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

Most 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.     

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.     

p‐Times differentiable unbounded functions for robust control of uncertain switched nonlinear systems with tracking constraints

This paper investigates the problem of robust controller design for output‐constrained and state‐constrained uncertain switched nonlinear systems. By using the idea of p‐times differentiable unbounded functions and the backstepping technique, a constructive method is proposed to design effective controllers such that the output of a class of uncertain switched nonlinear systems in lower triangular form can asymptotically track a constant reference signal without violation of the output tracking error constraint. Furthermore, the explored method is applied to the state‐constrained robust stabilization problem for a class of general uncertain switched nonlinear systems. Finally, a simulation example is provided to demonstrate the effectiveness of the developed results. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Robust stabilization of mimo nonlinear time-varying mismatched uncertain systems

This paper considers the problem of robust stabilization of multi-input-multi-output (MIMO) nonlinear systems in the presence of mismatched time-varying uncertainties. Combining the differential geometric feedback linearization with the deterministic approach, it derives two robust stabilizing controllers i.e. the high-gain feedback controller and the variable structure controller. These two controllers only require the knowledge of the nominal system and the bounds of the uncertainties. Therefore, they are more feasible to be implemented. Both controllers reduce the effects of arbitrarily large bounded mismatched uncertainties successfully to achieve uniform ultimate boundedness stabilization of the MIMO nonlinear timevarying uncertain systems.     

Adaptive control of feedback linearizable systems: a modelling error compensation approach

An adaptive output feedback controller for single input feedback linearizable systems is proposed. The output derivatives are estimated with a state high-gain observer, and the matched uncertainties are handled using a modelling error compensation method. Compared with existing adaptive methods, this approach avoids overparameterizations yielding an (n+1)-order compensator, where n is the system dimension. Semiglobal stability is proven with the aid of existing results on the stability of controlled nonlinear systems with high-gain state observation. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

Global output regulation of a class of lower triangular nonlinear systems with unknown control direction via output feedback

In this paper, we study the global output regulation problem of a class of lower triangular systems under measurement output feedback. A novel high-gain filter is proposed to estimate the unmeasured states of the systems. Furthermore, we integrate the robust stabilisation technique and Nussbaumgain technique to achieve asymptotic regulation when the control direction is unknown. The simulation results illustrate the effectiveness of the proposed method.     

Global output feedback regulation of uncertain nonlinear systems with unknown time delay

This paper investigates the problem of global output feedback regulation for a class of nonlinear systems with unknown time delay. It is also allowed to contain uncertain functions of all the states and input as long as the uncertainties satisfying certain bounded condition for the considered systems. In this paper, a constructive control technique has been proposed for controlling the systems. By using dynamic high-gain scaling approach and choosing an appropriate Lyapunov-Krasovskii functional, a delay-independent robust adaptive output feedback controller is constructed such that the states of the considered systems achieve global regulation. Two simulation examples are provided to demonstrate the effectiveness of the proposed design scheme.     

A note on stability, robustness and performance of output feedback nonlinear model predictive control

In recent years, nonlinear model predictive control (NMPC) schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in the framework of nonlinear predictive control. This paper combines stabilizing instantaneous state feedback NMPC schemes with high-gain observers to achieve output feedback stabilization. For a uniformly observable MIMO system class it is shown that the resulting closed loop is asymptotically stable. Furthermore, the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme can be recovered to any degree of accuracy for large enough observer gains, thus leading to semi-regional results. Additionally, it is shown that the output feedback controller is robust with respect to static sector bounded nonlinear input uncertainties.     

Adaptive regulation of uncertain nonlinear systems by output feedback: A universal control approach

The problem of global state regulation via output feedback is investigated for uncertain nonlinear systems. The class of uncertain systems under consideration is assumed to be dominated by a bounding system which is linear growth in the unmeasurable states but can be a polynomial function of the system output, with unknown growth rates. To achieve global state regulation in the presence of parametric uncertainty, we propose a non-identifier based output feedback control scheme by employing the idea of universal control integrated with the design of a linear high-gain observer, whose gains are composed of two components, both of them are not constant and need to be dynamically updated. In particular, we explicitly design a universal output feedback controller which globally regulates all the states of the uncertain system while maintaining global boundedness of the closed-loop system.     

Adaptive neural network control of nonlinear systems by state andoutput feedback

This paper presents a novel control method for a general class of nonlinear systems using neural networks (NNs). Firstly, under the conditions of the system output and its time derivatives being available for feedback, an adaptive state feedback NN controller is developed. When only the output is measurable, by using a high-gain observer to estimate the derivatives of the system output, an adaptive output feedback NN controller is proposed. The closed-loop system is proven to be semi-globally uniformly ultimately bounded (SGUUB). In addition, if the approximation accuracy of the neural networks is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussions.     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

Adaptive nonlinear output feedback tracking with a partialhigh-gain observer and backstepping

An adaptive output feedback controller for nonlinear systems with nonlinearities depending on the first r (1⩽r⩽n) derivatives of the output is proposed. The derivatives are estimated with a partial state high-gain observer, and the remaining states are handled using a backstepping method. Compared with methods based on full state high-gain observer, this approach improves robustness with respect to measurement noise and avoids overparametrization. Semiglobal tracking is proven under the assumption that the regressor is persistently exciting     

Robust state feedback synthesis for control of non-square multivariable nonlinear systems

In this paper, a robust nonlinear controller is designed in the Input/Output (I/O) linearization framework, for non-square multivariable nonlinear systems that have more inputs than outputs and are subject to parametric uncertainty. A nonlinear state feedback is synthesized that approximately linearizes the system in an I/O sense by solving a convex optimization problem online. A robust controller is designed for the linear uncertain subsystem using a multi-model H₂/H_∞ synthesis approach to ensure robust stability and performance of non-square multivariable, nonlinear systems. This methodology is illustrated via simulation of a regulation problem in a continuous stirred tank reactor.     

Adaptive output feedback control for a class of nonlinear systems with quantised input and output

This paper aims at addressing the problem of global adaptive stabilisation by output feedback for a class of nonlinear systems, in which both the input and output are logarithmically quantised. The nonlinear functions of the systems are not necessary to be completely known and contain time-varying parameters that belong to an unknown bounded set. Based on dynamic high-gain technique, a linear-like quantised controller computed from quantised output is constructed and a guideline is derived to select the parameters of the quantisers. It is proved that, with the proposed scheme, all the states of the system can be globally steered to the origin while keeping the other signals of the closed-loop system bounded.     

Multi‐parametric extremum seeking‐based iterative feedback gains tuning for nonlinear control

We study in this paper the problem of iterative feedback gains auto‐tuning for a class of nonlinear systems. For the class of input–output linearizable nonlinear systems with bounded additive uncertainties, we first design a nominal input–output linearization‐based robust controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model‐free multi‐parametric extremum seeking control to iteratively auto‐tune the feedback gains. We analyze the stability of the whole controller, that is, the robust nonlinear controller combined with the multi‐parametric extremum seeking model‐free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust decentralized direct adaptive output feedback fuzzy control for a class of large-sale nonaffine nonlinear systems

In the previous work of Huang et al., a decentralized direct adaptive fuzzy H_∞ tracking controller of large-scale nonaffine nonlinear systems is obtained predicated upon the assumption that the mismatching error dynamics stay squared integrable. In this note, we focus in the absence of the conservative assumption upon developing a robust decentralized direct adaptive output feedback fuzzy controller. By combination of a state observer, a fuzzy inference system and robust control technique, the previous controller design is modified and no a priori knowledge of bounds on lumped uncertainties is required. All the signals of the closed-loop large-scale system are proved to be uniformly ultimately bounded. The effectiveness of the developed scheme is demonstrated through the simulation results of interconnected inverted pendulums.