Robust MIMO disturbance observer analysis and design with application to active car steering

A multi‐input–multi‐output extension of the well‐known two control degrees‐of‐freedom disturbance observer architecture that decouples the problem into single‐input–single‐output disturbance observer loops is presented in this paper. Robust design based on mapping D‐stability and the frequency domain specifications of weighted sensitivity minimization and phase margin bound to a chosen controller parameter space is presented as a part of the proposed design approach. The effect of the choice of disturbance observer Q filter on performance is explained with a numerical example. This is followed by the use of structured singular values in the robustness analysis of disturbance observer controlled systems subject to structured, real parametric and mixed uncertainty in the plant. A design and simulation study based on a four wheel active car steering control example is used to illustrate the methods presented in the paper. Copyright © 2009 John Wiley & Sons, Ltd.     

An algorithm for the structural analysis of state space: synthesis of nonlinear observers

The problem addressed is the linearization of multi‐input multi‐output (MIMO) nonlinear systems by a generalized state coordinates transformation and generalized input–output injection, in order to design an observer. This observer will have linear error dynamics. The goal is to bring together two observers design approaches: a structural one and a numerical one. Necessary and sufficient conditions for the existence of a linearizing generalized state transformation are obtained by an algebraic way and without computing the input–output differential equations. The main result tests integrability conditions of differential one‐forms derived from the state space representation and is applicable to a large subclass of nonlinear systems. Copyright © 2001 John Wiley & Sons, Ltd.     

Nonlinear output‐feedback control of torsional vibrations in drilling systems

This paper considers the design of a nonlinear observer‐based output‐feedback controller for oil‐field drill‐string systems aiming to eliminate (torsional) stick–slip oscillations. Such vibrations decrease the performance and reliability of drilling systems and can ultimately lead to system failure. Current industrial controllers regularly fail to eliminate stick–slip vibrations under increasingly challenging operating conditions caused by the tendency towards drilling deeper and inclined wells, where multiple vibrational modes play a role in the occurrence of stick–slip vibrations. As a basis for controller synthesis, a multi‐modal model of the torsional drill‐string dynamics for a real rig is employed, and a bit–rock interaction model with severe velocity‐weakening effect is used. The proposed model‐based controller design methodology consists of a state‐feedback controller and a (nonlinear) observer. Conditions, guaranteeing asymptotic stability of the desired equilibrium, corresponding to nominal drilling operation, are presented. The proposed control strategy has a significant advantage over existing vibration control systems as it can effectively cope with multiple modes of torsional vibration. Case study results using the proposed control strategy show that stick–slip oscillations can indeed be eliminated in realistic drilling scenarios in which industrial controllers fail to do so. Moreover, key robustness aspects of the control system involving the robustness against uncertainties in the bit–rock interaction and changing operational conditions are evidenced. Copyright © 2017 John Wiley & Sons, Ltd.     

Fixed‐Time Synchronization of a Class of Second‐Order Nonlinear Leader‐Following Multi‐Agent Systems

The fixed‐time synchronization problem for a class of second‐order nonlinear multi‐agent systems with a leader‐follower architecture is investigated in this paper. To achieve the fixed‐time tracking task, the design procedure is divided into two steps. At the first step, a distributed fixed‐time observer is designed for each agent to estimate the leader's state in a fixed time. Then, at the second step, based on the technique of adding a power integrator, a fixed‐time tracking controller for each agent is proposed such that the estimate leader's state can be tracked in a fixed time. Finally, an observer‐based fixed‐time controller is developed such that the leader can be tracked by all the followers in a fixed time, which can be predetermined. Simulations are presented to verify the effectiveness of the proposed approach.     

Composite stratified anti‐disturbance control for a class of MIMO discrete‐time systems with nonlinearity

Anti‐disturbance control and estimation problem are investigated for nonlinear system subject to multi‐source disturbances. The disturbances classified model is proposed based on the error and noise analysis of priori knowledge. The disturbance observers are constructed separately from the controller design to estimate the disturbance with partial known information. By integrating disturbance‐observer‐based control with discrete‐time sliding‐mode control (DSMC), a novel type of composite stratified anti‐disturbance control scheme is presented for a class of multiple‐input–multiple‐output discrete‐time systems with known and unknown nonlinear dynamics, respectively. Simulations for a flight control system are given to demonstrate the effectiveness of the results compared with the previous schemes. Copyright © 2011 John Wiley & Sons, Ltd.     

Transformation of Nonlinear MIMO Discrete‐Time Systems into the Extended Observer Form

The paper addresses the problem of transforming discrete‐time multi‐input multi‐output nonlinear state equations into the extended observer form, which, besides the inputs and outputs, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of the extended coordinate transformation are formulated in terms of differential one‐forms, associated with the input‐output equations, corresponding to the state equations. The difference between the single‐input single‐output and multi‐input multi‐output cases is described. The applicability of the conditions is illustrated by an example.     

非线性MIMO系统的降维状态观测器

研究一类多输入多输出（ＭＩＭＯ）非线性时变系统的降维状态观测器设计问题,提出了一种非线性降维状态观测器设计方案,并从理论上证明了状态观测误差的指数收敛性,其中设计的降维状态观测器具有收敛速度可调的特性,最后给出了数值算例,仿真结果表明了本文方法的有效性。     

Full‐Order and Reduced‐order Observer Design for a Class of Fractional‐order Nonlinear Systems

The paper is concerned with problem of the full‐order and reduced‐order observer design for a class of fractional‐order one‐sided Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full‐order observer error dynamic system is presented. Furthermore, the proposed design method was extended to reduced‐order observer design for fractional‐order nonlinear systems. All the stability conditions are obtained in terms of LMI, which are less conservative than some existing ones. Finally, a numerical example demonstrates the validity of this approach.     

Observer‐Based Consensus Tracking for Nonlinear Multi‐Agent Systems With Intermittent Communications

This paper addresses the observer‐based consensus tracking problem of multi‐agent systems with intermittent communications. The agent dynamics are modeled as general linear systems with Lipschitz nonlinearity. Under the assumption that each agent can intermittently share its relative output with neighbors, a class of an observer‐type protocol is proposed, and the consensus tracking problem can be converted further into the stability problem of the nonlinear switching systems. Using a combined tool from M matrix theory, switching theory and the averaging approach, a multi‐step algorithm is presented to construct the observer gains and protocol parameters, and the sufficient criteria established not only can ensure the state estimates convergence to the real values but also can guarantee the follower states synchronize to those of the leader. The obtained results reveal the relationships among the communication rate, the convergence rate, and the dwell time of switching topologies. Finally, the theoretical findings are validated by a numerical example.     

Nonlinear H∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay

This paper investigates the H_∞ observer design problem for a class of nonlinear discrete‐time singular systems with time‐varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one‐sided Lipschitz condition and quadratically inner‐bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality–based approach for the nonlinear observer design is proposed. The resulting nonlinear H_∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance γ. The synthesis condition of H_∞ observer design for nonlinear discrete‐time singular systems without time delays is also presented. The design is first addressed for one‐sided Lipschitz discrete‐time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.     

H ∞ observer design for uncertain nonlinear discrete‐time systems with time‐delay: LMI optimization approach

We present a robust H _∞ observer for a class of nonlinear discrete‐time systems. The class under study includes an unknown time‐varying delay limited by upper and lower bounds, as well as time‐varying parametric uncertainties. We design a nonlinear H _∞ observer, by using the upper and lower bounds of the delay, that guarantees asymptotic stability of the estimation error dynamics and is also robust against time‐varying parametric uncertainties. The described problem is converted to a standard optimization problem, which can be solved in terms of linear matrix inequalities (LMIs). Then, we expand the problem to a multi‐objective optimization problem in which the maximum admissible Lipschitz constant and the minimum disturbance attenuation level are the problem objectives. Finally, the proposed observer is illustrated with two examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust control approach for input–output linearizable nonlinear systems using high‐gain disturbance observer

This paper addresses a robust control approach for a class of input–output linearizable nonlinear systems with uncertainties and modeling errors considered as unknown inputs. As known, the exact feedback linearization method can be applied to control input–output linearizable nonlinear systems, if all the states are available and modeling errors are negligible. The mentioned two prerequisites denote important problems in the field of classical nonlinear control. The solution approach developed in this contribution is using disturbance rejection by applying feedback of the uncertainties and modeling errors estimated by a specific high‐gain disturbance observer as unknown inputs. At the same time, the nonmeasured states can be calculated from the estimation of the transformed system states. The feasibility and conditions for the application of the approach on mechanical systems are discussed. A nonlinear multi‐input multi‐output mechanical system is taken as a simulation example to illustrate the application. The results show the robustness of the control design and plausible estimations of full‐rank disturbances.Copyright © 2012 John Wiley & Sons, Ltd.     

Observer‐based leader‐following consensus of uncertain nonlinear multi‐agent systems

In this paper, the leader‐following consensus problem of uncertain high‐order nonlinear multi‐agent systems on directed graph with a fixed topology is studied, where it is assumed that the relative states of a follower and its neighbors are immeasurable and only the relative outputs are available. Nonlinear adaptive observers are firstly proposed for each follower to estimate the states of it and its neighbors, and an observer‐based distributed adaptive control scheme is constructed to guarantee that all followers asymptotically synchronize to a leader with tracking errors being semi‐globally uniform ultimate bounded. On the basis of algebraic graph theory and Lyapunov theory, the closed‐loop system stability analysis is conducted. Finally, numerical simulations are presented to illustrate the effectiveness and potential of the proposed new design techniques. Copyright © 2017 John Wiley & Sons, Ltd.     

Nonlinear robust observer design using an invariant manifold approach

This paper presents a method to design a reduced order observer using an invariant manifold approach. The main advantages of this method are that it enables a systematic design approach, and (unlike most nonlinear observer design methods), it can be generalized over a larger class of nonlinear systems. The method uses specific mapping functions in a way that minimizes the error dynamics close to zero. Another important aspect is the robustness property which is due to the manifold attractivity: an important feature when an observer is used in a closed loop control system. A two degree-of-freedom system is used as an example. The observer design is validated using numerical simulation. Then experimental validation is carried out using hardware-in-the-loop testing. The proposed observer is then compared with a very well known nonlinear observer based on the off-line solution of the Riccati equation for systems with Lipschitz type nonlinearity. In all cases, the performance of the proposed observer is shown to be very high.     

Adaptive discrete neural observer design for nonlinear systems with unknown time‐delay

This paper focuses on the adaptive observer design for nonlinear discrete‐time MIMO systems with unknown time‐delay and nonlinear dynamics. The delayed states involved in the system are arguments of a nonlinear function and only the estimated delay is utilized. By constructing an appropriate Lyapunov–Krasovskii function, the delay estimation error is considered in the observer parameter design. The proposed method is then extended to the system with a nonlinear output measurement equation and the delayed dynamics. With the help of a high‐order neural network (HONN), the requirement for a precise system model, the linear‐in‐the‐parameters (LIP) assumption of the delayed states, the Lipschitz or norm‐boundedness assumption of unknown nonlinearities are removed. A novel converse Lyapunov technical lemma is also developed and used to prove the uniform ultimate boundedness of the proposed observer. The effectiveness of the proposed results is verified by simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

Fault estimation observer design for a class of nonlinear multiagent systems in finite‐frequency domain

This paper focuses on the fault estimation observer design problem in the finite‐frequency domain for a class of Lipschitz nonlinear multiagent systems subject to system components or actuator fault. First, the relative output estimation error is defined based on the directed communication topology of multiagent systems, and an observer error system is obtained by connecting adaptive fault estimation observer and the state equation of the original system. Then, sufficient conditions for the existence of the fault estimation observer are obtained by using a generalized Kalman‐Yakubovich‐Popov lemma and properties of the matrix trace, which guarantee that the observer error system satisfies robustness performance in the finite‐frequency domain. Meanwhile, the pole assignment method is used to configure the poles of the observer error system in a certain area. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.     

非线性系统观测器的计算机代数分析与设计方法*

本文介绍了控制系统非线性观测器的分析和设计方法，根据扩展Ｌｕｅｎｂｅｒｇｅｒ观测器设计过程中放大系数向量的计算公式，用计算机代数方法进行非线性观测器设计，本文给出了用Ｍａｔｈｅｍａｔｉｃａ符号编程语言实现的算法软件包，并使用该软件包对一个具体实例进行了分析和设计。     

基于神经网络的非线性观测器及在线故障检测

提出一种基于径向基函数神经网络的非线性观测器的设计方法，并将其应用于复杂非线性系统的故障检测与隔离。该方法将神经网络离线学习与在线学习相结合，获取系统输入输出的非线性动力学特性，进而实时计算出残差并进行逻辑判决，可显著提高故障检测的快速性、鲁棒性及准确率。最后，针对非线性同步交流电机的结构损伤故障进行了仿真，结果表明本文所提方法的有效性。     

Composite hierarchical anti‐disturbance control for nonlinear systems with DOBC and fuzzy control

Anti‐disturbance control and estimation problem is introduced for a class of nonlinear system subject to disturbances. The adaptive disturbance observers are constructed separately from the controller design to estimate the disturbance with partial known information. By integrating disturbance‐observer‐based control with fuzzy control, a novel type of composite hierarchical anti‐disturbance control scheme is presented for a class of nonlinear system with unknown nonlinear dynamics. Simulations for a flight control system are given to demonstrate the effectiveness of the results compared with the previous schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

Distributed Observer‐based Stabilization of Nonlinear Multi‐agent Systems with Sampled‐data Control

In this paper, the distributed observer‐based stabilization problem of multi‐agent systems under a directed graph is investigated. Distributed observer‐based control protocol with sampled‐data information is proposed. The dynamics of each agent contain a nonlinear part, which is supposed to be general Lipschitz. In order to stabilize the states of the whole network, all the nodes utilize the relative output estimation error at sampling instants and only a small fraction of nodes use the absolute output estimation error additionally. By virtue of the input‐to‐state stability (ISS) property and the Lyapunov stability theory, an algorithm to design the control gain matrix, observer gain matrix, coupling strength as well as the allowable sampling period are derived. The conditions are in the form of LMIs and algebraic inequality, which are simple in form and easy to verify. Some further discussions about the solvability of obtained linear matrix inequalities (LMIs) are also given. Lastly, an example is simulated to further validate the obtained results.