Shouping Guan

Quadratically convex combination approach to stability of T–S fuzzy systems with time-varying delay

Abstract This paper develops a novel stability analysis method for Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for time-varying delayed T–S fuzzy systems are derived by the newly proposed augmented Lyapunov–Krasovski (L–K) functional. This functional contains the cross terms of variables and quadratic terms multiplied by a higher degree scalar function. Different from previous results, our derivation applies the idea of second-order convex combination, and the property of quadratic convex function without resorting to the Jensens inequality. Two numerical examples are provided to verify the effectiveness of the presented results.

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.

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.

An improved interval PSO algorithm with dynamic shrinking

Considering the slow convergence problem of conventional interval particle swarm optimization algorithm based on static shrinking strategy (SIPSO), this paper proposes a new dynamic shrinking strategy to form a new interval particle swam optimization algorithm (DIPSO) to improve the SIPSO, which can make the interval shrinking more flexible and be conducive to the quick convergence. The simulation results show that the efficiency of DIPSO is superior to SIPSO, and demonstrate the improvement for SIPSO is effective.

Robust state and input simultaneous estimation for discrete-time linear time-varying uncertain systems

State and input simultaneous estimation for discrete-time linear time varying systems with norm-bounded parametric uncertainty are addressed in H∞ setting. Using linear quadratic game formulation, sufficient solvable conditions for the problem are presented in terms of solution to two Riccati equations. One possible estimator is then presented with separation innovation structure, where innovation is used to update state observation tuned by a gain matrix and simultaneously to provide input estimation through a projector matrix. With state and input simultaneous estimation ability, the proposed estimator has a wide application in control, filtering, signal processing and fault diagnosis.

Controller reconfiguration design based on stability analysis

Two improved controller reconfiguration approaches are proposed based on the stabilization goal. For a class of single-variable systems, aimed at defects of reconfiguration using the static gains of their transfer functions to compensate for the failure loop with stability ignored, an algorithm of control law rescheduling via Routh Criterion or root locus is presented which can ensure the stability of each inner loop in the reconfigured system. For a class of multivariable systems, in order to avoid the phenomenon that pseudo-inverse method (PIM) may lead to instability, a stability-guaranteed pseudo-inverse reconfiguration method is also put forward. Simulation results show the effectiveness of two modified methods.

Robust H ∞ hybrid estimation for continuous linear time-varying uncertain systems with known input

This letter presents an approach to deal with robust H∞ state and input hybrid estimation for continuous linear time-varying systems, where norm-bounded parameter uncertainty is appeared in the state and output matrices and a known input is incorporated in the state-space model. The known input will influence the estimation due to parameter uncertainty. Using differential game theory approach, a sufficient solvable condition for the problem is proposed as well as a design method for the optimal estimator. Compared with those based on nominal systems, the proposed approach significantly improves the estimators robustness to parameter uncertainty and known input. One simulation example about a second-order resonant system illustrates the effectiveness of such an approach.

An architecture of interval random vector function-link networks and its numerical analysis

This paper extends the random vector functional-link (RVFL) networks with single-hidden-layer to interval ones (IRVFLNs) with interval model parameters. The analytic solutions are derived for the interval network parameters using the well-known least square methods, which can overcome the problems such as local minimal, slow convergence. In order to evaluate the performance of IRVFLNs, we choose two data sets in different levels of complexity to be modeled, and compare the aspects of generalization and train time with the interval feed-forward BP neural networks (IBPNNs). The simulation results show that the proposed IRVFLNs have the better properties than the IBPNNs in the network converging and approximating.