一类非线性系统的自适应观测器设计

在故障诊断应用中, 状态方程中的未知参数和输出方程中的未知参数分别表征执行机构故障和传感器故障, 所以研究状态方程和输出方程同时含有未知参数的自适应观测器有着实际的应用意义. 本文基于高增益观测器和自适应估计理论, 针对状态方程和输出方程同时含有未知参数的一类一致可观的非线性系统, 用构造性方法设计了一种联合估计状态和未知参数的自适应观测器. 该自适应观测器的参数估计采用时变增益矩阵, 结构形式及参数设置简单. 给出了使该自适应观测器满足全局指数收敛性的持续激励条件, 并在理论上简洁地证明了该自适应观测器的全局指数收敛性. 数值仿真结果表明该自适应观测器具有良好的快速收敛性、跟踪性等期望性能.     

Continuous–discrete-time adaptive observers for nonlinear systems with sampled output measurements

This paper considers the continuous–discrete-time adaptive observer (CDAO) design for a class of nonlinear systems with unknown constant parameters and sampled output measurements. The proposed observer is actually an impulsive system, since the observer state flows according to a set of differential equations and with instantaneous state jumps corresponding to measured samples and their estimates, and an inter-sample output predictor is used to predict the output during sampling intervals. By assuming appropriate persistent excitation conditions and following a technical lemma, an upper bound of the sampling intervals is derived, with which the convergence of the observer state and unknown parameters can be ensured. Finally, the proposed observer is used in examples of chaotic oscillators and single-link flexible-joint robot manipulator to show the effectiveness.     

Adaptive observers for nonlinearly parameterized class of nonlinear systems

In this paper, one proposes adaptive observers for a class of uniformly observable MIMO nonlinear systems with general nonlinear parameterizations. The state and the unknown parameters of the considered systems are supposed to lie in bounded domains which size can be arbitrarily large and the exponential convergence of the observers is shown to result under a well-defined persistent excitation condition. Moreover, the gain of the observers involves a design function that has to satisfy a simple condition which is given. Different expressions of such a function are proposed and it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function. The theory is supported by simulation results related to the estimation of the biomass concentration and the Contois model parameters in a bioreactor.     

Sampled-data extended state observer for uncertain nonlinear systems

In this paper, we present a sampled-data nonlinear extended state observer (NLESO) design method for a class of nonlinear systems with uncertainties and discrete time output measurement. To accommodate the inter-sample dynamics, an inter-sample output predictor is employed in the structure of the NLESO to estimate the system output in the sampling intervals, where the prediction is used in the proposed observer instead of the system output. The exponential convergence of the sampled-data NLESO is also discussed and a sufficient condition is given by the Lyapunov method. A numerical example is provided to illustrate the performance of the proposed observer.     

Cascade high-gain observers for a class of nonlinear systems with large delayed measurements

This paper proposes a cascade high-gain observer for a class of triangular nonlinear systems with large and diverse time delays at states and output equation. Compared with some existing results in the literature, the main contribution is to consider the simultaneous and diverse delays in both states and output and further, to propose a cascade observer in dealing with arbitrarily large delayed measurements. By choosing a suitable Lyapunov-Krasovskii functional, the sufficient condition is presented that guarantees the exponential convergence of observation error to the origin. Simulation results on a numerical example and a practical case study involving inverted pendulum are finally given to illustrate the effectiveness of the proposed approach.     

High gain observer for a class of nonlinear systems with coupled structure and sampled output measurements: application to a quadrotor

This paper proposes a new high gain observer for a class of non-uniformly observable nonlinear systems with coupled structure driven by sampled outputs. The considered class of systems is particularly constituted by several subsystems where each subsystem is associated to a subset of the output variables. The observer design is carried out through two steps. First, a high-gain observer is proposed in the continuous-time output case under the assumption that an adequate persistent excitation condition is satisfied by each subsystem. Then, the proposed observer is redesigned to handle the case of sampled outputs leading thereby to a continuous-discrete time observer. The latter property is achieved thanks to the approach pursued along the convergence analysis. The effectiveness of the proposed observer is emphasised in a realistic simulation framework involving a mathematical model of a quadrotor which is diffeomorphic to the proposed class of considered systems.     

Predictor-based continuous-discrete nonlinear observer design subject to aperiodic sampled and delayed measurement

In this paper, a predictor-based continuous-discrete nonlinear observer is proposed for a class of nonaffine Lipschitz nonlinear systems with aperiodic sampled delayed output measurements and external disturbance. Firstly, this study introduces a class of delayed sampling hybrid nonlinear systems. By employing Lyapunov techniques and trajectory-based stability theory, sufficient conditions are established for ensuring input-to-state stability of the delayed sampling hybrid nonlinear system with respect to external disturbances. Then the predictor-based continuous-discrete nonlinear observer is designed which consists of a continuous-time observer, a compensating injector and a predictor. The continuous-time observer is utilized to obtain continuous and delay-free state estimation. The compensating injector is designed to compensate for output errors that occur between sampling instants. Furthermore, the predictor is employed to obtain delay-free output error information, which is then utilized by the continuous-time observer for feedback correction. The proposed observer's exponential input-to-state property against the disturbance is proved via the proposed hybrid system stability theory. The effectiveness of the proposed observers has been demonstrated through numerical simulations and performance comparisons with the zero-order holder-based observer and the output predictor-based observer designs in order to highlight the effectiveness and advantages of the proposed observer.     

基于观测器的一类连续非线性系统的采样控制

首先使用反演方法分别设计了系统的连续时间状态反馈控制器、连续时间观测器和基于连续时间观测器的连续时间控制器. 接下来, 利用零阶保持法对连续时间状态反馈控制器进行离散化, 获得了状态反馈采样控制器; 利用零阶保持法对基于连续时间观测器 的连续时间控制器离散化, 获得了基于连续时间观测器的采样控制器; 利用Euler法对连续时间观测器离散化, 同时利用零阶保持法对控制器离散化, 从而获得了采样观测器和基于采样观测器的采样控制器. 本文论证了上述状态反馈采样控制器和基于连续时间观测器的采样控制器可以保证闭环系统渐近稳定, 而基于采样观测器的采样控制器可以保证被控对象的状态是有界的, 其最终边界依赖于设计参数与采样周期. 最后, 通过选择适当的采样周期, 完成了闭环采样控制系统的设计. 一个船舶航向控制的例子表明应用本文 所提方法设计出的三种采样控制器具有良好的控制效果.     

Redesign of adaptive observers for improved parameter identification in nonlinear systems

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.     

Adaptive Impulsive Observers for a Class of Switched Nonlinear Systems with Unknown Parameter

This work investigates and solves the design of adaptive impulsive observers for a class of uncertain switched nonlinear systems with unknown parameter. Sufficient conditions are derived for designing such observers for each subsystem to reconstruct asymptotically and update system states in real time. The state observer is represented in terms of impulsive differential equations. The parameter estimation law is modelled by an impulse‐free, time‐varying differential equation associated with the impulse time sequence in order to determine when the observer estimated state is updated. The asymptotic convergence to zero of the observation errors is established by applying the method of multiple time‐varying Lyapunov functions. Sufficient conditions are derived that guarantee the convergence of parameter estimation. An example of switched Lorenz system along with numeric and simulation results is presented to demonstrate the effectiveness of the proposed method.     

Nonlinear system fault diagnosis based on adaptive estimation

An approach to fault diagnosis for a class of nonlinear systems is proposed in this paper. It is based on a new adaptive estimation algorithm for recursive estimation of the parameters related to faults. This algorithm is designed in a constructive manner through a nontrivial combination of a high gain observer and a recently developed linear adaptive observer, without resort to any linearization. Its global exponential convergence is ensured by an easy-to-check persistent excitation condition. A numerical example is presented for illustration.     

非线性不确定系统的自适应观测器设计

非线性状态观测器可改善过程控制性能和故障诊断,针对一类参数不确定非线性系统提出了自适应观测器设计方法。通过微分同胚变换,将非线性系统转换为仅依赖原系统输入、输出的自适应观测器规范形式。利用自适应调节器估计未知参数,用构造的观测器实现状态的重构。Lyapunov稳定性理论分析了状态观测误差动态方程的稳定性,用来证明所设计的自适应观测器为全局渐近收敛的,既实现了系统状态的渐近重构又确保了在持续激励条件下未知参数估计以指数快速收敛到真值,并通过仿真试验。仿真结果表明提出方法的有效性。     

Disturbance-observer-based sampled-data adaptive output feedback control for a class of uncertain nonlinear systems

In this paper, a sampled-data adaptive output feedback controller is proposed for a class of uncertain nonlinear systems with unmeasured states, unknown dynamics and unknown time-varying external disturbances. To approximate uncertain nonlinear functions, radial basis function neural networks (RBFNNs) are employed. The state observer and the disturbance observer (DO) are constructed to estimate the unmeasured state and the external disturbance, respectively. Then, the sampled-data adaptive output feedback controller and adaptive laws are designed by using the backstepping design technique. The allowable sampling period T is derived to guarantee that all states of the resulting closed-loop system are semi-globally uniformly ultimately bounded. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed approach.     

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。     

State observer-based adaptive fuzzy output-feedback control for a class of uncertain nonlinear systems

This paper aims to develop state observer-based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances. An adaptive fuzzy observer is proposed to estimate the system state variables. It is shown that the observation errors obtained from the observer are uniformly ultimately bounded. Applying the estimated system state for design of an output-feedback controller, the uniformly ultimate boundedness of the tracking errors for the resulting closed-loop system can be guaranteed. A typical robot arm system is employed in our simulation studies, and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances.     

Nonlinear observer design in the presence of delayed output measurements

The present work proposes a new approach to the nonlinear observer design problem in the presence of delayed output measurements. The proposed nonlinear observer possesses a state-dependent gain which is computed from the solution of a system of first-order singular partial differential equations, and in particular, consists of a chain of state observation algorithms that reconstruct the unmeasurable state vector at different delayed time-instants within the time-delay window introduced by the available output measurements. Therefore, the proposed nonlinear observer exhibits a chain-like structure that explicitly reflects and takes into account the magnitude of the output delay. Furthermore, a set of conditions is derived under which convergence of the estimation error to zero is established. Finally, the performance of the proposed observer and its convergence properties are evaluated in an illustrative biological reactor example.     

基于自适应滑模观测器的不匹配非线性系统执行器故障重构

针对一类含有未知干扰的不匹配非线性Lipschitz系统,提出了基于自适应滑模观测器的执行器故障重构方法.首先引入辅助输出矩阵,使得辅助输出系统的观测器匹配条件得以满足,同时设计了高增益观测器实现对未知辅助输出的精确估计;然后针对辅助输出系统建立故障重构滑模观测器,设计了自适应律在线修正滑模控制器增益,考虑故障上界未知的前提下,提出了观测器状态估计误差稳定的存在定理,运用Schur补引理将观测器反馈增益矩阵设计方法转化为求解线性矩阵不等式约束优化问题,同时引入线性变换矩阵,在故障上界未知的前提下设计了滑模控制增益,使得输出估计误差收敛稳定,确保了滑模运动在有限时间内发生,在此基础上利用等效控制输出误差注入原理实现了执行器故障重构;最后通过仿真算例验证了本文方法的有效性.     

Time-varying increasing-gain observers for nonlinear systems

A full-order state observer for a class of nonlinear continuous-time systems is presented as generalization of the high-gain observer for having a time-varying gain that is let to be small in the first time instants, increases over time up to its maximum, and then is kept constant. The global stability of the resulting estimation error is proved by means of a Lyapunov functional via a change of coordinate. The design of such an observer is obtained by solving a nonlinear programming problem and using series expansions to set the time-varying gain.     

Impulsive observer-based consensus control for multi-agent systems with time delay

The paper deals with the distributed consensus problem of a class of general linear multi-agent systems with time delay. Assuming that the state of the multi-agent system cannot be measured and the output of the multi-agent system is measured discontinuously, a novel impulsive observer is constructed. Based on the impulsive observer, a distributed consensus protocol is proposed for the multi-agent system with a directed communication topology. In view of the hybrid characteristic of the multi-agent system with the impulsive observer, a novel type of piecewise Lyapunov functional which can overcome the jump phenomena at impulsive times is introduced. Based on this, some sufficient conditions in terms of linear matrix inequalities are presented such that the consensus of the multi-agent system can be achieved with an exponential convergence rate. A numerical example under two cases is given to show the effectiveness of the theoretical results.     

一类非线性系统的控制器和观测器设计

研究一类非线性系统的全状态反馈控制问题、观测器设计问题及输出反馈控制设计问题.首先设计出非线性全状态反馈控制器,获得了系统指数镇定的充分条件.然后提出了非线性观测器,并证明了该观测器是指数稳定观测器.进一步,在控制器和观测器问题的充分条件满足的假设下,证明了提出的带估计状态的反馈控制能达到指数镇定.最后,仿真实例验证了所得结果的有效性.