Robust Fuzzy Observer Research Articles

Robust fault estimation and fault‐tolerant tracking control for uncertain Takagi–Sugeno fuzzy systems: Application to single link manipulator

SummaryThis article concerns the estimation and tracking control problems for Takagi–Sugeno systems with disturbances and norm bounded uncertainties in presence of sensor and actuator faults (SAF). First, we propose a robust fuzzy observer (RFO) design method to estimate both state and SAF for the considered class of the nonlinear systems. Then, this RFO‐based fault tolerant tracking control is developed not only to compensate the SAF effects but also to ensure the state convergence to desired trajectories in spite of their presence. To reduce the conservatism of design conditions, observer and controller gains are calculated in a single step by solving a set of linear matrix inequality constraints. H∞ criterion is used to attenuate disturbance effects and to reduce the tracking error. Finally, simulation results by considering two types of actuator fault and comparative study on a single link flexible joint manipulator are provided to underline the performances of the mentioned process.

Dynamic positioning of ships based on robust fuzzy observer

In this study, the robust fuzzy observer-based control scheme for the dynamic positioning of marine vessels is presented. The proposed controller assumes that the environmental disturbances are unknown but bounded with known upper limit. First, the authors apply the Takagi–Sugeno fuzzy model to approximate the ship model. Using formulated fuzzy model, the robust fuzzy observer is developed to approximate the unknown states. Then, by employing optimal H ∞ disturbance attenuation technique, the effects of the environmental disturbances can be attenuated to least value. Finally, the linear matrix inequality technique is hired for solving the optimal robust problem. Model ship is used for simulation, and results are given to prove the validity of the presented controller.

Observer and Adaptive Fuzzy Control Design for Nonlinear Strict-Feedback Systems With Unknown Virtual Control Coefficients

This paper considers the problems of designing a robust observer and developing a backstepping-based adaptive fuzzy control scheme for a class of strict-feedback systems, in which the virtual control coefficients are unknown. By using convex combination method, a robust fuzzy observer has been constructed to estimate the unmeasurable system state variables. Further, an observer-based adaptive fuzzy control scheme has been proposed. During the controller design procedure, fuzzy logic systems are used to model the unknown nonlinear functions, adaptive technique and backstepping are combined to construct the ideal virtual and the real laws. The proposed adaptive fuzzy output feedback controller guarantees that the tracking error converges to a small neighborhood of the origin and all the signals in the adaptive closed-loop system are bounded. Simulation results are provided to demonstrate the effectiveness of the presented approach.

Secure communication for non-ideal channel via robust TS fuzzy observer-based hyperchaotic synchronization

This paper proposes a novel hyperchaotic secure communication scheme for non-ideal communication channels. The proposed approach employs Takagi–Sugeno (TS) fuzzy model and linear matrix inequality (LMI) technique to design a controller which synchronizes the hyperchaotic transmitter and receiver systems. In the presented method, only few numbers of states are needed to be transformed which is consistent with the practical limitations of a non-ideal channel and highly secure communication. Therefore, a robust fuzzy observer is proposed to estimate the other states of the transmitter at the receiver side. Furthermore, since the channel is non-ideal, H∞ performance criterion is employed to derive robust observer and controller against the external disturbance and noise. In order to make the proposed approach more applicable, the sufficient controller and observer design conditions are formulated in terms of linear matrix inequalities (LMIs) which can be solved by convex optimization techniques. In addition, to further remove the effect of the noise on the information recovery, a moving average filter is utilized. Finally, to show the effectiveness and advantages of the proposed approach, the hyperchaotic Lorenz system is considered and the signal is analyzed at the transmitter and receiver sides. Then, the results obtained show the superiority and effectiveness of the proposed method compared with those of the existing approaches.

Robust Fuzzy Observer-Based Fault Tolerant Tracking Control for Nonlinear Systems with Simultaneous Actuator and Sensor Faults: Application to a DC Series Motor Speed Drive

In this paper, a detailed design scheme for observer-based robust fault estimation and fault tolerant tracking control (FTTC) is developed for a class of nonlinear system described by a T-S fuzzy model subjected to both sensor and actuator faults simultaneously. The proposed scheme includes a single robust fuzzy observer (using the extended state system formulation) and an observer-based FTTC (using compensation scheme) to guarantee given stability requirements, while limiting the influence of noises and disturbances. Sufficient conditions for the robust stability of the proposed fuzzy observer are formulated in terms of linear matrix inequalities (LMIs) that can be conveniently solved using LMI optimization techniques. Based on the idea of a corrective control law and a corrective measurement output, the estimation results of the proposed observer are used to provide the FTTC system without changing the existing nominal control law. Thus this approach can be applied to general nonlinear control system. Finally, the validity and applicability of the proposed approach are shown by a numerical example of a DC series motor speed drive system.

Detection of impending vehicle rollover with road bank angle consideration using a robust fuzzy observer

This article describes a method of vehicle dynamics estimation for impending rollover detection. We estimate vehicle dynamic states in presence of the road bank angle as a disturbance in the vehicle model using a robust observer. The estimated roll angle and roll rate are used to compute the rollover index which is based on the prediction of the lateral load transfer. In order to anticipate rollover detection, a new method is proposed to compute the time to rollover (TTR) using the load transfer ratio (LTR). The nonlinear model, deduced from the vehicle lateral and roll dynamics, is represented by a Takagi-Sugeno (T-S) fuzzy model. This representation is used to account for the nonlinearities of lateral cornering forces. The proposed T-S observer is designed with unmeasurable premise variables to cater for non-availability of the slip angles measurement. The proposed approach is evaluated using CarSim simulator under different driving scenarios. Simulation results show good efficiency of the proposed T-S observer and the rollover detection method.

Road curvature estimation for vehicle lane departure detection using a robust Takagi–Sugeno fuzzy observer

In this paper, a lane departure detection method is studied and evaluated via a professional vehicle dynamics software. Based on a robust fuzzy observer designed with unmeasurable premise variables with unknown inputs, the road curvature is estimated and compared with the vehicle trajectory curvature. The difference between the two curvatures is used by the proposed algorithm as the first driving risk indicator. To reduce false alarms and take into account the driver corrections, a second driving risk indicator is considered, which is based on the steering dynamics, and it gives the time to the lane keeping. The used nonlinear model deduced from the vehicle lateral dynamics and a vision system is represented by an uncertain Takagi–Sugeno fuzzy model. Taking into account the unmeasured variables, an unknown input fuzzy observer is then proposed. Synthesis conditions of the proposed fuzzy observer are formulated in terms of linear matrix inequalities using Lyapunov method. The proposed approach is evaluated under different driving scenarios using a software simulator. Simulation results show good efficiency of the proposed method.

Design of observers for Takagi-Sugeno fuzzy models for Fault Detection and Isolation

This paper addresses the design of an unknown input fuzzy observer for Takagi-Sugeno (T-S) fuzzy model subject to unknown inputs. The main contribution of the paper is the development of a robust fuzzy observer in presence of disturbances. Based on Lyapunov function, it is shown how to determine observers gains in linear matrix inequalities (LMI). The proposed T-S observer is used for detection and isolation of faults which can affect a T-S model. The proposed methodology is illustrated by estimating the yaw rate and the fault of automatic steering vehicle.

Fuzzy observer for fault detection and reconstruction of unknown input fuzzy models

This paper addresses the design of a fuzzy observer for unknown input Takagi-Sugeno (T?S) fuzzy model. The main contribution of this paper is the development of a robust fuzzy observer in the presence of disturbances. Based on Lyapunov function, it is shown how to determine the observers gains in Linear Matrix Inequalities (LMI) terms. The proposed observer structure allows to estimate simultaneously and systematically the unknown inputs and state variables. The designed T?S observer is used for detection and reconstruction of faults which can affect a non-linear model and can be applied directly for fault detection and isolation of actuator faults. The validity of the proposed methodology is illustrated by estimating the state and faults of an automatic steering vehicle.

Design of a sliding mode fuzzy observer for uncertain Takagi-Sugeno fuzzy model: application to automatic steering of vehicles

This paper addresses the analysis and design of a Sliding Mode Fuzzy Observer (SMFO) on the basis of a Takagi-Sugeno (T-S) fuzzy model. The main contribution of the paper is the development of a robust fuzzy observer with respect to the uncertainties as well as the synthesis of sufficient stability conditions of this observer. The stabilisation of the fuzzy observer is performed by the search of suitable Lyapunov matrices. It is shown how to determine the gains of the local observers, these gains being solutions of a set of Linear Matrix Inequalities (LMIs). The validity of the proposed methodology is illustrated by an estimation of the yaw rate of automatic steering of vehicles.