Constructive algorithm for dynamic observer error linearization via integrators: single output case

Dynamic observer error linearization which has been introduced recently is a new framework for observer design. Although this approach unifies several existing results on the problem and extends the class of systems that can be transformed into an observable linear system with an injection term of known signals, constructive algorithms to check the applicability are not available yet. In this paper, a constructive algorithm is proposed to solve the problem under some restrictions on the system structure and on the auxiliary dynamics introduced in the problem. The algorithm is constructive in the sense that the components of the transformation can be obtained step‐by‐step. Copyright © 2006 John Wiley & Sons, Ltd.     

Dynamic observer error linearization

In this paper, a new framework of observer error linearization problem is proposed. The main idea of our approach is twofold. The one is to introduce an auxiliary dynamics whose input is the system output, and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics. It is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output. It is also shown that whenever an n dimensional system is immersible into an n+d dimensional linear system up to an output injection, then it can be also dynamically observer error linearizable in our sense with a d dimensional auxiliary dynamics. Moreover, we show that the converse is not true by providing a counterexample, which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method.     

Observer design for nonlinear discrete‐time systems: Immersion and dynamic observer error linearization techniques

This paper focuses on the observer design for nonlinear discrete‐time systems by means of nonlinear observer canonical form. At first, sufficient and necessary conditions are obtained for a class of autonomous nonlinear discrete‐time systems to be immersible into higher dimensional observer canonical form. Then a method called dynamic observer error linearization is developed. By introducing a dynamic auxiliary system, the augmented system is shown to be locally equivalent to the generalized observer form, whose nonlinear terms contain auxiliary states and output of the system. A constructive algorithm is also provided to obtain the state coordinate transformation. These results are an extension of their counterparts of nonlinear continuous‐time systems to nonlinear discrete‐time systems (Syst. Control Lett. 1986; 7 :133–142; SIAM. J. Control Optim. 2003; 41 :1756–1778; Int. J. Control 2004; 77 :723–734; Automatica 2006; 42 :321–328; IEEE Trans. Automat. Control 2007; 52 :83–88; IEEE Trans. Automat. Control 2004; 49 :1746–1750; Automatica 2006; 42 :2195–2200; IEEE Trans. Automat. Control 1996; 41 :598–603; Syst. Control Lett. 1997; 31 :115–128). Copyright © 2009 John Wiley & Sons, Ltd.     

Gap-metric-based robustness analysis of nonlinear systems with full and partial feedback linearisation

This paper uses gap metric analysis to derive robustness and performance margins for feedback linearising controllers. Distinct from previous robustness analysis, it incorporates the case of output unstructured uncertainties, and is shown to yield general stability conditions which can be applied to both stable and unstable plants. It then expands on existing feedback linearising control schemes by introducing a more general robust feedback linearising control design which classifies the system nonlinearity into stable and unstable components and cancels only the unstable plant nonlinearities. This is done in order to preserve the stabilising action of the inherently stabilising nonlinearities. Robustness and performance margins are derived for this control scheme, and are expressed in terms of bounds on the plant nonlinearities and the accuracy of the cancellation of the unstable plant nonlinearity by the controller. Case studies then confirm reduced conservatism compared with standard methods.     

一类非线性系统故障诊断观测器设计

大多故障诊断算法集中在线性系统方面, 在非线性方面只考虑故障对状态起线性影响的那些系统. 本文根据系统的非线性本质特性, 提出了基于模型的一类非线性系统故障诊断观测器设计方法. 应用系统的(B;K; á)实现精确分解后的系统模型, 对它们的状态故障起非线性的影响. 采用干扰解耦技术,获得的残差对未知扰动有很好的鲁棒性. 在Lyapunov意义下, 验证了算法的稳定性. 仿真验证表明, 所提算法具有快速收敛性, 对一类非线性系统诊断效果较好.     

Reduced-order hybrid interval observer for verified state estimation of an induction machine

In this paper, a reduced-order hybrid interval observer for the verified state estimation of an induction machine is designed. The main advantage of this approach over existing ones is the provision of guarantees regarding the estimated states. These guarantees are of particular interest in the case of safety critical systems. In contrast to existing approaches for reduced-order interval observers, the developed observer is applicable to linear time-variant systems. So far, only reduced-order interval observers for time-delay systems have been studied extensively (Perruquetti & Richard, 2013). The presented approach is based on a hybridization to bound the real system states between lower and upper bounds. One further novelty is the consideration of a time-variant observer gain whose influence on the estimation is bounded by an interval and included into the observer structure. Finally, it is shown by an experiment that this approach provides a real-time capable way to bound the unmeasurable states of an induction machine.     

基于动态递归神经网络的一类非线性不确定系统的自适应观测器

针对一类非线性不确定系统，当其状态不可测时，在基于动态递归神经网络的观测器中，对用来抑制不确定性、保证观测器鲁棒观测的控制项进行恰当的设计。仿真结果证实了该设计的有效性。     

Non-linear observer design by approximate error linearization

For a given non-linear system, an observer that provides exactly linear error dynamics can be computed by solving the so-called generalized characteristic equation (GCE). Unfortunately, the existence of a solution to the GCE is not a generic property. For unforced, scalar-output systems, we show how spline functions may be used to construct approximate solutions that minimize a norm of the non-linear terms obstructing linearization of the error dynamics. The resulting error dynamics are shown to be locally exponentially stable. A numerical example illustrates the design and performance of the observer.     

Feedback linearisation of a heat exchanger

A discrete-time nonlinear heat exchanger model is linearised via the feedback linearisation technique. Explicit necessary and sufficient conditions for feedback linearisation of the heat exchanger model in terms of parameters directly related to heat transfer parameters are derived. Some useful results relating to independence of distributions with respect to input are also derived in the process.     

Adaptive fuzzy controller design with observer for a class of uncertain nonlinear MIMO systems

In this paper, an adaptive fuzzy control approach is proposed to stabilize a class of uncertain nonlinear MIMO systems with the unmeasured states and the external disturbances. The fuzzy logic systems are used to approximate the unknown functions. Because it does not required to assume that the system states are measurable, it needs to design an observer to estimate the system unmeasured states. The considered MIMO systems are more general, i.e. they consist of N subsystems and each subsystem is in the non‐affine form. The stability of the closed‐loop system is verified by using Lyapunov analysis method. Two simulation examples are utilized to verify the effectiveness of the proposed approach. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

State observer based dynamic fuzzy logic system for a class of SISO nonlinear systems

This paper presents an observer based dynamic fuzzy logic system (DFLS) scheme for a class of unknown single-input single-output (SISO) nonlinear dynamic systems with external disturbances. The proposed approach does not need the availability of the state variables. Within this scheme, the DFLS is employed to identify the unknown nonlinear dynamic system. The control law and parameter adaptation laws of the DFLS are derived based on Lyapunov synthesis approach. The control law is robustfied in H _∞ sense to attenuate external disturbance, model uncertainties, and fuzzy approximation errors. It is shown that under appropriate assumptions, it guarantees the boundedness of all the signals in the closed-loop system and the asymptotic convergence to zero of tracking errors. The proposed method is applied to an inverted pendulum system to verify the effectiveness of the proposed algorithms.     

Adaptive dynamic surface control using disturbance observer for nonlinear systems with input saturation and output constraints

An adaptive dynamic surface control (DSC) approach using fuzzy approximation and nonlinear disturbance observer (NDO) for uncertain nonlinear systems in the presence of input saturation, output constraint and unknown external disturbances is proposed in this paper. The issue of input saturation is addressed by introducing a lower bound assumption on the approximation function of saturation. The output constraint is handled by introducing an appropriate barried Lyapunov function. The nonlinear disturbance observer (NDO) is employed to estimate the unknown unmatched disturbances. It is manifested that the ultimately bounded convergence of all the variables in the closed-loop system is guaranteed and the tracking error can be made farely small by tuning the design parameters. Finally, two simulation examples illustrate the effectiveness and feasibility of the proposed approach.     

基于非线性观测器设计的混沌同步控制

提出一种基于非线性观测器设计的混沌同步控制方法,给出了一类含有不确定参数混沌系统的观测器实现条件.该控制策略可满足混沌系统中存在一些不确定参数的要求.通过对Lorenz混沌系统的理论分析和数字仿真,证明了其有效性.     

动力定位船舶自适应滑模无源观测器设计

针对带有模型参数不确定性的动力定位船舶,提出一种动力定位船全速域自适应滑模无源观测器,解决了现有观测器只能应用于低速作业动力定位系统的问题.采用速度估计误差作为滑模面,设计切换自适应律估计模型不确定项上界,保证了观测器增益的有界性和系统鲁棒性.对速度估计回路的无源性进行了分析,并证明了观测器的稳定性.最后利用船舶动力定位系统半实物仿真平台,验证了算法的有效性.     

基于高增益观测器的船舶动力定位系统的输出反馈控制

针对动力定位船舶的速度向量不可测的问题, 考虑外部环境扰动, 将高增益观测器、动态面控制技术和矢量backstepping方法相结合, 设计仅依赖于船舶位置和艏摇角测量值的船舶动力定位系统输出反馈控制律. 动态面控制技术的引入, 使控制律结构简单, 易于工程实现. 应用Lyapunov函数证明了所设计的控制律能迫使船舶的位置和艏摇角收敛于期望值, 并保证船舶动力定位输出反馈闭环系统所有信号均一致最终有界. 基于一艘供给船的仿真研究验证了所设计的基于高增益观测器的船舶动力定位输出反馈控制律的有效性.     

High gain observer based on a triangular structure

A high gain observer based on a triangular structure of nonlinear systems is proposed. An algorithm capable of calculating a gain of the observer is given. This observer synthesis is then extended to a class of multi‐output nonlinear systems which contains the model of binary distillation columns. Finally, we illustrate the performance of the estimator using numerical simulations of a methanol–ethanol distillation column. Copyright © 2002 John Wiley & Sons, Ltd.     

基于动态神经网络的非线性组合系统自适应观测器

基于动态神经网络，对一类非线性组合系统提出一种观测器设计方法．在观测器设计中，充分考虑了神经网络逼近误差项对观测器性能的影响，增加了鲁棒控制项，并设计了相应的参数自适应律，以保证良好的观测性能．神经网络的连接权值在线调整，无需离线学习．仿真结果表明了该方法的有效性．     

Stochastic contraction-based observer and controller design algorithm with application to a flight vehicle

This paper focuses on a stochastic version of contraction theory to construct observer-controller structure for a flight dynamic system with noisy velocity measurement. A nonlinear stochastic observer is designed to estimate the pitch rate, the pitch angle, and the velocity of an aircraft example model using stochastic contraction theory. Estimated states are used to compute feedback control for solving a tracking problem. The structure and gain selection of the observer is carried out using Itô's stochastic differential equations and the contraction theory. The contraction property of integrated observer-controller structure is derived to ensure the exponential convergence of the trajectories of closed-loop nonlinear system. The upper bound of the state estimation error is explicitly derived and the efficacy of the proposed observer-controller structure has been shown through the numerical simulations.     

Differentially private nonlinear observer design using contraction analysis

Real‐time information processing applications such as those enabling a more intelligent infrastructure are increasingly focused on analyzing privacy‐sensitive data obtained from individuals. To produce accurate statistics about the habits of a population of users of a system, this data might need to be processed through model‐based estimators. Moreover, models of population dynamics, originating for example from epidemiology or the social sciences, are often necessarily nonlinear. Motivated by these trends, this paper presents an approach to design nonlinear privacy‐preserving model‐based observers, relying on additive input or output noise to give differential privacy guarantees to the individuals providing the input data. For the case of output perturbation, contraction analysis allows us to design convergent observers as well as set the level of privacy‐preserving noise appropriately. Two examples illustrate the proposed approach: estimating the edge formation probabilities in a social network using a dynamic stochastic block model, and syndromic surveillance relying on an epidemiological model.