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。     

非线性系统降维观测器设计

对Lipschitz非线性系统降维观测器进行了讨论.首先考虑了降维观测器存在之条件, 然后给出了此条件下的降维观测器的具体设计方法,该设计方法基于与非线性函数的Lipschitz 常数有关的代数Riccati不等式的求解.最后,针对一个具体实际控制模型的仿真,验证了文中 所提出之方法的实用性.     

基于输入输出线性化方法的一类多输入多输出非线性系统的观测器设计

研究一类多输入多输出仿射非线性系统的状态观测器设计问题. 基于输入输出线性化方法提出了一类多输入多输出仿射非线性系统的状态观测器设计的新方法, 并给出保证状态估计误差渐近趋于零的充分条件. 算例表明了所得结果的有效性.     

Observer design for a class of multi-input multi-output nonlinear systems

In this article, the problem of state observer design for a class of multi-input multi-output nonlinear systems is considered. Via state transformation and the constructive use of a Lyapunov function, the new observer design approach is addressed by introducing a parameter ? in the observer. Some sufficient conditions are given which guarantee the estimation error to asymptotically converge to zero under adaptive conditions. An example is included to illustrate the method.     

基于优化方法的非线性观测器设计

本文提出了一种方法,将非线性系统观测器的误差收敛速度的确定和增益阵的设计统一 归结为一个非线性优化问题,并给出了这种方法的流体管线上的应用.     

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.     

一类分布参数系统辨识及其状态观测器设计

本文研究了一类非线性分布参数系统的模型辨识及其状态观测器的设计方法,为这类系统的研究提供了新的途径。将这种方法应用于沸腾炉空气埋管动态过程的研究时,其有效性得到证实。     

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.     

Online exact differentiation and notion of asymptotic algebraic observers

In recent years, the availability of computer-based methods has created a revival of interests in exploring algebraic methods in nonlinear context. This paper proposes a new approach to algebraic nonlinear observer design. After giving the notion of algebraic observability, and based on a novel algorithm of exact differentiation, the formulation of the nonlinear observer is realized via the construction of a set of linear time-varying differentiators. An example of a chemical reaction is given to show the effectiveness of our approach.     

Unknown input observer for state affine systems: A necessary and sufficient condition

The problem of designing an unknown input observer for linear systems and its application to fault detection is widely studied in the literature. For nonlinear systems, only subclasses of nonlinear systems and sufficient conditions have been stated. In this paper an unknown input observer design for state affine systems is considered. Based on the geometric approach, a necessary and sufficient condition is given for the existence of an unknown input observer.     

On Maximum Stability Margin Design of Nonlinear Uncertain Systems: Fuzzy Control Approach

This paper studies the maximum stability margin design for nonlinear uncertain systems using fuzzy control. First, the Takagi and Sugeno fuzzy model is employed to approximate a nonlinear uncertain system. Next, based on the fuzzy model, the maximum stability margin for a nonlinear uncertain system is studied to achieve as much tolerance of plant uncertainties as possible using a fuzzy control method. In the proposed fuzzy control method, the maximum stability margin design problem is parameterized in terms of a corresponding generalized eigenvalue problem (GEVP). For the case where state variables are unavailable, a fuzzy observer‐based control scheme is also proposed to deal with the maximum stability margin for nonlinear uncertain systems. Using a suboptimal approach, we characterize the maximum stability margin via fuzzy observer‐based control in terms of a linear matrix inequality problem (LMIP). The GEVP and LMIP can be solved very efficiently via convex optimization techniques. Simulation examples are given to illustrate the design procedure of the proposed method.     

Sliding mode control-based linear functional observers for discrete-time stochastic systems

Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method.     

Lipschitz非线性系统观测器设计新方法

考虑了非线性项满足Lipschitz条件的非线性系统观测器设计问题, 利用Lyapunov方法给出了新的判断观测误差稳定性的条件, 并由所给的条件通过求解线性矩阵不等式来设计观测器. 通过算例与其它方法进行的比较, 说明了所提方法的有效性.     

Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

This paper investigates the problem of state observer design for a class of nonlinear uncertain dynamical systems with interval time‐varying delay and the one‐sided Lipschitz condition. By constructing the novel Lyapunov–Krasovskii functional while utilizing the free‐weighting matrices approach, the one‐sided Lipschitz condition and the quadratic inner‐bounded condition, novel sufficient conditions, which guarantee the observer error converge asymptotically to zero, are established for a class of nonlinear dynamical systems with interval time‐varying delay in terms of the linear matrix inequalities. The computing method for observer gain matrix is given. Finally, two examples illustrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Global stabilization of a class of delay discrete-time nonlinear systems via state and output feedback

This paper deals with stabilization of a class of delay discrete-time nonlinear systems through state and output feedback. We provide an explicit bounded state feedback law as an extension of the Jurdjevic-Quinn method, from nonlinear theory, to this class of systems. Next, we present a useful and systematic approach to design an observer for the same class of systems. Then, we show how the global stabilization problem via dynamic output feedback can be solved by using the two previous results. Finally, numerical examples are given to illustrate the effectiveness of the proposed design method.     

A Robust Fault Detection Approach for Nonlinear Systems

In this paper, we study the robust fault detection problem of nonlinear systems. Based on the Lyapunov method, a robust fault detection approach for a general class of nonlinear systems is proposed. A nonlinear observer is first provided, and a sufficient condition is given to make the observer locally stable. Then, a practical algorithm is presented to facilitate the realization of the proposed observer for robust fault detection. Finally, a numerical example is provided to show the effectiveness of the proposed approach.     

Discrete-time nonlinear observer design using functional equations

The present research work proposes a new approach to the discrete-time nonlinear observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer, the proposed approach develops a nonlinear analogue. The formulation of the discrete-time nonlinear observer design problem is realized via a system of first-order linear nonhomogeneous functional equations, and a rather general set of necessary and sufficient conditions for solvability is derived using results from functional equations theory. The solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package.     

Magnetic sensor-based simultaneous state and parameter estimation using a nonlinear observer

This paper presents an observer design technique for a newly developed non-intrusive position estimation system based on magnetic sensors. Typically, the magnetic field of an object as a function of position needs to be represented by a highly nonlinear measurement equation. Previous results on observer design for nonlinear systems have mostly assumed that the measurement equation is linear, even if the process dynamics are nonlinear. Hence, a new nonlinear observer design method for a Wiener system composed of a linear process model together with a nonlinear measurement equation is developed in this paper. First, the design of a two degree-of-freedom nonlinear observer is proposed that relies on a Lure system representation of the observer error dynamics. To improve the performance in the presence of parametric uncertainty in the measurement model, the nonlinear observer is augmented to estimate both the state and unknown parameters simultaneously. A rigorous nonlinear observability analysis is also presented to show that a dual sensor configuration is a sufficient and necessary condition for simultaneous state and parameter estimation. Finally, the developed observer design technique is applied to non-intrusive position estimation of the piston inside a pneumatic cylinder. Experimental results show that both position and unknown parameters can be reliably estimated in this application.     

Nonlinear observer design using Lyapunov’s auxiliary theorem

The present work proposes a new approach to the nonlinear observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer theory, the proposed approach develops a nonlinear analogue. The formulation of the observer design problem is realized via a system of singular first-order linear PDEs, and a rather general set of necessary and sufficient conditions for solvability is derived by using Lyapunov’s auxiliary theorem. The solution to the above system of PDEs is locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package.