Output Regulation Of Nonlinear Systems Research Articles

Exact Output Regulation for Nonlinear Systems Described by Takagi–Sugeno Fuzzy Models

The exact output regulation for Takagi-Sugeno (T-S) fuzzy models depends on two conditions: 1) The local steady-state zero-error manifolds have to be the same for every local subsystem, and 2) the local input matrices have to be the same for every local subsystem included in the T-S fuzzy model. These conditions are difficult to satisfy in general. In this paper, those conditions are relaxed by solving the fuzzy regulation problem directly on the overall T-S fuzzy model, instead of constructing the fuzzy regulator on the basis of linear local controllers. By considering the fuzzy model as a special class of linear time-varying systems, existence conditions are rigorously derived. These new conditions, which can be solved by means of any mathematical software, depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and/or the exosystem. Two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach.

Matched disturbance suppression for nonlinear systems stabilizable by logic-based feedback

We focus on a class of nonlinear systems that can be stabilized at a desired compact set by means of logic-based continuous feedback and we show how to design regulators that are robust to matched exosystem-generated disturbances. The proposed design methodology, of interest also for purely continuous-time systems, combines recent advances in the field of hybrid control systems and output regulation for nonlinear systems. As an illustrative example, the problem of global stabilization of a 6-DOF rigid body affected by a force periodic disturbance of uncertain amplitude, phase and frequency is presented.

Output Regulation of the Simplified Lorenz Chaotic System

This paper investigates the problem of designing feedback controllers for regulating the output of the simplified Lorenz system, which is a novel chaotic system recently discovered by K.H. Sun and J.C. Sprott (2009). The simplified Lorenz chaotic system is a three-dimensional chaotic system with one bifurcation parameter and it includes the Lorenz attractor (1963) as a special case. In this paper, state feedback control laws to regulate the output of the simplified Lorenz chaotic system have been derived so as to track the constant reference signals. The control laws are derived using the regulator equations of C.I. Byrnes and A. Isidori (1990), who solved the problem of output regulation of nonlinear systems involving neutrally stable exosystem dynamics. Numerical simulations are shown to illustrate the results.

Backstepping Design for Incremental Stability

Stability is arguably one of the core concepts upon which our understanding of dynamical and control systems has been built. The related notion of incremental stability, however, has received much less attention until recently, when it was successfully used as a tool for the analysis and design of intrinsic observers, output regulation of nonlinear systems, frequency estimators, synchronization of coupled identical dynamical systems, symbolic models for nonlinear control systems, and bio-molecular systems. However, most of the existing controller design techniques provide controllers enforcing stability rather than incremental stability. Hence, there is a growing need to extend existing methods or develop new ones for the purpose of designing incrementally stabilizing controllers. In this technical note, we develop a backstepping design approach for incremental stability.

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 of nonlinear systems using conditional servocompensators

This paper studies the output regulation of nonlinear systems using conditional servocompensators. Previous work introduced the conditional servocompensator, which acts as a traditional servocompensator in the neighborhood of a zero-error manifold while acting as a stable system otherwise, leading to improvement in the transient response while achieving zero steady-state regulation error. The conditional servocompensator tool was introduced for sliding-mode feedback controllers. This paper extends the technique to more general feedback controllers by using Lyapunov redesign and saturated high-gain feedback.

A reduction paradigm for output regulation

AbstractThe goal of this paper is to provide a reduction paradigm for the design of output regulators which can be of interest for nonlinear as well as linear uncertain systems. The main motivation of the work is to provide a systematic design tool to deal with non‐minimum‐phase uncertain systems for which conventional high‐gain stabilization methods are not effective. The contribution of the work is two‐fold. First, this work extends a previous reduction paradigm for output regulation of nonlinear systems. Furthermore, in the case of the uncertain controlled dynamics being linear, we show how the proposed framework leads to a number of systematic design tools of interest for non‐minimum‐phase linear systems affected by severe uncertainties. A numerical control example of a linearized model of an inverted pendulum on a cart is presented. Copyright © 2007 John Wiley & Sons, Ltd.

Output regulation for nonlinear systems: some recent theoretical and experimental results

This brief summarizes recent theoretical and presents experimental results of output regulation for nonlinear systems. The main contribution of this brief consists of the first experimental study of output regulation using a two-link underactuated mechanical system-the Pendubot.

A note on global output regulation of nonlinear systems in the output feedback form

This note shows how the adaptive control method developed recently for nonlinearly parameterized systems can be used to solve the problem of global output regulation, for nonlinear systems in the so-called output-feedback form with unknown parameters and exogenous signals belonging to a compact set whose bound is also unknown.

Output regulation of nonlinear systems with delay

Output regulation of retarded type nonlinear systems is considered. Regulator equations are derived, which generalize Francis–Byrnes–Isidori equations to the case of systems with delay. It is shown that, under standard assumptions, the regulator problem is solvable if and only if these equations are solvable. In the linear case, the solution of these equations is reduced to linear matrix equations. An example of a delayed Van der Pol equation illustrates the efficiency of the results.

Adaptive Output Regulation for Nonlinear Systems with Unknown Periodic Disturbances

Many mechanical systems are subjected to periodic disturbances which may adversely influence control performance. When the plants are nonlinear systems with unknown parameters, this disturbance compensation problem has been considered as adaptive output regulation problem. This paper discusses the problem about adaptive output regulation for nonlinear systems with arbitrary relative degree, which can be transformed into the output feedback form. The nonlinear plant is affected by unknown constant parameters and periodic disturbances with unknown frequencies, magnitudes and phases. The periodic disturbances are considered as signals generated from a linear time invariant exosystem. It is not assumed that the disturbances meet the matching condition for the control input. The design method of the adaptive controller and its parameter update law is based on adaptive backstepping manner for the coordinates-changed extended system, which is generated from the nonlinear plant and the exosystem. Then, it can be achieved that the output asymptotically converges to the output reference and that all signals in the closed-loop system are bounded.

1213 バックステッピング手法に基づく非線形出力レギュレーション

1213 バックステッピング手法に基づく非線形出力レギュレーション

Output regulation of nonlinear systems by sliding mode

This paper focuses on the design of an output feedback sliding mode regulator able to achieve the asymptotic tracking of a reference trajectory for nonlinear systems. It is assumed that the reference trajectory is generated by means of a neutrally stable unforced system (exosystem) whose state is known. The design methodology is based on the center manifold theory and on the “equivalent control” concept and can be applied to both minimum and nonminimum-phase systems.

Semi-global nonlinear output regulation with adaptive internal model

We address the problem of output regulation for nonlinear systems driven by a linear, neutrally stable exosystem whose frequencies are not known a priori. We present a classical solution in terms of the parallel connection of a robust stabilizer and an internal model, where the latter is adaptively tuned to the device that reproduces the steady-state control necessary to maintain the output-zeroing condition. We obtain robust regulation (i.e. in presence of parameter uncertainties) with a semi-global domain of convergence for a significant class of nonlinear minimum-phase system.

Editorial

International Journal of Robust and Nonlinear ControlVolume 10, Issue 5 p. 321-322 EditorialFree Access Editorial Jie Huang, Jie Huang Guest EditorSearch for more papers by this author Jie Huang, Jie Huang Guest EditorSearch for more papers by this author First published: 03 April 2000 https://doi.org/10.1002/(SICI)1099-1239(20000430)10:5<321::AID-RNC486>3.0.CO;2-DCitations: 3AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. REFERENCES 1 Isidori A, Byrnes CI. Output regulation of nonlinear systems. IEEE Transactions on Automatic Control 35(2): 131– 140. Citing Literature Volume10, Issue5Special Issue: Output Regulation for Nonlinear Systems30 April 2000Pages 321-322 ReferencesRelatedInformation

Output regulation for nonlinear systems: an overview

Output regulation for nonlinear systems: an overview

Output regulation for nonlinear systems: an overview

The problem of controlling the output of a system so as to achieve asymptotic tracking of prescribed trajectories and/or asymptotic rejection of disturbances is one of the most fundamental problems in control theory. In linear system theory, a powerful approach to the solution of this problem is the design of a controller incorporating an internal model of all exogenous inputs. The extension of this approach to nonlinear systems has been thoroughly investigated in the past 10 years. The purpose of this paper is to review the major achievements in this area as well as to outline the major problems on which the research is presently progressing. Copyright © 2000 John Wiley & Sons, Ltd.

Approximate output regulation of nonlinear systems

Abstract This paper deals with output regulation of nonlinear systems driven by exogenous signals whose dynamics are not exactly known. Output regulation with high order approximation is formulated and the solvability is characterized by the existence of certain invariant manifolds. Under the proposed control, the closed-loop system exhibits ultimate boundedness properties with respect to high order time-derivatives of the exogenous signals. Besides the high order approximation, another advantage of the proposed control design is that the measurement of derivatives of the exogenous signals is not essential for control design.

On the output regulation of nonlinear systems by sliding mode

Abstract In this paper the problem of output regulation by error feedback by adopting a Sliding Mode controller is addressed. The reference signal to track, or equivalently the disturbance to reject, is supposed to be generated by a neutrally stable autonomous system whose state is supposed to be known. The design procedure of the controller, which holds for nonlinear systems (both minimum and non-minimum phase) having unitary relative degree, as well as simulation results are presented.

Structurally stable output regulation of nonlinear systems

We address a number of issues that were left open in earlier works on the subject of output regulation of nonlinear systems, and we describe an approach to structurally stable regulation that unifies and extends a number of existing results. Moreover, we also address in part the issue of robust regulation, i.e. the issue of achieving regulation in the presence of parameter uncertainties ranging within a prescribed set.