This technical note investigates the problem of fault estimation for a class of nonlinear systems with Lipschitzian nonlinearities. In most of the existing fault estimation approaches, the observer matching condition should be satisfied. However, this condition is hard to meet for many systems. To overcome this restriction, a new fault estimation method is proposed, where an intermediate variable is introduced and a specially designed intermediate estimator is proposed to estimate the state and the faults simultaneously by exploiting the properties of fault distribution matrix. It is proved that the states of the error system are uniformly ultimately bounded. Simulation examples verify the effectiveness of the proposed method.

Fault Estimation for a Class of Nonlinear Systems Based on Intermediate Estimator

This paper examines quantized stabilization for Takagi–Sugeno (T–S) fuzzy systems with a hybrid-triggered mechanism and stochastic cyber-attacks. A hybrid-triggered scheme, which is described by a Bernoulli variable, is adopted to mitigate the burden of the network. By taking the effect of the hybrid-triggered scheme and stochastic cyber-attacks into consideration, a mathematical model for a closed-loop control system with quantization is constructed. Theorems for main results are developed to guarantee the asymptotical stability of networked control systems by using Lyapunov stability theory and linear matrix inequality techniques. Based on the derived sufficient conditions in theorems, the controller gains are presented in an explicit form. Finally, two practical examples demonstrate the feasibility of designed algorithm.

Quantized Stabilization for T–S Fuzzy Systems With Hybrid-Triggered Mechanism and Stochastic Cyber-Attacks

This paper studies the aperiodic sampled-data control for the sliding-mode control (SMC) scheme of fuzzy systems with communication-induced delays via the event-triggered method. In practice, it is impossible to update control in continuous manner; thus, an event-based control technique has become popular with the advantage that the control task is executed only if it is triggered by an event. In this paper, the event-based sliding-mode control (ESMC) is designed for each linear subsystem of the global fuzzy model first. Then, the conditions for “fuzzily” amalgamated ESMC are discussed to stabilize the global fuzzy model. This ensures that the SMC is executed only when necessary. Furthermore, the results are extended to the fuzzy systems with communication-induced delays. Finally, case studies are carried out to demonstrate the effectiveness of the derived results.

Aperiodic Sampled-Data Sliding-Mode Control of Fuzzy Systems With Communication Delays Via the Event-Triggered Method

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults

The issue of observer-based adaptive sliding mode control of nonlinear Takagi–Sugeno fuzzy systems with semi-Markov switching and immeasurable premise variables is investigated. More general nonlinear systems are described in the model since the selections of premise variables are the states of the system. First, a novel integral sliding surface function is proposed on the observer space, then the sliding mode dynamics and error dynamics are obtained in accordance with estimated premise variables. Second, sufficient conditions for stochastic stability with an ${H}_{\infty }$ performance disturbance attenuation level ${\gamma }$ of the sliding mode dynamics with different input matrices are obtained based on generally uncertain transition rates. Third, an observer-based adaptive controller is synthesized to ensure the finite time reachability of a predefined sliding surface. Finally, the single-link robot arm model is provided to verify the control scheme numerically.

Adaptive Control of Nonlinear Semi-Markovian Jump T–S Fuzzy Systems With Immeasurable Premise Variables via Sliding Mode Observer

This paper is concerned with the problem of robust fault estimation and fault-tolerant control for a class of Takagi–Sugeno (T–S) fuzzy systems with time-varying state delay and actuator faults. Based on the ( $k-1$ )th fault estimation information, a novel $k$ -step fault-estimation observer is proposed to construct the $k$ th fault error dynamics. The obtained fault estimates via $k$ -step fault-estimation can practically better depict the size and shape of the faults. Then, based on the information of online $k$ -step fault-estimation, a dynamic output feedback fault tolerant controller is designed to compensate the fault effects on the closed-loop fuzzy system. Furthermore, some less conservative delay dependent sufficient conditions for the existence of fault estimation observers and fault tolerant controllers are given in terms of solution to a set of linear matrix inequalities. Finally, simulation results of two numerical examples are presented to show the effectiveness and merits of the proposed methods.

Fault Tolerant Controller Design for T–S Fuzzy Systems With Time-Varying Delay and Actuator Faults: A K-Step Fault-Estimation Approach

This paper mainly focuses on the problem of fault estimation for a class of Takagi–Sugeno fuzzy systems with state delays. A minimum norm least squares solution (MNLSS) approach is first introduced to establish a fault estimation compensator, which is able to optimize the fault estimator. Compared with most of the existing fault estimation methods, the MNLSS-based fault estimation method can effectively decrease the effect of state errors on the accuracy of fault estimation. Finally, three examples are given to illustrate the effectiveness and merits of the proposed method.

Fault Estimation for Fuzzy Delay Systems: A Minimum Norm Least Squares Solution Approach

This paper is concerned with the problem of fault estimation for a class of Takagi–Sugeno fuzzy systems with local nonlinear parts and actuator faults. The system matrices in consideration contain unknown components, whereas in most of the literature, the system matrices are required to be known completely. An input–output based fault-estimation approach for the fuzzy system is proposed, by which, the estimation error for time-varying faults can asymptotically converge to zero in the absence of disturbances. The estimation convergence is proved theoretically. Based on the information of fault estimation, the design of fault-tolerant controller can be updated online to compensate the fault effect on systems so as to maintain the original performance of the system. Numerical examples are given to show the effectiveness and merits of the proposed method.

Input–Output Based Fault Estimation for T-S Fuzzy Systems With Local Nonlinear Parts

This paper studies the problem of fault estimation for a class of linear parameter varying (LPV) Markovian jump systems (MJSs) with actuator and sensor faults. A new fault estimation scheme is presented for the LPV MJS, where a novel min–max regulator (MMR) based on the Cholesky decomposition technique is designed to adjust the parameters in the fault estimator so that the states, actuator and sensor faults are able to be estimated simultaneously with good accuracy. Then, the designed observer gains guarantee the stochastic stability of the overall error system with a prescribed H ∞ performance. Finally, a numerical example is given to illustrate the effectiveness and advantages of the proposed methods.

Fault estimation for a class of linear parameter varying systems with Markovian jumps

The problem of fault estimation for a class of non-linear systems with Lipschitzian non-linearities and faults is studied. In most of the existing fault estimation methods, the coefficient matrix of the fault vector is required to be full column rank, which leads to that the corresponding estimation approaches are conservative and unsuitable commonly for systems with multiple faults or/and subject to disturbances. In this study, this restriction is relaxed. A novel fault estimation method is proposed, where a full-column-rank state variable substitution is introduced so as to meet the requirement of fault estimation. The designed estimation observer guarantees the asymptotic stability of the overall error system with a prescribed H∞ performance. The states and faults can be estimated with good accuracy simultaneously. Then, the proposed estimation approach is further extended to solve the problem of fault estimation for non-linear systems with multiple faults or/and subject to disturbances. Finally, numerical examples illustrate the effectiveness and advantages of the proposed method.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-cta.2016.0331

Sheng-Juan Huang

Papers

Fault Tolerant Controller Design for T–S Fuzzy Systems With Time-Varying Delay and Actuator Faults: A K-Step Fault-Estimation Approach

Fault Estimation for Fuzzy Delay Systems: A Minimum Norm Least Squares Solution Approach

Input–Output Based Fault Estimation for T-S Fuzzy Systems With Local Nonlinear Parts

Fault estimation for a class of linear parameter varying systems with Markovian jumps

Fault estimation for a class of non-linear systems via full-column-rank state variable substitution