Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications

A direct adaptive fuzzy control algorithm is developed for a class of uncertain SISO nonlinear systems. In this algorithm, it doesn’t require to assume that the system states are measurable. Therefore, it is needed to design an observer to estimate the system states. Compared with the numerous alternative approaches with respect to the observer design, the main advantage of the developed algorithm is that on-line computation burden is alleviated. It is proven that the developed algorithm can guarantee that all the signals in the closed-loop system are uniformly ultimately bounded and the tracking error converges to a small neighborhood around zero. The simulation examples validate the feasibility of the developed algorithm. Recommended by Editorial Board member Zhong Li under the direction of Editor Young-Hoon Joo. This work is supported by National Natural Science Foundation of China under grant 60674056, 60874056, and the Foundation of Educational Department of Liaoning Province (2008312). Yan-Jun Liu received the B.S. degree in Applied Mathematics from Shenyang University of Technology in 2001. He received the M.S. degree in Control Theory and Control Engineering from Shenyang University of Technology in 2004 and the Ph.D. degree in Control Theory and Control Engineering from Dalian University of Technology, China, in 2007. His research interests include fuzzy control theory, nonlinear control and adaptive control. Shao-Cheng Tong received the B.S. degree in Department of Mathematics from Jinzhou Normal College, China, in 1982. He received the M.S. degree in Department of Mathematics from Dalian Marine University in 1988 and the Ph.D. degree in Control Theory and Control Engineering from Northeastern University, China, in 1997. His research interests include fuzzy control theory, nonlinear control, adaptive control, and system identification etc. Wei Wang received the B.S. degree in Department of Automation from Northeastern University, China, in 1982. He received the M. S. degree in Department of Automation from Northeastern University in 1984 and the Ph.D. degree in Department of Automation from Northeastern University, China, in 1988. His research interests include adaptive predictive control, intelligent control, and production scheduling method etc. Yong-Ming Li received the B.S. degree in Applied Mathematics from Liaoning University of Technology in 2004. He received the M.S. degree in Applied Mathematics from Liaoning University of Technology in 2007. His research interests include fuzzy control theory, nonlinear control and adaptive control.     

Estimating stable delay intervals with a discretized Lyapunov–Krasovskii functional formulation

In general, a system with time delay may have multiple stable delay intervals. Especially, a stable delay interval does not always contain zero. Asymptotically accurate stability conditions such as discretized Lyapunov–Krasovskii functional (DLF) method and sum-of-square (SOS) method are especially effective for such systems. In this article, a DLF-based method is proposed to estimate the maximal stable delay interval accurately without using bisection when one point in this interval is given. The method is formulated as a generalized eigenvalue problem (GEVP) of linear matrix inequalities (LMIs), and an accurate estimate may be reached by iteration either in a finite number of steps or asymptotically. The coupled differential–difference equation formulation is used to illustrate the method. However, the idea can be easily adapted to the traditional differential–difference equation setting.     

基于主动滑模控制实现一类含有非匹配不确定混沌系统的同步

讨论了一类非匹配不确定混沌系统的同步问题.基于主动控制思想,提出了一种主动滑模控制策略,使得从任意初始条件出发的不确定混沌系统在有限时间内到达滑模面.利用线性矩阵不等式(LMI)技术设计了一个鲁棒稳定的滑模面,以降低非匹配不确定对系统的影响.给出了线性矩阵不等式形式的稳定滑模面存在的充分条件.通过对Rssler系统的同步仿真,验证了该方法的可行性.     

Robust Output Tracking for MIMO Nonlinear Time-Varying Mismatched Uncertain Systems Via Hybrid Control Strategy

This paper considers the problem of robust output tracking control for multi-input multi-output (MIMO) nonlinear systems in the presence of mismatched time-varying uncertainties. Using singular perturbation method and variable structure control technique, we derive a new hybrid controller for MIMO systems with unknown time-varying uncertainties and disturbances to track a desired trajectory. It is shown that the hybrid controller not only stabilizes the closed-loop systems, but also guarantees the tracking errors remain in an O() neighbourhood of the origin where is a small design parameter of the controller. Moreover, by selecting the parameter properly, the tracking errors can be made arbitrarily small.     

FD-ZKF: A Zonotopic Kalman Filter optimizing fault detection rather than state estimation

Enhancing the sensitivity to faults with respect to disturbances, rather than optimizing the precision of the state estimation using Kalman Filters (KF) is the subject of this paper. The stochastic paradigm (KF) is based on minimizing the trace of the state estimation error covariance. In the context of the bounded-error paradigm using Zonotopic Kalman Filters (ZKF), this is analog to minimize the covariation trace. From this analogy and keeping a similar observer-based structure as in ZKF, a criterion jointly inspired by set-membership approaches and approximate decoupling techniques coming from parity-space residual generation is proposed. Its on-line maximization provides an optimal time-varying observer gain leading to the so-called FD-ZKF filter that allows enhancing the fault detection properties. The characterization of minimum detectable fault magnitude is done based on a sensitivity analysis. The effect of the uncertainty is addressed using a set-membership approach and a zonotopic representation reducing set operations to simple matrix calculations. A case study based on a quadruple-tank system is used both to illustrate and compare the effectiveness of the results obtained from the FD-ZKF approach compared to a pure ZKF approach.     

H∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

This paper aims to solve the H_∞ stabilization problem for networked semi‐Markovian jump systems subject to randomly occurring uncertainties by an improved event‐triggered technique. A new measurement error that is defined as the difference value between the latest transmitted data and the mean value of both current data and latest transmitted data is introduced into the event‐triggered condition. Compared with traditional dynamic event‐triggered scheme, more unexpected data could be avoided to be transmitted, which is demonstrated in the simulation through sufficient comparison experiments. Furthermore, by employing a Lyapunov‐Krasovskii functional method and a free‐weighting matrix method, sufficient conditions are derived to guarantee the stabilization of the closed‐loop semi‐Markovian jump time‐delay system with uncertainties and a prescribed performance index. Then, a codesign method for H_∞ controller gains and event‐triggered parameters is presented. Finally, simulations are given to verify the effectiveness of our improved dynamic event‐triggered scheme.     

Robust H-infinity filtering for time-delay systems with missing measurements: a parameter-dependent approach

Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method. Robust H-infinity filtering; Polytopic uncertainties; Missing measurements; Time-delays; Parameter dependent; Linear matrix inequalities (LMIs)     

Worst‐case stability and performance with mixed parametric and dynamic uncertainties

This work deals with computing the worst‐case stability and the worst‐case H_∞ performance of linear time‐invariant systems subject to mixed real‐parametric and complex‐dynamic uncertainties in a compact parameter set. Our novel algorithmic approach is tailored to the properties of the nonsmooth worst‐case functions associated with stability and performance, and this leads to a fast and reliable optimization method, which finds good lower bounds of μ. We justify our approach theoretically by proving a local convergence certificate. Because computing μ is known to be NP‐hard, our technique should be used in tandem with a classical μ upper bound to assess global optimality. Extensive testing indicates that the technique is practically attractive. Copyright © 2016 John Wiley & Sons, Ltd.     

Response analysis under stochastic loading in presence of structural uncertainties

The response of a structure with random parameters (e.g. stiffness, or damping coefficients) is investigated, when it is subjected to a random load. The structural behaviour can be either linear or non‐linear, but the forcing process has been assumed to be second‐order Gaussian. A modified series expansion is used to determine response statistics, in the various cases of a Duffing oscillator with random stiffness and damping coefficients being subjected to a deterministic sinusoidal force, a random amplitude sinusoidal force, a Kanai–Taijimi‐type earthquake. Copyright © 1999 John Wiley & Sons, Ltd.