非线性系统变结构观测器

本文研究了非线性系统的变结构观测器，分别讨论了干扰满足及不满足匹配条件下观测器的鲁棒性，证明了观测器的构造误差是一致最终有界的。     

一类不确定奇异摄动系统的鲁棒控制

本文研究了一类不确定奇异摄动系统，给出了亲折鲁棒控制器的设计方法，仿真结果表明，对这里研究的系统类型，本文所给控制具有更好的抗干扰能力。     

基于有限时间输出反馈的线性扩张状态观测器

为快速、准确地观测系统中的未知扰动及状态, 提出一种有限时间线性扩张状态观测器(Finite-time linear extended state observer, FT-LESO), 它具有期望的收敛性能且结构简单、易于设计. 假设系统的状态无法量测, 观测器设计问题转化为扰动下的输出反馈控制问题. 针对该问题, 提出一种扰动下的有限时间线性输出反馈控制方法, 得到控制器参数与闭环系统状态向量2-范数间的解析关系. 在此基础上, 提出有限时间线性扩张状态观测器, 得到观测器参数与观测误差收敛速度及稳态观测误差间的解析关系, 给出一充分条件保证观测误差有限时间有界、且能以不低于指数收敛的速度收敛到给定范围内, 为观测器参数设计提供理论依据. 通过数值仿真验证提出的观测器, 仿真结果与理论分析相符, 提出的观测器是有效的.     

On invariant sets and closed‐loop boundedness of Lure‐type nonlinear systems by LPV‐embedding

We address the problem of achieving trajectory boundedness and computing ultimate bounds and invariant sets for Lure‐type nonlinear systems with a sector‐bounded nonlinearity. Our first contribution is to compare two systematic methods to compute invariant sets for Lure systems. In the first method, a linear‐like bound is considered for the nonlinearity, and this bound is used to compute an invariant set by regarding the nonlinear system as a linear system with a nonlinear perturbation. In the second method, the sector‐bounded nonlinearity is treated as a time‐varying parameterised linear function with bounded parameter variations, and then invariant sets are computed by embedding the nonlinear system into a convex polytopic linear parameter varying (LPV) system. We show that under some conditions on the system matrices, these approaches give identical invariant sets, the LPV‐embedding method being less conservative in the general case. The second contribution of the paper is to characterise a class of Lure systems, for which an appropriately designed linear state feedback achieves bounded trajectories of the closed‐loop nonlinear system and allows for the computation of an invariant set via a simple, closed‐form expression. The third contribution is to show that, for disturbances that are ‘aligned’ with the control input, arbitrarily small ultimate bounds on the system states can be achieved by assigning the eigenvalues of the linear part of the system with ‘large enough’ negative real part. We illustrate the results via examples of a pendulum system, a Josephson junction circuit and the well‐known Chua circuit. Copyright © 2015 John Wiley & Sons, Ltd.     

On dynamic output feedback robust MPC for constrained quasi-LPV systems

This paper considers the dynamic output feedback robust model predictive control (MPC) of a quasi-linear parameter varying (quasi-LPV) system with bounded noise. In our previous works, for the unknown true state, either its ellipsoidal bounds or its polyhedral bounds were solely applied in the main optimisation problem. The recursive feasibility of the main optimisation problem was guaranteed by a simple refreshment of the ellipsoidal bound, but might be lost by applying the polyhedral bounds. This paper shows how and to what extent the recursive feasibility can be restored when the polyhedral bounds are still utilised. First, we propose a new approach which, at each sampling time, utilises either the ellipsoidal bound or the polyhedral bound in the main optimisation problem, the latter being used if and only if it is contained in the former. Then, we show the sufficient conditions under which the approaches based on polyhedral bounds preserve the property of recursive feasibility. A numerical example is given to illustrate the effectiveness of the controller.     

Integrated design of a linear/neuro-adaptive controller in the presence of norm-bounded uncertainties

Adaptive neural controllers are often criticised for the lack of clear and easy design methodologies that relate adaptive neural network (NN) design parameters to performance requirements. This study proposes a methodology for the design of an integrated linear-adaptive model reference controller that guarantees component-wise boundedness of the tracking error within an a priori specified compact domain. The approach is based on the design of a robust invariant ellipsoidal set where both the NN reconstruction error and the neuro-adaptive control are considered as bounded persistent uncertainties. We show that all the performance and control requirements for the closed-loop system can be expressed as linear matrix inequality constraints. This brings the advantage that feasibility and optimal design parameters can be effectively computed while solving a linear optimisation problem. An advantage of the method is that it allows a systematic and quantitative evaluation of the interplay between the design parameters and their impact on the requirements. This produces an integrated linear/neuro-adaptive performance-oriented design methodology. A numerical example is used to illustrate the approach.     

Stabilising feedback control schemes of dynamical systems with completely unknown saturated inputs: an adaptive design method

The objective of this paper is mainly to present a simple design method to synthesise the stabilising feedback control schemes for dynamical systems with input saturations. In this paper, such a simple design method, called an adaptive design method, is presented so that (i) the presented design method is easy to understand for the system designers; (ii) it is not necessary to know any information on the saturated input nonlinearities; and (iii) the resulting control schemes are simple and easy to implement in practical control problems. Here, a linear dynamical system with any unknown saturated input nonlinearities is used to describe this method. For such dynamical systems, by making use of the presented design method, the resulting feedback control schemes consist of a conventional optimal control law and an adaptive control gain, and the resulting closed-loop control dynamical systems are globally stable. By combining the presented adaptive design method with other control ones, a number of interesting results can be expected for a rather large class of dynamical systems with saturation in the actuators. Finally, some illustrative numerical examples are provided to demonstrate the validity of the presented adaptive design method.     

非线性多变量零阶接近有界系统的多模型自适应控制

针对一类多变量非线性离散时间系统,提出一种新的基于神经网络的多模型自适应控制方法.为了将非线性系统的高阶非线性项的限制条件放宽到零阶接近有界,该方法引入了一种新的非线性模型.该模型在传统线性回归模型基础上增加了非线性补偿项,使模型的估计误差有界.一个神经网络模型与非线性模型同时被用来对系统进行辨识.基于性能指标的切换机构选择性能较好的模型对应的控制器 对系统进行控制. 理论分析证明了零阶接近有界多模型自适应控制系统的有界输 入和有界输出稳定性. 仿真实验说明了提出的多模型自适应控制方法的有效性.     

Robust adaptive control of nonlinearly parametrized multivariable systems with unmatched disturbances

A new robust adaptive control scheme is developed for nonlinearly parametrized multivariable systems in the presence of parameter uncertainties and unmatched disturbances. The developed control scheme employs a new integrated framework of a functional bounding technique for handling nonlinearly parametrized system dynamics, an adaptive parameter estimation algorithm for dealing with parameter uncertainties, a nonlinear feedback controller structure for stabilization of interconnected system states, and a robust adaptive control design for accommodating unmatched disturbances. It is proved that such a new robust adaptive control scheme is capable of ensuring the global boundedness and mean convergence of all closed‐loop system signals. A complete simulation study on an air vehicle system with nonlinear parametrization in the presence of an unmatched wind disturbance is conducted, and its results verify the effectiveness of the proposed robust adaptive control scheme.     

Event‐triggered approach for finite‐time state estimation of delayed complex dynamical networks with random parameters

This article emphasizes the finite‐time state estimation problem for delayed complex dynamical networks with random parameters. In order to reduce the amount of transmission process, an aperiodic sampled‐data event‐triggered mechanism is introduced to determine whether the measurement output should be released at certain time points which incorporate an appropriate triggering condition and sampling moments. Furthermore, a concept of finite‐time boundedness in the pth moment is proposed to access the performance of state estimator. The objective of this article is to design an event‐triggered state estimator to estimate the states of nodes such that, in the presence of time delays, uncertainties, and randomly changing coupling weights, the estimation error system is finite‐time bounded in the pth moment related to a given constant. Some sufficient conditions in form of linear matrix inequalities and algebraic inequalities are established to guarantee finite‐time boundedness. Finally, a numerical example is presented to show the effectiveness of the theoretical results.