Nonlinear observer design for state and disturbance estimation

A new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed. The nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in [N. Kazantzis, C. Kravaris, Nonlinear observer design using Lyapunov's auxiliary theorem, Systems Control Lett. 34 (1998) 241; A.J. Krener, M. Xiao, Nonlinear observer design in the Siegel domain, SIAM J. Control Optim. 41 (2002) 932.] for state estimation purposes only. From a mathematical standpoint, the problem under consideration is addressed through a system of first-order singular PDEs for which a rather general set of solvability conditions is derived. A nonlinear observer is then designed with a state-dependent gain that is computed from the solution of the system of singular PDEs. Under the aforementioned conditions, both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor.     

Nonlinear vehicle side-slip estimation with friction adaptation

A nonlinear observer for estimation of the longitudinal velocity, lateral velocity, and yaw rate of a vehicle, designed for the purpose of vehicle side-slip estimation, is modified and extended in order to work for different road surface conditions. The observer relies on a road-tire friction model and is therefore sensitive to changes in the adhesion characteristics of the road surface. The friction model is parametrized with a single friction parameter, and an update law is designed. The adaptive observer is proven to be uniformly globally asymptotically stable and uniformly locally exponentially stable under a persistency-of-excitation condition and a set of technical assumptions, using results related to Matrosov's theorem. The observer is tested on recorded data from two test vehicles and shows good results on a range of road surfaces.     

非参数不确定性非线性系统的自适应观测器设计

本文考虑一类不确定非线性系统的自适应观测器设计问题.系统的不确定性不能参数化,这类非线性系统的观测器无法用传统方法设计.首先用神经网络对系统的不确定性进行逼近,然后利用神经网络的基函数向量对系统进行滤波变换,再由此构造自适应观测器.给出了观测误差估计.本文结果表明适当选定神经网络的逼近精度和调整观测器的设计参数可使观测误差任意地小.     

逆系统方法中非线性系统状态观测器的应用

将Lipschitz非线性系统状态观测器设计方法应用于非线性系统的逆系统方法设计中,解决了在利用逆系统方法实现非线性系统反馈线性化的过程中由于系统状态的不可知,而使系统不能满足反馈补偿的问题。针对以往的Lipschitz非线性系统状态观测器设计方法中通过Riccati方程对增益矩阵的求取过程比较繁琐的问题,着重讨论了采用线性矩阵不等式来改进增益矩阵的求取方法,利用Matlab中的LMI工具箱对其进行求取,计算简单,并给出了证明。最后通过实例仿真,验证了方法的有效性。     

Nonlinear state estimation with robust convergence

The problem of designing a dynamic measurement processor for the on-line estimation of the state of a multi-input multi-output nonlinear plant is addressed. The plant can be either observable or detectable, encompassing a broad range of cases in process systems engineering. On the basis of the structure of a suitable property of robust nonlinear estimability, an estimator is built and its convergence studied, yielding sufficient conditions for robust convergence, a systematic construction, and a tractable gain tuning procedure. The estimability property has a verifiable test, and the execution of the tuning procedure, as well as the interpretation of its convergence features can be achieved within a conventional control framework for linear single-input controllers or single-output filters. The estimation of a continuous polymer reactor is considered as an application example.     

Set-Valued Observers for Control Systems

We extend the usual definition of observers with known inputs to nonlinear dynamic systems that are not completely observable. To achieve this, we use set-valued analysis and invariance tools. In particular, the set of indistinguishable states that plays a key role in the problem is characterized in terms of an invariance kernel. A numerical example illustrates the results.     

一类不确定非线性系统的鲁棒自适应控制

针对一类输入带有一定的不确定性的非线性系统 ,设计了一种鲁棒自适应控制器。该控制器作用与系统 ,能保证闭环系统信号的全局有界性 ,又能使闭环系统输出任意小。     

Nonlinear state estimation for rigid-body motion with low-pass sensors

In this paper, we consider the state estimation problem for the nonlinear kinematic equations of a rigid body observed under low-pass sensors. The problem is motivated from a walking robot application where inclinometers and gyros are the sensors used. We show that a non-local high gain observer exists for the nonlinear rigid-body kinematic equations and that it under a small angle assumption is possible to use one inclinometer only to estimate two angles.     

Robust Analytical Redundancy Relations for Fault Diagnosis In Nonlinear Systems

The problem of robust analytical redundancy relations design for fault diagnosis in nonlinear systems is investigated. An approach is proposed to solve this problem through an extension of the system state‐space by means of constant (or slow varying) unknown parameters, followed by designing analytical redundancy relations that are insensitive both to state variables and unknown parameters. To make the design practicable, some problems related to nonlinear transformation of the extended system model into observable one are considered. The quasi‐linear computational form for robust analytical redundancy relations is described. Fault detectability and distinguishability conditions are formulated, and a recommendation for choosing the size of the moving time window is made. The results are demonstrated through an example involving an SISO nonlinear model of an underwater vehicle.     

Nonlinear observers comprising high-gain observers and extended Kalman filters

A full order observer is designed for a class of nonlinear systems that can potentially admit unstable zero dynamics. The structure of the observer is composed of an Extended High Gain Observer (EHGO), for the estimation of the derivatives of the output, augmented with an Extended Kalman Filter (EKF) for the estimation of the states of the internal dynamics. The EHGO is also utilized to estimate a signal that is used as a virtual output to an auxiliary system comprised of the internal dynamics. In the special case of the system being linear in the states of the internal dynamics, we achieve semi-global asymptotic convergence of the estimation error. We demonstrate the efficacy of the observer in two examples; namely, a synchronous generator connected to an infinite bus and a Translating Oscillator with a Rotating Actuator (TORA) system.     

不确定非线性系统的鲁棒输出反馈自适应控制

针对一类具有一般不确定性的非线性系统,设计一种新的鲁棒输出反馈自适应控制器。在较弱条件下,该控制器不仅能保证闭环系统全局稳定,且能使跟踪误差以指数速度收敛到零的小领域内。仿真结果验证了所给控制方案的有效性。     

可补的非时变非线性系统的自适应控制算法

本文对确定的非线性提出了非时变非线性可补性的概念，并应用于自适应控制器算法中，以实现补偿非线性的目的。系统性能逼近于线性系统，并且保证在确定和随机的情况下，控制算法均具有大范围渐近稳定性。     

一类非线性系统的自适应模糊控制

针对一类非线性系统,利用模糊推理系统对非线性函数的逼近能力,导出基于Ｌｙａｐｕｎｏｖ稳定性理论的自适应控制器,不但能解决这类非线性系统的跟踪问题,而且可保证闭环系统的稳定性。仿真结果表明这一算法的有效性。     

Adaptive-Predictive Control of a Class of SISO Nonlinear Systems

In this paper, an adaptive-predictive control algorithm is developed for a class of SISO nonlinear discrete-time systems based on a generalized predictive control (GPC) approach. The design is model-free, based directly on pseudo-partial-derivatives derived on-line from the input and output information of the system using a recursive least squares type of identification algorithm. The proposed control is especially useful for nonlinear systems with vaguely known dynamics. Robust stability of the closed-loop system is analyzed and proven in the paper. Simulation and real-time application examples are provided for real nonlinear systems which are known to be difficult to model and control.