converters is a challenging problem due to the fast switching behavior in the presence of the uncertainty/variation in the model, input, and load. In this paper, the Zeta converter is first analyzed and then using the Linear Matrix Inequality (LMI) theory a robust controller is designed to cope with this issue. Inspired by the photovoltaic applications of the Zeta converter, and due to the nature of the solar cells, not only the load variations but also the input voltage variations are considered in the controller design. Finally, the proposed controller is implemented in a DSP-based controller and its performance is experimentally verified and compared with the widely used PI controller.

Data‐driven, robust output regulation in finite time for LTI systems

SummaryIn this paper, a novel data‐driven approach is proposed to obtain output regulation for linear systems in finite time, requiring only limited information about the plant and the exosystem. The resulting regulator is robust because it does not rely on the knowledge of perturbed or even nominal plant parameters. Finite‐time regulation is achieved, combining the use of the external‐model technique with the deadbeat controller design. The core of the method lies in an error‐feedback reset logic for the state of the external model to compensate for the contribution of the exosystem on the plant output response, then an ancillary control law is introduced to steer the error to zero in a preassigned time interval, trading‐off between convergence rate, and control effort.

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.

Robust Linear Output Regulation Using Extended State Observer

This paper presents a disturbance rejection-based solution to the problem of robust output regulation. The mismatch between the underlying plant and its nominal mathematical model is formulated by two disturbance classes. The first class is assumed to be generated by an autonomous linear system while for the second class no specific dynamical structure is considered. Accordingly, the robustness of the closed-loop system against the first disturbance class is achieved by following the internal model principle. On the other hand, in the framework of disturbance rejection control, an extended state observer (ESO) is designed to approximate and compensate for the second class, i.e., unstructured disturbances. As a result, the proposed output regulation method can deal with a vast range of uncertainties. Finally, the stability of the closed-loop system based on the proposed compound controller is carried out via Lyapunov and center manifold analyses, and some results on the robust output regulation are drawn. A representative simulation example is also presented to show the effectiveness of the control method.

Robust State Feedback Regulator Design for General Linear Heterodirectional Hyperbolic Systems

The topic of this paper is the backstepping-based solution of the robust state feedback regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients. Thereby, a large class of outputs is considered, i.e., mixed distributed and pointwise in-domain or boundary outputs. The state feedback regulator design is based on the $\boldsymbol {p}$ -copy internal model principle. This results in a stabilization problem for a cascade of $\boldsymbol {m+p}$ boundary controlled transport partial differential equations (PDEs) with $\boldsymbol {p}$ ordinary differential equations (ODEs). For this, a systematic backstepping approach is presented, in which all design equations are explicitly solvable in backstepping coordinates. Furthermore, the solvability conditions for the considered output regulation problem can be evaluated in closed form utilizing the plant transfer behavior. Robust output regulation is verified for nondestabilizing model uncertainties and unknown disturbance input locations. A $\boldsymbol {4 \times 4}$ hyperbolic system with uncertain transport velocities and couplings in the transport PDEs illustrates the results of this paper.

Robust cooperative output regulation under exosystem detectability constraint

ABSTRACTThis paper revisits the robust cooperative output regulation problem for a class of linear uncertain multi-agent systems. In particular, it is assumed here that the agents in the system can only access incomplete measurements of the exosystem, and the local regulated error signals are not available to the agents to be used in control. Under these assumptions, the agents in the system cannot independently reconstruct the exosystem dynamics, or rely on their own local measurements to achieve the objectives of the output regulation problem. The solution to the regulation problem proposed in this paper is a distributed dynamic control law that reconstructs the exosystem states, given a mild collective detectability assumption. Furthermore, the proposed distributed control law incorporates an internal model of the exosystem to allow for uncertain dynamics of the multi-agent system. A numerical example is offered to illustrate the effectiveness of the proposed control solution.

Robust Output Regulation for a Class of Linear Differential-Algebraic Systems

This letter addresses the problem of robust output regulation of systems described by linear differential-algebraic equations (DAEs). Taking advantage of some recent relevant results concerned with the development of normal forms for general DAEs, it is shown how an internal model can be designed in such a way that the problem in question is reduced to the problem of robustly stabilizing an augmented system modeled by DAEs. Then, a suitable enhancement—within the context of systems modeled by DAEs—of the theory of extended observers is proposed, by means of which such robust stabilization problem is solved.

Robust leader-following output regulation of uncertain multi-agent systems with time-varying delay

In this paper, the robust analysis and design of leader-following output regulation for multi-agent systems described by general linear models is given in presence of time-varying delay and model uncertainty. To this aim, a new regulation protocol for the closed-loop multi-agent system under a directed graph is proposed. An important specification of the proposed protocol is to guarantee the leader-following output regulation for uncertain multi-agent systems with both stable and unstable agents. Since many signals can be approximated by a combination of the stationary and ramp signals, the presented results work for adequate variety of the leaders. The analysis and design conditions are presented in terms of certain matrix inequalities. The method proposed can be used for both stationary and ramp leaders. Simulation results are presented to show the effectiveness of the proposed method.

Cooperative robust output regulation of linear uncertain multiple multivariable systems with performance constraint

This paper is to pursue a general investigation of cooperative robust output regulation for linear continuous-time multiple multivariable systems with unknown system parameters and unmodeled external disturbances. We show that, under standard minimum-phase and relative degree like assumptions, an internal model principle based output-feedback protocol can be constructed by incorporating suitable dynamic compensators, even when the parametric uncertainties are arbitrarily large in some sense. Moreover, we are able to establish a redesigned protocol by means of adapting the H∞ control method. It assures a desired robustness property for the closed-loop system of attenuating external unmodeled disturbances. Hence, our study offers a performance-constrained robust control solution in a distributed control fashion.

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.

Adaptive output regulation of right-invertible MIMO LTI systems, with application to vessel motion control

The problem of robust output regulation for MIMO linear time-invariant systems with harmonic exogenous inputs and parameter uncertainties is addressed. We discuss two methods to handle stability in the presence of plant uncertainties, that take full advantage of all controls and all available measurements. One method, appeals to a general notion of “robust” minimum-phase. The other method, that addresses the case of unstructured uncertainties, reposes on the solution of appropriate LMIs. In both cases, the critical issue is to show how adaptive tuning of the internal model can be implemented, so as to obtain a controller that guarantees asymptotic convergence of the regulated output to zero. A numerical example of vessel motion control is given to illustrate one of the proposed approaches.

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.

A Framework for Global Robust Output Regulation of Nonlinear Lower Triangular Systems With Uncertain Exosystems

This technical note considers global robust output regulation for nonlinear lower triangular systems with uncertain exosystems. The problem, under standing minimum phase and solvability of regulator equations conditions, has not been well solved in the literature. It has attracted many researchers to contribute efforts to build solutions, however only partially from different aspects, mostly utilizing adaptive internal models. The bottleneck is that the usual adaptive approach is not suitable for recursive implementation due to the so-called “propagation of uncertainties” while recursion is usually indispensable for global control of lower triangular systems. This motivates the present development of an expanded and “nonadaptive” internal model based design framework. As a major consequence, we are able to avoid propagation of uncertainties and establish a constructive solution for the problem.