Robust H∞ output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions

The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearched. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function.Then,based on the characterization,a linear matrix inequality (LMI)approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system.A numerical example is presented to demonstrate the application of the proposed method.     

Fault Detection for Uncertain Delta Operator Systems with Two-Channel Packet Dropouts via a Switched Systems Approach

This paper utilizes a switched systems approach to deal with the problem of fault detection(FD) for uncertain delta operator networked control systems(NCSs) with packet dropouts and timevarying delays. Uncertainties exist in the matrices of the systems and are norm-bounded time-varying.Two parts of packet dropouts are considered in this paper: From sensors to controllers, and from controllers to actuators. Two independent Bernoulli distributed white sequences are introduced to account for packet dropouts. Then an FD filter is designed under an arbitrary switching law. Furthermore, the sufficient conditions for the NCSs under consideration that are exponentially stable in the mean-square sense and satisfy H∞ performance are obtained in terms of linear matrix inequalities(LMIs), multiple Lyapunov functions(MLF) and average dwell-time(ADT) approach. The explicit expression of the desired filter parameters is given. Finally, a numerical example verifies the effectiveness of the proposed method.     

Neural network-based H∞ filtering for nonlinear systems with time-delays

A novel H∞ design methodology for a neural network-based nonlinear filtering scheme is addressed. Firstly, neural networks are employed to approximate the nonlinearities. Next, the nonlinear dynamic system is represented by the mode-dependent linear difference inclusion （LDI）. Finally, based on the LDI model, a neural network-based nonlinear filter （NNBNF） is developed to minimize the upper bound of H∞ gain index of the estimation error under some linear matrix inequality （LMI） constraints. Compared with the existing nonlinear filters, NNBNF is time-invariant and numerically tractable. The validity and applicability of the proposed approach are successfully demonstrated in an illustrative example.     

基于粒子群算法的开关系统最优控制问题的数值算法

针对开关系统,给出了数学模型并引出了其最优控制问题,提出开关系统最优控制问题的加权粒子群算法,给出了相关的推理过程及算法步骤。加权粒子群算法不必找出支付泛函关于时间的显式表达,就可以找到其最优解,同样适用于其子系统为非线性的情形。分析了粒子群算法快速全局优化的特点,说明该算法能找到优化问题的全局最优解。以开关动态系统和一般开关线性二次问题的数值算例验证了该方法的有效性。     

Functional coefficient autoregressive conditional root model

This paper proposes an extended model based on ACR model:Functional coefficient autoregressive conditional root model（FCACR）.Under some assumptions,the authors show that the process is geometrically ergodic,stationary and all moments of the process exist.The authors use the polynomial spline function to approximate the functional coefficient,and show that the estimate is consistent with the rate of convergence O_p(h^v+1+n^-1/3).By simulation study,the authors discover the proposed method can approximate well the real model.Furthermore,the authors apply the model to real exchange rate data analysis.     

Regression Analysis of Interval-Censored Data with Informative Observation Times Under the Accelerated Failure Time Model

This paper discusses regression analysis of interval-censored failure time data arising from the accelerated failure time model in the presence of informative censoring. For the problem, a sieve maximum likelihood estimation approach is proposed and in the method, the copula model is employed to describe the relationship between the failure time of interest and the censoring or observation process. Also I-spline functions are used to approximate the unknown functions in the model, and a simulation study is carried out to assess the finite sample performance of the proposed approach and suggests that it works well in practical situations. In addition, an illustrative example is provided.

     

A novel approach to characterizing hesitations in intuitionistic fuzzy numbers

Building upon the concept of D_a operator introduced by Atanassov(1989),this article proposes an improved objective approach and a hybrid approach to operationalize D_a so that the hesitation in an intuitionistic fuzzy number(IFN) can be further refined and characterized.Numerical experiments are carried out to demonstrate the features and novelty of the proposed approach compared to existing methods in the literature.The aim is to furnish an effective way to refine hesitations in intuitionistic fuzzy assessments for more reliable and confident decision aids.     

Admissibility analysis and control synthesis for switched linear singular systems

The problem of admissibility analysis and control synthesis of discrete-time switched linear singular (SLS) systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities (LMIs). Based on the admissibility results, control synthesis is then to design switched state feedback and static output feedback controllers, guaranteeing that the resulting closed-loop system is admissible. The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.     

H ∞ filtering for continuous-time systems with pointwise time-varying delay

The problem of H_∞filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper.By applying an innovation analysis in Krein space,a necessary and sufficient condition for the existence of an H_∞filter is derived in two methods:One is the partial differential equation approach,the other is the reorganized innovation analysis approach.The former gives a solution to the proposed H_∞filtering problem in terms of the solution of a partial differential equation with boundary conditions.The later gives an analytical solution to the proposed H_∞filtering problem in terms of the solutions of Riccati and matrix differential equations.     

Robust exponential stability of switched interval interconnected systems with unbounded delay

In this paper, a class of switched interval interconnected systems with unbounded delay were investigated. On the assumption that the interconnected functions of the systems satisfied the global Lipschitz condition, by using vector Lyapunov methods and M-matrix theory, the integrodifferential inequalities with unbounded delay were constructed. By the stability analysis of the integrodifferential inequalities, the sufficient conditions to ensure the robust exponential stability of the interval interconnected systems were obtained. By using average dwell time approach, conditions for guaranteeing the robust exponential stability of the switched delay interval interconnected systems were derived. Finally, two numerical examples were given to illustrate the correction and effectiveness of the proposed theory.     

New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

This paper deals with H_∞ control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities(LMIs) approach. Then, by introducing a new concepts of H_∞ control problem for nonlinear conformable fractional order systems, the authors study H_∞ performance analysis and H_∞ state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H_∞ performance γ. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H_∞performance γ. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.     

Design of unknown input observer with H∞ performance for linear time-delay systems

A unknown input observer (UIO) design for a class of linear time-delay systems when the observer error can't completely decouple from unknown input is dealt with. A sufficient condition to its existence is presented based on Lyapunov stability method Design problem of the proposed observer is formulated in term of linear matrix inequalities. Two design problems of the observer with internal delay and without internal delay are formulated Based on H_∞ control theory in time-delay systems, the proposed observer is designed in term of linear matrix inequalities (LMI). A design algorithm is proposed The effective of the proposed approach is illustrated by a numerical example     

The adaptive LASSO spline estimation of single-index model

In this paper, based on spline approximation, the authors propose a unified variable selection approach for single-index model via adaptive L ₁ penalty. The calculation methods of the proposed estimators are given on the basis of the known lars algorithm. Under some regular conditions, the authors demonstrate the asymptotic properties of the proposed estimators and the oracle properties of adaptive LASSO (aLASSO) variable selection. Simulations are used to investigate the performances of the proposed estimator and illustrate that it is effective for simultaneous variable selection as well as estimation of the single-index models.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for nonlinear stochastic Markov systems with time-delay and multiplicative noise

This paper is concerned with the H_∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input- and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities (HJIs), the exponential mean square H_∞ controller design of delayed nonlinear stochastic Markov systems is presented. Secondly, by using fuzzy T-S model approach, the H_∞ controller can be designed via solving a set of linear matrix inequalities (LMIs) instead of HJIs. Finally, two numerical examples are provided to show the effectiveness of the proposed design methods.     

Stabilization of the quadruple inverted pendulum by variable universe adaptive fuzzy controller based on variable gain H ∞ regulator

In this paper,the variable universe adaptive fuzzy controller based on variable gain H_∞ regulator(VGH_∞ R.) is designed to stabilize a quadruple inverted pendulum.The VGH_∞ R is a novel robust gain-scheduling approach.By utilizing VGH_∞ R technique,a more precise real-time feedback gain matrix,which is changing with states,is obtained.Via the variable gain matrix 10 state variables of quadruple inverted pendulum are transformed into a kind of synthesis error(E) and synthesis rate of change of error(EC) at sampling time.Therefore,the dimension of the multivariable system is reduced and the variable Universe adaptive fuzzy controller is built.Experiments illustrate the effectiveness of the proposed control scheme.     

分布参数切换系统的建模及仿真方法

讨论分布参数切换系统的建模与仿真问题.运用算子半群理论建立了分布参数切换系统的发展方程模型,并设计了系统仿真的方法.对于切换律与系统状态相关时切换律难以得出数值解的情况,运用广义正交多项式求出系统的逼近切换律,进而完成系统的仿真.最后,通过两个仿真实例,验证文中提出方法的可行性和有效性.     

Fuzzy Static Output Feedback <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Control for Nonlinear Systems Subject to Parameter Uncertainties

This study is concerned with the stabilization issue of nonlinear systems subject to parameter uncertainties. An interval type-2 T-S fuzzy model is used to represent the nonlinear systems subject to parameter uncertainties. An interval type-2 fuzzy static output feedback controller is designed to synthesize the interval type-2 T-S fuzzy systems. The membership-function-dependent stability conditions are derived by utilizing the information of upper and lower membership functions. The proposed stability conditions are presented in the form of linear matrix inequalities (LMIs). LMI-based stability conditions for interval type-2 fuzzy static output feedback H_∞ control synthesis are also developed. Several simulation examples are given to show the superiority of the proposed approach.     

Robust H∞ output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions

The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearched. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function.Then,based on the characterization,a linear matrix inequality (LMI)approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system.A numerical example is presented to demonstrate the application of the proposed method.     

Robust Stabilization of Non-minimum Phase Switched Nonlinear Systems with Uncertainty

This paper investigates the problem of robust stabilization of a class of switched nonlinear system with uncertain dynamics where each subsystem represents a non-minimum phase. The authors first construct a stabilizing sliding mode controller for each subsystem to stabilize individually its own unstable internal dynamics. Then, a switching strategy is introduced to select the most appropriate diffeomorphism through an infinity of diffeomorphisms. Sufficient conditions are specifically given for the exponential stability and the exponential upper bound of the trajectory of the switched subsystem,which guarantees the global asymptotical stability of the resulting switched system. Obviously, the proposed control approach can improvemore the transient state, compared to a feedback linearization based on only one diffeomorphism. Simulation studies illustrate the effectiveness of the suggested approach.     

Exponential L_1 Filtering of Networked Linear Switched Systems: An Event-Triggered Approach

The issues of event-triggered exponential L_1 filtering are studied for a class of networked linear switched systems. An event-triggered mechanism is proposed to enhance resource utilization in transmission, and save the communication cost of systems as well. Then, the filtering error system is reconstructed as a switched delay system with bounded disturbance through the input delay system approach. By resorting to the Lyapunov-Krasovskii functional approach and the average dwell time(ADT) technique, some interesting results are derived to guarantee the exponential stability with a prescribed L_1 disturbance rejection level. Further, an event-triggered exponential L_1 filter is designed via solving a set of feasible linear matrix inequalities(LMIs). Finally, the efficiency of the proposed results is verified through a numerical example and a PWM-driven boost converter circuit system.