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1.
This paper proposes a probabilistic fuzzy proportional - integral (PFPI) controller for controlling uncertain nonlinear systems. Firstly, the probabilistic fuzzy logic system (PFLS) improves the capability of the ordinary fuzzy logic system (FLS) to overcome various uncertainties in the controlled dynamical systems by integrating the probability method into the fuzzy logic system. Moreover, the input/output relationship for the proposed PFPI controller is derived. The resulting structure is equivalent to nonlinear PI controller and the equivalent gains for the proposed PFPI controller are a nonlinear function of input variables. These gains are changed as the input variables changed. The sufficient conditions for the proposed PFPI controller, which achieve the bounded-input bounded-output (BIBO) stability are obtained based on the small gain theorem. Finally, the obtained results indicate that the PFPI controller is able to reduce the effect of the system uncertainties compared with the fuzzy PI (FPI) controller.  相似文献   

2.
A linear matrix inequality based mixed H2-dissipative type state observer design approach is presented for smooth discrete time nonlinear systems with finite energy disturbances. This observer is designed to maintain H2 type estimation error performance together with either H∞ or a passivity type disturbance reduction performance in case of randomly varying perturbations in its gain. A linear matrix inequality is used at each time instant to find the time-varying gain of the observer. Simulation studies are included to explore the performance in comparison to the extended Kalman filter and a previously proposed constant gain observer counterpart.  相似文献   

3.
This paper is concerned with the problem of event-triggered dynamic output-feedback H∞ control for networked control system with sensor and actuator saturations. The event-triggered scheme combined with sensor saturation is first introduced to judge whether the newly sampled signal should be transmitted to the dynamic output-feedback controller or not. Under this scheme, the concurrent closed-loop system is first modeled as a control system with an interval time-varying delay and nonlinear items. Through constructing the Lyapunov–Krasovskii functional and employing linear matrix inequality approach, sufficient conditions for H∞ asymptotical stability are derived for the networked control system; furthermore, under the above stability condition, a dynamic output-feedback controller and the corresponding event-triggered parameters are co-designed through linear matrix inequality approach. Lastly, a numerical example is employed to prove the practical utility of this method.  相似文献   

4.
In this paper, the event-triggered non-fragile H∞ fault detection filter is designed for a class of discrete-time nonlinear systems subject to time-varying delays and channel fadings. The Lth Rice fading model is utilized to reflect the actual received measurement signals, and its channel coefficients own arbitrary probability density functions on interval [0,1]. The event-based filter is constructed to reduce unnecessary data transmissions in the communication channel, which only updates the measurement signal to the filter when the prespecified “event” is triggered. Multiplicative gain variations are utilized to describe the phenomenon of parameter variations in actual implementation of the filter. Based on Lyapunov stability theory, stochastic analysis technology along with linear matrix inequalities (LMIs) skills, sufficient conditions for the existence of the non-fragile fault detection filter are obtained which make the filtering error system stochastically stable and satisfy the H∞ constraint. The gains of the filter can be calculated out by solving the feasible solution to a certain LMI. A simulation example is given to show the effectiveness of the proposed method.  相似文献   

5.
This paper develops a robust state-feedback controller for active suspension system with time-varying input delay and wheelbase preview information in the presence of the parameter uncertainties. By employing system augmentation technique, a multi-objective control optimization model is first established and then this controller design is converted to a static full-state feedback controller design with robust H∞ and generalized H2 performance, wherein the model-dependent control gain is evaluated by transforming the related nonlinear matrix inequalities into their corresponding linear matrix inequality forms based on Lyapunov theory, and then LMI (Linear-Matrix-Inequality) technique is applied to solve and obtain the desired controller. A numerical simulation case is finally provided to reveal the effectiveness and advantages of the proposed controller.  相似文献   

6.
This paper investigates the problem of mean-square exponential stability for a class of discrete-time nonlinear singular Markovian jump systems with time-varying delay. The considered systems are with mode-dependent singular matrices Er(k)Er(k). By using the free-weighting matrix method and the Lyapunov functional method, delay-dependent sufficient conditions which guarantee the considered systems to be mean-square exponentially stable are presented. Finally, some numerical examples are employed to demonstrate the effectiveness of the proposed methods.  相似文献   

7.
《Journal of The Franklin Institute》2019,356(18):11561-11580
This paper addresses the robust H∞ filter design problem for a class of uncertain fuzzy neutral stochastic system with time-delay through Takagi–Sugeno (T–S) fuzzy model. By constructing an augmented Lyapunov–Krasovskii functional, some novel delay-dependent stability criteria for uncertain fuzzy neutral stochastic system with time varying delay are obtained in terms of linear matrix inequalities. By using the integral inequality in the neutral stochastic setting combined with delay decomposition approach, the H∞ fuzzy filter is designed to guarantee the corresponding filtering error systems robustly asymptotically stable with a specified H∞ performance index. At last, two numerical examples are presented to show the less conservatism than the previous results.  相似文献   

8.
This paper deals with the problems of non-fragile robust stochastic stabilization and robust H∞ control for uncertain stochastic nonlinear time-delay systems. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in both state and input matrices. The time-delay is unknown and time-varying with known bounds. The non-fragile robust stochastic stabilization problem is to design a memoryless non-fragile state feedback controller such that the closed-loop system is robustly stochastically stable for all admissible parameter uncertainties. The purpose of robust H∞ control problem, in addition to robust stochastical stability requirement, is to reduce the effect of the disturbance input on the controlled output to a prescribed level. Using the Lyapunov functional method and free-weighting matrices, delay-dependent sufficient conditions for the solvability of these problems are established in terms of linear matrix inequality (LMI). Numerical example is provided to show the effectiveness of the proposed theoretical results.  相似文献   

9.
This paper studies the finite-time guaranteed cost control problem for switched nonlinear stochastic systems with parameter uncertainties and time-varying delays. By choosing a model-dependent and delay-dependent Lyapunov-Krasovskii functional, applying the average dwell time approach and the Gronwall inequality, some novel sufficient conditions are derived to ensure that the switched nonlinear stochastic closed-loop system is finite-time stochastically stable and an upper bound is given on the performance index. The obtained nonlinear matrix is transformed into a linear matrix form, and then the feedback controller gains of the switched nonlinear stochastic systems with time-varying delay are obtained. Finally, two simulation examples are designed to verify the effectiveness of the suggested approach.  相似文献   

10.
This paper discusses the problem of H∞ finite time control for a discrete time-varying system with interval time-varying delay. By constructing a new augmented time-varying Lyapunov functional involving triple summation items and using discrete Wirtinger-type inequalities, delay-dependent conditions are derived, which guarantee that the closed-loop system is not only finite time bounded (FTB) but also satisfies an H∞ performance. Furthermore, the time-varying feedback controller can be derived by solving a series of recursive linear matrix inequalities (RLMIs). Simulation results show the effectiveness and superiority of the proposed method.  相似文献   

11.
This paper concerns the simultaneous fault detection and control (SFDC) problem for a class of nonlinear stochastic switched systems with time-varying state delay and parameter uncertainties. The switching signal of detector/controller unit (DCU) is assumed to be with switching delay, which results in the asynchronous switching between the subsystems and DCU. By constructing a switching strategy depending on the state and switching delays, new sufficient conditions expressed by a set of linear matrix inequalities (LMIs) is derived to design DCU gains. This problem is formulated as an H∞ optimization problem and both mean square exponential stability and fault detection of augmented system are considered. A numerical example is finally exploited to verify the effectiveness and potential of the achieved scheme.  相似文献   

12.
In this paper, the problem of robust H∞ filtering for uncertain systems with time-varying distributed delays is considered. The uncertainties under discussion are time varying but norm bounded. Based on the Lyapunov stability theory, sufficient condition for the existence of full order H∞ filters is proposed by linear matrix inequality (LMI) approach such that the filtering error system is asymptotically sable and satisfies a prescribed attenuation level of noise. A numerical example is given to demonstrate the availability of the proposed method.  相似文献   

13.
This paper concerns the problem of designing a robust observer-based modified repetitive-control system with a prescribed H∞ disturbance rejection level for a class of strictly proper linear plants with unknown aperiodic disturbances and time-varying structural uncertainties. A correction to the amount of the delay in the repetitive controller is introduced that leads to a significant improvement in tracking performance. An integrated performance index is defined to quantify the overall effect of rejecting the aperiodic disturbances and tracking the periodic reference input. A Lyapunov functional with two tuning parameters is used to derive a linear-matrix-inequality based robust stability condition for the system with a prescribed disturbance-rejection bound. Combining the performance indices, an optimization algorithm that searches for the best combination of state-observer gain and the feedback control gains is developed. A numerical example illustrates the design procedure and demonstrates the effectiveness of the method.  相似文献   

14.
In this paper, the composite anti-disturbance resilient control is considered for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters under multiple disturbances. Three kinds of disturbances are included in the studied system. One is generated by an external system and it enters the hybrid system from the channel of the control input. The other one is stochastic white noise. And the third one is the external unknown time-varying disturbance and it is supposed to be H2 norm bounded. By combining the disturbance-observer-based-control scheme, H∞ control technique and resilient control method, a composite anti-disturbance resilient controller is constructed to attenuate and eliminate the affection of these disturbances, and ensures the whole closed-loop system regular, impulse free and stochastically stable with the corresponding control performance. Then, some sufficient conditions and the gains of the controller and observer are obtained by using Lyapunov function method and the linear matrix inequalities (LMIs) technique. Finally, two numerical examples are given to show the effectiveness of presented method.  相似文献   

15.
This paper is concerned with the non-fragile dynamic output feedback control for uncertain T–S fuzzy systems with time-varying delay and randomly occurring gain variations (ROGVs). Considering the imperfect premise matching that the T–S fuzzy model and the fuzzy controller do not have the same membership function, the purpose is to enhance the robustness of the system and the flexibility of the controller design. By adjusting the free weight matrix in the concept of extended dissipative, H∞, L2−L∞, passive and (Q, S, R)-dissipative performance are solved in a unified framework. Stochastic phenomenon ROGVs is considered to describe the impact of the controller gain variations in the system, which is designed into two sequences of random variables and obey the Bernoulli distribution. Based on Lyapunov–Krasovskii functional (LKF) and integral inequality technique, some less conservative sufficient conditions are obtained to guarantee the close-loop system is asymptotically stable and extended dissipative. By solving the linear matrix inequalities (LMIs), a non-fragile dynamic output feedback controller can be developed. The advantage and effectiveness of the proposed design method can be illustrated by several numerical examples.  相似文献   

16.
In traditional analysis of system performance, Markovian jump system is often considered in the full frequency domain. However, some unknown factors, such as noise interference, often act on a specific frequency domain, so there is a big defect in putting the system analysis in the full frequency domain. In this paper, the finite frequency domain is introduced into the Markovian jump system. By using generalized KYP lemma, the system is divided into three frequency bands: low, medium and high. The disturbance in different frequency domain is analyzed and the H∞ filter is designed. In addition, in dealing with inequality relations, the improved Wirtinger inequality method is used, and the Projection lemma is used in dealing with filter coupling terms, and time-varying delay problem in finite frequency domain is also considered. Finally, some examples are given to illustrate the effectiveness of our methods and the specific parameters and convergence graph of the finite frequency domain filter are obtained.  相似文献   

17.
This paper is concerned with the stability analysis of linear systems with time-varying delays. First, by introducing the quadratic terms of time-varying delays and some integral vectors, a more suitable Lyapunov-Krasovskii functional (LKF) is constructed. Second, two new delay-dependent estimation methods are developed in the stability analysis of linear system with time-varying delays, which include a reciprocally convex matrix inequality and an integral inequality. More information about time-varying delays and more free matrices are introduced into the two estimation approaches, which play a key role for obtaining an accurate upper bound of the integral terms in time derivative of LKFs. Third, based on the novel LKFs and new estimation approaches, some less conservative criteria are derived in the form of linear matrix inequality (LMI). Finally, three numerical examples are applied to verify the advantages and effectiveness of the newly proposed methods.  相似文献   

18.
This paper is concerned with the robust H∞ control problem for a general class of uncertain nonlinear systems with mixed time-delays. The mixed time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is robustly stable for all admissible uncertainties with guaranteed H∞ disturbance rejection attenuation level. By introducing a new Lyapunov–Krasovskii functional that reflects the mixed delays, sufficient conditions are established for the closed-loop system ensuring the robust stability as well as the H∞ performance requirement. The controller design is facilitated in terms of the solvability of a Hamilton–Jacobi inequality. Two numerical examples are utilized to demonstrate the effectiveness of the proposed methods.  相似文献   

19.
This paper gives a general review of the Theory of Nonlinear Systems. In 1960, the author presented a paper “Theory of Nonlinear Control” at the First IFAC Congress at Moscow. Professor Norbert Wiener, who attended this Congress, drew attention to his work on the synthesis and analysis of nonlinear systems in terms of Hermitian polynomials in the Laguerre coefficients of the past of the input.Wiener's original idea was to use white noise as a probe on any nonlinear system. Applying this input to a Laguerre network gives u1, u2,…, us, and then to a Hermite polynomial generator gives V(α)'s. Applying the same input to the actual nonlinear system gives output c(t). Putting c(t) and V(α)'s through a product averaging device, we get c(t)V(α) = Aα2лs2, where the upper bar denotes time average and Aα's can be considered as characteristic coefficients of the nonlinear system. A desired output z(itt) may replace c(itt) to get a new set of Aα's.The Volterra functional method suggested by Wiener in 1942 has been greatlydeveloped from 1955 to the present. The method involves a multi-dimensional convolution integral with multi- dimensional kernels. The associated multi-dimensional transforms are given by Y.H. Ku and A.A. Wolf (J. Franklin Inst., Vol. 281, pp. 9–26, 1966). Wiener extended the Volterra functionals by forming an orthogonal set of functionals known as G-functionals, using Gaussian white noise as input. Volterra kernels and Wiener kernels can be correlated and form the characteristic functions of nonlinear systems.From an extension of the linear system to the nonlinear system, the input-output crosscorrelation φxy can be shown to be equal to the convolution of system impulse response h1 with the autocorrelation φxx. Using the white noise as input, where its power density spectrum is a constant, say, A, the crosscorrelation is given by φxy(σ) = Ah1(σ), while the autocorrelation is φxx(τ) = Au(τ). This extension forms the basis of an optimum method for nonlinear system identification. Measurement of kernels can be made through proper circuitry.Parallel to the Volterra series and the Wiener series, another series based on Taylor-Cauchy transforms developed since 1959 are given for comparison. The Taylor-Cauchy transform method can be applied in the analysis of simultaneous nonlinear systems. It is noted that the Volterra functional method and the Taylor-Cauchy transform method give identical final results.A selected Bibliography is appended not only to include other aspects of nonlinear system theory but also to show the wide application of nonlinear system characterization and identification to problems in biology, ecology, physiology, cybernetics, control theory, socio- economic systems, etc.  相似文献   

20.
In this paper, a new approach to robust H∞ filtering for a class of nonlinear systems with time-varying uncertainties is proposed in the LMI framework based on a general dynamical observer structure. The nonlinearities under consideration are assumed to satisfy local Lipschitz conditions and appear in both state and measured output equations. The admissible Lipschitz constants of the nonlinear functions are maximized through LMI optimization. The resulting H∞ observer guarantees asymptotic stability of the estimation error dynamics with prespecified disturbance attenuation level and is robust against time-varying parametric uncertainties as well as Lipschitz nonlinear additive uncertainty.  相似文献   

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