Fuqiang You

Hybrid Estimation of State and Input for Linear Discrete Time-varying Systems: A Game Theory Approach

Abstract The H∞ hybrid estimation problem for linear discrete time-varying systems is investigated in this paper, where estimated signals are linear combination of state and input. Design objective requires the worst-case energy gain from disturbance to estimation error to be less than a prescribed level. Optimal solution of the hybrid estimation problem is the saddle point of a two-player zero sum differential game. On the basis of the differential game approach, necessary and sufficient solvable conditions for the hybrid estimation problem are provided in terms of solutions to a Riccati differential equation. Moreover, one possible estimator is proposed if the solvable conditions are satisfied. The estimator is characterized by a gain matrix and an output mapping matrix, where the latter reflects the internal relations between unknown input and output estimation error. At last, a numerical example is provided to illustrate the proposed approach.

Robust fast adaptive fault estimation for systems with time-varying interval delay

This paper studies the problem of actuator fault estimation for linear continuous systems, which is subject to time-varying interval delay and norm-bounded external disturbance. Based on the fast adaptive fault estimation (FAFE) algorithm, our attention is focused on the design of fault estimation filters to guarantee the filtering error system to be asymptotically stable with a prescribed H∞ performance. A delay-dependent criterion is established to reduce the conservatism of designing procedure, and the FAFE algorithm can enhance the performance of fault estimation. A novel Lyapunov–Krasovskii function is employed, which includes the information of the upper and the lower bounds of the time delay. An improved sufficient condition for the existence of such a filter is established in terms of the linear matrix inequality (LMI) by the Schur complements and the cone complementary linearization algorithm. In addition, the results for the systems with time-varying interval delay are simplified when the delay is constant and the delay is not considered. Four illustrative examples are given to show the effectiveness of the proposed method.

Active Fault-tolerant Control Design for a Class of Time-delay Systems

This paper deals with the problem of active fault-tolerant control design for a class of linear systems with time-delays. For a class of linear time delay system, firstly, adaptive observer was designed to estimate fault, then a new active fault-tolerant controller is designed which can guarantee that the controlled system keep stable in faulty status, thus the active fault-tolerant control design for this systems is realized. Finally, a numerical example is given to illustrate the efficiency of the proposed design method

Game theory approach to state and input simultaneous estimation for discrete-time LTV systems

This article aims to provide a simple approach realising state observation and input estimation simultaneously for discrete-time LTV systems in H∞ setting. Through solving a two-player zero sum differential game, appealing results are obtained in two folds. First, necessary and sufficient solvability conditions for state and input simultaneous estimation problem are given in terms of solution to a set of difference Riccati recursion. Second, one estimator is presented with special innovation structure, where innovation information is used to update state observation tuned by gain matrix and to provide input estimation through a projector matrix, where gain matrix and projector matrix are constructed from solution to difference Riccati recursion. At last, simulation results are provided to justify proposed approach.

A novel sensor fault diagnosis approach for time-varying delay systems with non-linear uncertainty

In this paper, a sensor fault diagnosis approach is presented for a class of time delay non-linear systems via the use of adaptive updating rules. The considered system is represented by a time-varying delay dynamical state space model, and is subjected to a non-linear vector, which represents the modelling uncertainty in the state equation. Firstly, a fault detector observer is constructed to detect the fault. Then, the method for choosing the threshold value is given. Furthermore, a fault diagnosis device is constructed to diagnose the fault. The Lyapunov stability theory is used to obtain the required adaptive tuning rules for the estimation of the sensor fault. An adaptive diagnosis algorithm is developed to obtain information on the sensor fault. Finally, a simulated numerical example and a robotic example are included to demonstrate the use of the proposed approach, and experimental results show that the proposed adaptive diagnosis algorithm can track the fault signal and that the proposed method is valid.

Robust fast adaptive fault estimation and tolerant control for T-S fuzzy systems with interval time-varying delay

ABSTRACT This paper studies the problem of fault estimation (FE) and the active fault tolerant control (FTC) for Takagi–Sugeno (T-S) fuzzy systems with interval time-varying delay and norm-bounded external disturbance. Based on the fast adaptive fault estimation (FAFE) algorithm, our attention focuses on designing an adaptive observer-based controller to guarantee the filtering error system to be asymptotically stable and satisfy theH∞ performance index. By constructing a new Lyapunov–Krasovskii functional including the information of the lower and upper delay bounds, the sufficient delay-dependent conditions have been established to guarantee the existence of adaptive observer-based controller in terms of linear matrix inequalities (LMIs). Compared with the constant delay and time-varying delay, the interval time-varying delay is the less conservative form. Furthermore, we make full use of the information of the delay and no terms are ignored when the stability of the system is analysed. In addition, the results for the systems with time-varying structured uncertainties are established. The results of the active FTC are showed in terms of LMIs. Finally, two examples are given to verify the effectiveness of the proposed method.

Improved set-membership guaranteed state estimation for uncertain non-linear systems

This paper presents a new improved set-membership algorithm for guaranteed state estimation for non-linear discrete-time systems with an unknown but bounded description of disturbance and noise. In this paper, the non-linear model is linearized first and the difference of convex (DC) programming method is used to outer-bound the linearization error, which is regarded as a disturbance of the system, and the improved set-membership algorithm guaranteed state estimation for the linearization system. An example is given to illustrate the proposed algorithm.

A new set-membership estimation method based on zonotopes and ellipsoids

This paper presents a new approach for guaranteed state estimation based on zonotopes and ellipsoids for linear discrete-time systems with unknown but bounded perturbations and noises. At each sample time, a predicted state set is calculated by zonotopes and an outer bounding ellipsoid of the predicted state set is calculated. State estimation is calculated directly by intersects with an outer bounding ellipsoid and strip. The precision of the state estimation will increase as output order improves by this method. Two examples have been provided to clarify the algorithm.

Fault tolerant control for T-S fuzzy systems with simultaneous actuator and sensor faults

This paper studies the problem of fault estimation (FE) and the active fault tolerant control (FTC) for a class of Takagi-Sugeno (T-S) fuzzy systems with time-varying delay and simultaneous actuator and sensor faults. Based on the fault estimation algorithm, an adaptive observer-based controller is designed to guarantee the dynamic error system to be asymptotically stable and satisfy the H∞ performance index. Then, based on the information of online fault-estimation information, a dynamic output feedback fault tolerant controller is designed to compensate the fault effects on the closed-loop fuzzy system. Finally, simulation results are given to verify the effectiveness of the proposed method.

Fault detection for sampled-data systems in H ∞ setting

Fault detection problem for sampled-data systems is investigated in the framework of linear systems with jumps. Incipient actuator is a great challenge in fault detection for sampled-data systems. Utilizing H∞ filtering technique, fault estimator is designed. One sufficient existence condition and the design algorithm for the detector are then both provided in terms of solution to a set of Riccati differential equation with finite discrete jumps.