Global robust output regulation of multivariable systems with nonlinear exosystem

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.     

Speed tracking control of surface‐mounted permanent‐magnet synchronous motor with unknown exosystem

The surface‐mounted permanent‐magnet synchronous motor is a two‐input, two‐output nonlinear system. The multi‐input, multi‐output nature of the system has posed some specific challenges to various control methods. Recently, the robust output regulation problem of the system subject to a known neutrally stable exosystem was studied. The problem came down to a global robust stabilization problem of an augmented system composed of the original plant and an internal model. In this paper, we will further study the robust output regulation problem of the system subject to an unknown neutrally stable exosystem. Like in the case where the exosystem is known, the current problem can be solved by globally stabilizing an augmented system. But unlike in the case where the exosystem is known, the augmented system takes a much more complicated form because of uncertainty in the exosystem than the case where the exosystem is known. In particular, the dynamic uncertainty in the current augmented system contains linearly parameterized uncertainty, and hence is not input‐to‐state stable. By utilizing some dynamic coordinate transformation technique, and combining some robust control and adaptive control techniques, we will solve the problem via a recursive approach. Copyright © 2014 John Wiley & Sons, Ltd.     

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

The 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.     

具有自适应内模的一类非线性系统输出调节问题

研究一类包含未知非线性项的非线性系统的鲁棒输出调节问题.此类非线性系统由一包含未知参数的线性中性稳定的外系统驱动.首先运用调节器方程组解和标准内模将输出调节问题转化为镇定问题;然后给出控制律镇定闭环系统,同时利用镇定输入项和外系统信息设计出自适应内模方程.控制律使得闭环系统的信号全局最终有界,且误差被调节至预先设定的任意小的精度值.仿真结果验证了所提出设计方法的有效性.     

一类非线性输出反馈系统的自适应输出调节问题

本文讨论一类非线性系统的全局鲁棒输出调节问题.假定被控非线性系统的系统输入方向未知,且产生参考或扰动信号的外部系统含未知参数,这为控制律的设计带来了挑战.文章使用自适应控制方法和内模原理,解决了一类相对阶为1的非线性输出反馈系统的输出调节问题,并将结果应用于处理Lorenz系统的渐近跟踪问题.     

Input disturbance suppression for a class of feedforward uncertain nonlinear systems

This paper deals with the problem of asymptotically rejecting bounded unknown disturbances affecting the input channel of a feedforward uncertain nonlinear system. The problem is solved assuming that the matched disturbance belongs to the class of signals generated by an autonomous neutrally stable exosystem whose state is not accessible. We design an internal model-based regulator capable on one hand to reject the matched disturbance for any initial state of the exosystem and, on the other hand, to robustly globally asymptotically stabilize the system using state feedback.     

Global robust output regulation for a class of nonlinear systems

The problem of global robust output regulation is solved for a class of nonlinear systems driven by a linear neutrally stable exosystem. The proposed scheme makes use of a dynamic controller which processes information from the regulated error only. Robust regulation is achieved for every initial condition in the state space, and for all possible values of the uncertain parameter vector and the exogenous signal ranging over arbitrary compact sets. The regulator synthesis is based upon a recursive procedure, and takes advantage of both the special normal form of the plant equations and the passivity property of the internal model.     

Semi-global nonlinear output regulation with adaptive internalmodel

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     

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 disturbance rejection for nonlinear lower triangular systems with iISS inverse dynamics and uncertain exosystem

This paper concerns about the global disturbance rejection problem for uncertain nonlinear lower triangular systems with integral input‐to‐state stable (iISS) inverse dynamics and an uncertain exosystem. The main challenges addressed in this paper include uncertain exosystem, unknown control direction, iISS inverse dynamics, and complex structure of lower triangular systems. Because of the presence of both uncertain exosystem and unknown control direction, simply combining the existing techniques for each of these challenges cannot solve the proposed problem. In fact, to handle the current case, appropriate new update laws for the estimators of the uncertain parameters are required, such that the estimators can be successfully integrated with the internal model principle. Furthermore, the changing supply function technique for iISS systems is utilized to deal with the iISS inverse dynamics. With the proposed controller, the closed‐loop system is globally asymptotically stable, and the disturbance is globally rejected. Two simulation examples are finally presented to show the effectiveness of the proposed control scheme and the practical relevance of our work. Copyright © 2016 John Wiley & Sons, Ltd.     

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

This 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.     

Cooperative global output regulation of heterogeneous second-order nonlinear uncertain multi-agent systems

In this paper, we study the cooperative global output regulation problem for a class of heterogeneous second order nonlinear uncertain multi-agent systems. We first introduce a type of distributed internal model that converts the cooperative global output regulation problem into the global robust stabilization problem of the so-called augmented multi-agent system. Then we further globally stabilize this augmented multi-agent system via a distributed state feedback control law, thus leading to the solution of the original problem. A special case of our result leads to the solution of the global leader-following consensus problem for the second order nonlinear multi-agent systems without satisfying the global Lipschitz condition.     

Robust output regulation with nonlinear exosystems

For over a decade, the solvability of the nonlinear robust output regulation problem relies on the assumption that the exosystem is linear and neutrally stable. Thus, the only exogenous signal that can be accommodated by the existing theory is a combination of finitely many step functions and sinusoidal functions. In this paper, we will show that it is possible to find controllers that can admit exogenous signals produced by nonlinear exosystems. An example with the well known van der Pol oscillator as the exosystem is given to illustrate our approach.     

A result on output regulation of lower triangular systems with unknown high‐frequency gain sign

This paper concerns global robust output regulation of a class of nonlinear lower triangular systems with an unknown high‐frequency gain as well as an unknown exosystem. A novel class of internal model candidates is integrated with the output regulation framework. As a result, stabilization of the augmented system can be performed without parameter estimators. However, the new internal models bring challenges to the stabilization of the augmented system. To overcome these challenges, we propose a new recursive controller design procedure and use it to develop a Nussbaum‐gain‐based controller. This work extends the existing results on nonlinear output regulation of lower triangular systems to the case where both the high‐frequency gain sign and the exosystem are unknown. Copyright © 2017 John Wiley & Sons, Ltd.     

一类带不确定输入动态非线性系统的输出反馈鲁棒镇定

研究一类带不确定输入动态非线性系统的输出反馈鲁棒镇定问题.通过在高增益观测器引入新的设计参数,改进了通常的高增益反馈控制的设计方法.在输入动态满足零相对阶最小相位的假设下,基于非分离设计原则给出了动态输出反馈控制器的设计方法,所设计的控制器实现了对任意可允许不确定输入动态的全局鲁棒镇定.     

Global adaptive output-feedback control of nonlinear systems. I.Linear parameterization

The problem of designing global adaptive output-feedback tracking controls for single-input single-output nonlinear systems which are linear with respect to the input and an unknown constant parameter vector is addressed. A class of systems which can be globally controlled by adaptive observer-based output-feedback compensators is identified by geometric coordinate-free conditions. The nonlinearities depend on the output only: growth conditions are not required. Each system in the class admits observers with linear error dynamics and is minimum phase, i.e., it has linear asymptotically stable zero dynamics. When the parameters are known, new sufficient conditions for global output-feedback tracking control are obtained as a special case. For linear systems the result recovers a well-known fundamental adaptive result. Three examples are discussed     

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

Hysteretic 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.     

Output regulation of time‐varying nonlinear systems

This paper considers the robust output regulation problem for time‐varying nonlinear systems with a time‐varying exosystem. A framework for converting the problem into a stabilization problem of an augmented system is established. The problem is solved for a class of time‐varying output feedback systems with a time‐varying exosystem. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Global robust output regulation for output feedback systems

The global robust output regulation problem for the class of nonlinear systems in output feedback form has been studied under the assumption that the solution of the regulator equations is polynomial. This assumption essentially requires these systems contain only polynomial nonlinearity and is due to the failure of finding a nonlinear internal model to account for more complex nonlinearities than polynomials. Recently, it was found that a nonlinear internal model can be constructed under some assumption much milder than the polynomial assumption. In this note, we will apply this type of internal model to solve the global robust output regulation problem for the class of nonlinear systems in output feedback form.     

Universal adaptive control of feedforward nonlinear systems with unknown input and state delays

This paper considers the problem of global asymptotic regulation via output feedback for a class of uncertain feedforward nonlinear systems with input and state delays, where the bounds of time delays are unknown. With the help of the high-gain scaling approach and the idea of universal adaptive control, we explicitly construct an adaptive output compensator with a novel positive dynamic gain which compensates simultaneously the unknown delays and the output growth rate with unknown constant. Based on such output compensator, we reduce the conservatism of the restrictive conditions imposed on nonlinearities to generalise the existing results. By the Lyapunov–Krasovskii theorem, a delay-independent controller design scheme is proposed to guarantee that all the closed-loop signals are globally bounded while rendering the states of original system and the estimate states to globally asymptotically converge to zero. Finally, two illustrative examples are given to show the usefulness of the proposed design method.