Fault-Tolerant Control for Markovian Jump Delay Systems with an Adaptive Observer Approach

This paper investigates the problem of fault estimation and fault-tolerant control for a class of Markovian jump systems with mode-dependent interval time-varying delay and Lipschitz nonlinearities. In this paper, a new adaptive fault observer is designed to solve the problem of fault estimation. The proposed observer can estimate the states and faults simultaneously, whether faults are of time-varying or constant characterization. Based on the fault estimation, a fault-tolerant controller is designed to stabilize the closed-loop system. Sufficient conditions for the existence of the observer gain and fault-tolerant controller gain are got by a set of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the proposed fault-tolerant control method.     

A Nonlinear Adaptive Resilient Observer Design for a Class of Lipschitz Systems Using LMI

This paper addresses the parameter and state estimation problem in the presence of the observer gain perturbations for Lipschitz systems that are linear in the unknown parameters and nonlinear in the states. A nonlinear adaptive resilient observer is designed, and its stability conditions based on the Lyapunov technique are derived. The gain for this observer is derived systematically using the linear matrix inequality approach. A numerical example and a physical setup are provided to show the effectiveness of the proposed method.     

A New Approach to Observer-Based Fault-Tolerant Controller Design for Takagi-Sugeno Fuzzy Systems with State Delay

This paper deals with the problem of active fault-tolerant control (FTC) for time-delay Takagi-Sugeno (T-S) fuzzy systems based on a fuzzy adaptive fault diagnosis observer (AFDO). A novel fuzzy fast adaptive fault estimation (FAFE) algorithm for T-S fuzzy models is proposed to enhance the performance of fault estimation, and sufficient conditions for the existence of the fault estimator are given in terms of linear matrix inequalities (LMIs). Using the obtained on-line fault estimation information, an observer-based fast active fault-tolerant controller is designed to compensate for the effect of faults by stabilizing the closed-loop system. Simulation results of a track trail system and a nonlinear numerical example are presented to illustrate the effectiveness of the proposed method.     

Observer-Based H ∞ Synchronization and Unknown Input Recovery for a Class of Digital Nonlinear Systems

This paper considers the synchronization and unknown input recovery problem for a class of digital nonlinear systems based on a nonlinear observer approach. A generalized Luenberger-like observer is introduced for a class of discrete-time Lipschitz nonlinear systems. Stability conditions for the existence of asymptotic observers are established in terms of some linear matrix inequalities. It is shown that the proposed conditions are less conservative than some existing ones in the recent literature. Moreover, an observer design method is used to address the problem of H _∞ synchronization and unknown input recovery for a class of Lipschitz nonlinear systems in the presence of disturbances in both the state and output equations. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design.     

Neural Network Based Adaptive Tracking of Nonlinear Multi-Agent System

In this paper, the problems of robust consensus tracking control for the second-order multi-agent system with uncertain model parameters and nonlinear disturbances are considered. An adaptive control strategy is proposed to smooth the agent’s trajectory, and the neural network is constructed to estimate the system’s unknown components. The consensus conditions are demonstrated for tracking a leader with nonlinear dynamics under an adaptive control algorithm in the absence of model uncertainties. Then, the results are extended to the system with unknown time-varying disturbances by applying the neural network estimation to compensating for the uncertain parts of the agents’ models. Update laws are designed based on the Lyapunov function terms to ensure the effectiveness of robust control. Finally, the theoretical results are verified by numerical simulations, and a comparative experiment is conducted, showing that the trajectories generated by the proposed method exhibit less oscillation and converge faster.     

Incipient Fault Detection Using an Associated Adaptive and Sliding-Mode Observer for Quadrotor Helicopter Attitude Control Systems

An associated adaptive and sliding-mode observer (AASMO) design is proposed to detect and estimate the incipient actuator faults of a quadrotor. The incipient faults considered are physical structure aging and quadrotor leakage. First, disturbances and nonlinear parameters are considered in system formulation for a realistic mathematical model of the quadrotor. Its fault model is also introduced. Second, the decomposed subsystems are obtained through coordinate transformations to separate the incipient faults from the disturbances. For the subsystem with no disturbance, the adaptive observer can estimate the incipient faults. For the subsystem with disturbances, the sliding-mode observer has strong robustness against the disturbances. Dynamic error convergence and system stability can also be guaranteed by Lyapunov stability theory. Finally, the simulation results of quadrotor helicopter attitude systems validate the efficiency of the proposed AASMO-based incipient fault detection algorithm.     

Robust Fault Detection of Uncertain Time-Delay Markovian Jump Systems with Different System Modes

In this paper, a robust fault detection filter (RFDF)design scheme is presented for uncertain nonlinear Markovian jump systems with mixed delays. By using a observer-based fault detection filter as residual generator, the RFDF design is formulated as an H _∞-filtering problem. Particularly, two different Markov processes are considered for modeling the randomness of system matrix and the state delay; meanwhile, the corresponding two kinds of transition rate matrices are assumed to be incompletely accessible, that is, the one with partially unknown entries and the other with polytopic uncertainties. By using a new convex polyhedron technique, some new sufficient conditions are established in terms of delay-dependent linear matrix inequalities (LMIs) to synthesize the residual generation scheme. Finally, a numerical example is given to illustrate the effectiveness of the proposed techniques.     

High-Gain Observers With Sliding Mode for State and Unknown Input Estimations

To handle the state estimation of a nonlinear system perturbed by a scalar disturbance distributed by a known nonlinear vector, a sliding-mode term is incorporated into the nonlinear high-gain observer (HGO) to realize a robust HGO. By imposing a structural assumption on the unknown input distribution vector, the observability of the disturbance with respect to the output is safeguarded, and the disturbance can be estimated from the sliding surface. Under a Lipschitz condition for the nonlinear part, the nonlinear observers are designed under the structural assumption that the system is observable with respect to any input. In the sliding mode, the disturbance under an equivalent control becomes an increment of Lipschitzian function, and the convergence of the estimation error dynamics can be proven similar to the analysis of HGOs. The proposed technique can be applied for fault detection and isolation. The simulation results for the bioreactor application demonstrate the effectiveness of the proposed method.      

Adaptive Variable Structure Control for Uncertain Switched Delay Systems

This paper investigates the robust H _∞ control problem for a class of uncertain switched delay systems with parameter uncertainties, unknown nonlinear perturbations, and external disturbance. Based on the multiple Lyapunov functions method, a sufficient condition for the solvability of the robust H _∞ control problem is derived by employing a hysteresis switching law and variable structure controllers. When the upper bounds of the nonlinear perturbations are unknown, an adaptive variable structure control strategy is developed. The use of the adaptive technique is to adapt the unknown upper bounds of the nonlinear disturbances so that the objective of asymptotic stabilization with an H _∞-norm bound is achieved under the hysteresis switching law. A numerical example illustrates the effectiveness of the proposed design methods.     

Robust Fault Estimation and Accommodation for a Class of T–S Fuzzy Systems with Local Nonlinear Models

This paper focuses on the problems of fault estimation and accommodation for a class of T–S fuzzy systems with local nonlinear models and having an external disturbance and sensor and actuator faults, simultaneously. A fuzzy robust fault estimation observer is designed to estimate the system state and sensor and actuator faults. Compared with existing results, the observer not only is robust to the disturbance but also has a wider application range and more freedom for design. To compensate for the effect of faults and to stabilize the closed-loop system, an observer-based fault-tolerant controller is proposed. The separate design of the observer and controller avoids coupling between them. Finally, a simulation is conducted to demonstrate the effectiveness of the proposed method.     

Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances

In this paper, we study the robust exponential filter design problem for a class of uncertain time-delay systems with both Markovian jumping parameters and nonlinear disturbances. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, and the parameter uncertainties appearing in the state and output equations are real, time dependent, and norm bounded. The time-delay and the nonlinear disturbances are assumed to be unknown. The purpose of the problem under investigation is to design a linear, delay-free, uncertainty-independent state estimator such that, for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. We address both the filtering analysis and synthesis issues, and show that the problem of exponential filtering for the class of uncertain time-delay jump systems with nonlinear disturbances can be solved in terms of the solutions to a set of linear (quadratic) matrix inequalities. A numerical example is exploited to demonstrate the usefulness of the developed theory.     

基于特征结构配置的飞控系统故障检测与诊断

针对具有未知扰动输入的飞行控制系统,运用特征值配置设计了一种用于故障检测和诊断的观测器,他通过对观测器进行左特征向量的配置使得残差与干扰分布方向正交,故障检验残差r与未知输入干扰d之间的传递函数阵为零,从而使残差与干扰直接解耦.通过这种方法,残差信号得以对干扰具有鲁棒性,使FDI算法不受系统不确定性干扰的影响,提高系统故障诊断的可靠性和精度.同时通过残差信号估计故障,能在线辨识故障的形态,仿真结果验证了该方法的有效性.     

State and Disturbance Estimator for Time-Delay Systems With Application to Fault Estimation and Signal Compensation

For a state-space time-delay system with linearly coupled input and output disturbances, a simultaneous state and disturbance estimation technique is developed. For a nonlinear state-space time-delay system with dependent input and output disturbances, a nonlinear estimator is also proposed to estimate system state and disturbance at the same time. The proposed estimator techniques are applied next to estimate system state and fault signal. Via actuator and/or sensor signal compensation, a simple and efficient fault-tolerant operation can be realized. In the developed design, no limitations and prior knowledge are required on the considered faults. Moreover, identical actuator and/or sensor switches and control gain reconstruction are not necessary. Therefore, the proposed estimation and fault-tolerant scheme is economical and convenient in practical applications. After that, the design techniques are extended to the case of systems with a class of uncoupled input and output faults. Examples and simulations given show excellent signal estimation and fault-tolerant performance.     

Fault Tolerant Control for Non-Gaussian Stochastic Distribution Systems

A new fault tolerant control (FTC) problem via the output probability density functions (PDFs) for non-Gaussian stochastic distribution control systems (SDC) is investigated. The PDFs can be approximated by the radial basis functions (RBFs) of neural networks. Differently from the conventional FTC problems, the measured information is in the form of probability distributions of the system output rather than the actual output values. The control objective is to use the output PDFs to design control algorithm that can compensate the faults and attenuate the disturbances. As a result, the concerned FTC problem subject to dynamic relation between the input and output PDFs can be transformed into a nonlinear FTC problem subject to dynamic relation between the control input and the weights of the RBFs neural networks. Feasible criteria to compensate the faults and attenuate the disturbances are provided in terms of linear matrix inequality (LMI) techniques. In order to improve FTC performances, H ^∞ optimization techniques are applied to the FTC design problem to assure that the faults can be compensated and the disturbances can be attenuated. At last, an illustrated example is given to demonstrate the efficiency of the proposed algorithm, and the satisfactory results have been obtained.     

Model based reduced-order observers for a class of mechatronic systems with mitigation of disturbances effects using the Attractive Ellipsoid Method

State-estimation of mechatronic systems is essential because, in addition to position and velocity, there are electric and magnetic signals that must be measured, and can lead to sophisticated and expensive instrumentation systems. This paper addresses the problem of state-estimation for underactuated mechanical systems whose active joints are driven by permanent magnet dc-motors. Luenberger-type structures are designed, where the measured state variables and the dynamic model are used to construct the unavailable ones, in presence of uncertainties and disturbances as inputs. To avoid the peaking phenomenon is one of the main challenges on state observation for nonlinear systems. Underactuated mechatronic systems are not immune to this problem, which is exacerbated when external disturbances are taken into account. The major purpose here is to use a robust reduced observer to estimate the unmeasured state variables. The Attractive Ellipsoid Method provides reliable estimation of unmeasured state signals because it reduces the influence of external disturbances on the estimate error signals. This ensures that the estimated signals converge to an invariant set of minimal size around the real ones. The first design is based on the quasi-linear representation that meets the observability condition. The second considers the entire nonlinear model, which necessitates the availability of the entire position vector. The major findings are demonstrated experimentally on a non-traditional mechatronic system: the linear double pendulum system whose last joint is constrained by two linear springs. This shows a significant improvement of the estimation response, concerning robust techniques based on the linear approximation, towards its application in designing an adaptive observer to provide state and parameters estimation simultaneously, which is essential in robust and adaptive control systems.     

Fault Estimation for Nonlinear Dynamic Systems

In this paper, the problems of fault detection and estimation for nonlinear dynamic systems are considered by using fault detection observer and adaptive fault diagnosis observer. Based on Lyapunov stability theory and linear matrix inequality (LMI) techniques, a new sufficient condition in terms of LMIs for the proposed problem is derived. At the same time, we get the adaptive fault estimation algorithm. The LMI condition can be easily solved by MATLAB LMI toolbox. Finally, a flexible joint robotic example is given to illustrate the efficiency of the proposed approach.     

Adaptive Iterative Learning Control for a Class of Uncertain Nonlinear Systems with Second-Order Sliding Mode Technique

This paper addresses the problem of robust adaptive iterative learning control for a chain of uncertain integral nonlinear systems, whose aim is to stabilize the tracking error of the system and improve convergence speed in the presence of uncertainties. In response to unknown bounded disturbances, a continuous second-order sliding mode adaptive iterative learning control scheme is proposed, in which an integral term is to attenuate the effects of the disturbances and achieve fast convergence performance. By designing a suitable controller and composite energy function, it is proved that the tracking error along iterative learning horizon will converge to a small neighborhood of zero. Numerical examples are provided to validate the efficacy of the proposed method.     

Disturbance Rejection for a Data Storage System via Sensitivity Loop Shaping and Adaptive Nonlinear Compensation

This paper investigates the disturbance rejection problem for a data storage servo system that contains a microactuator for high-accuracy positioning. For disturbances with known frequencies, their rejection is accomplished via the generalized Kalman-Yakubovic-Popov lemma together with the Youla parameterization approach, and a linear controller is computed via solving a number of linear matrix inequalities. To further improve the rejection of low-frequency disturbances such as nonlinear disturbances arising from friction torque or bias or other unknown disturbances, an adaptive nonlinear compensation scheme is adopted to cancel their effects on the positioning accuracy. Simulation together with implementation results demonstrate that the proposed design offers a remarkably improved positioning accuracy.