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1.
This paper considers the problem of sliding mode control for discrete-time stochastic systems with parameter uncertainties and state-dependent noise perturbation. An integral-like sliding surface is chosen and a discrete-time sliding mode controller is designed. The key feature in this work is that both the reachability of the quasi-sliding mode and the stability of system states are simultaneously analyzed, due to the existence of state-dependent noise perturbation. By utilizing an Lyapunov function involving system states and sliding mode variables, the sufficient condition for reachability is obtained. Finally, numerical simulation results are provided.  相似文献   

2.
We consider the leader–follower consensus problem for a multi-agent system where information is exchanged only on a non-uniform discrete stochastic time domain. For a second-order multi-agent system subject to intermittent information exchange, we model the tracking error dynamics as a μ?varying linear system on a discrete stochastic time scale, where μ is the graininess operator. Based on a Lyapunov operator and a positive perturbation operator on the space of symmetric matrices, we derive necessary and sufficient conditions to design a decentralized consensus protocol. This protocol allows us to cast the mean-square exponential consensus problem within the framework of dynamic equations on stochastic time scales. We establish some theoretical results which allow for the computation of the control gain matrix which guarantees the mean-square exponential stability with a given decay rate for the error dynamics. To show the effectiveness of the theoretical results, some simulation and experimental results on multi-robot systems have been performed.  相似文献   

3.
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4.
Finite-time stability concerns the boundness of system during a fixed finite-time interval. For switched systems, finite-time stability property can be affected significantly by switching behavior; however, it was neglected by most previous research. In this paper, the problems of finite-time stability analysis and stabilization for switched nonlinear discrete-time systems are addressed. First, sufficient conditions are given to ensure a class of switched nonlinear discrete-time system subjected to norm bounded disturbance finite-time bounded under arbitrary switching, and then the results are extended to H∞ finite-time boundness of switched nonlinear discrete-time systems. Finally based on the results on finite-time boundness, the state feedback controller is designed to H∞ finite-time stabilize a switched nonlinear discrete-time system. A numerical design example is given to illustrate the proposed results within this paper.  相似文献   

5.
This work is devoted to the study of symmetric control systems. It establishes a relation between internal symmetry and external one for a linear invariant control system having n real simple poles. The symmetric stabilization problem is studied using a symmetric feedback gain such that the output control stabilizes the closed-loop system. A necessary and sufficient condition is given to solve this stabilization problem for a symmetric control system (A,B,C) and a generalized symmetric control system (E,A,B,C).  相似文献   

6.
A quantitative stability analysis of the Carson-Cambi equation [(1 + ε cos t)(d2y/dt2) + py = 0] is carried through, using a new, effective approach. The results are compared with a recent perturbation analysis, and show that this should not be used for ε0.4. In the present analysis we go up to ε = 0.8, and, in fact, with less effort than the perturbation analysis involves. Detailed stability diagrams are presented.  相似文献   

7.
This paper presents the central finite-dimensional H∞ filter for nonlinear polynomial systems with multiplicative noise, that is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H∞ filtering problem to the corresponding optimal H2 filtering problem, using the technique proposed in [1]. The paper presents the central suboptimal H∞ filter for the general case of nonlinear polynomial systems with multiplicative noise, based on the optimal H2 filter given in [31]. The central suboptimal H∞ filter is also derived in a closed finite-dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H∞ filters available for polynomial systems with state-independent noise and the corresponding linearized system.  相似文献   

8.
The paper is concerned with the modeling and stabilization problem of networked control systems under simultaneous consideration of bounded packet dropouts and occasionally missing control inputs. In particular, the focus of the paper is to capture the case where the packet dropouts and control inputs missing are subject to multiple sampling periods, and not periodic as in existing results. By input-delay approach and then fully considering the probability distribution characteristic of packet dropouts in the modeling, the original linear system is firstly transformed to a switched stochastic time-delay system. Meanwhile, the probability distribution values of stochastic delay taking values in m(m ≥ 2) given intervals can be explicitly obtained, which is of vital importance to analyse the stabilization problem of considered system. Secondly, by means of the average dwell time technique, some sufficient conditions in terms of linear matrix inequalities for the existence of desired stabilizing controller are derived. Finally, an illustrative example is given to illustrate the effectiveness of the proposed stabilizing controller and some less conservative results are obtained.  相似文献   

9.
There are many hybrid stochastic differential equations (SDEs) in the real-world that don’t satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of pth moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory.  相似文献   

10.
In this paper we consider a class of fractional order linear time invariant (FO-LTI) interval systems with linear coupling relationships among the fractional order, the system matrix and the input matrix. We present the sufficient conditions for the robust stability and stabilization of such coupling FO-LTI interval systems with the fractional order α satisfying 0<α<1. All the results are proposed in terms of linear matrix inequalities (LMI). Two numerical examples show that our results are effective for checking the robust asymptotical stability and designing the stabilizing controller for FO-LTI interval systems.  相似文献   

11.
This paper is concerned with the observer-based H∞ finite-time control problem for linear parameter-varying (LPV) systems with parameter-varying time delays and external disturbance. The main contribution is to design an observer-based H∞ finite-time controller such that the resulting closed-loop system is uniformly finite-time bounded and satisfies a prescribed H∞ disturbance attenuation level in a finite-time interval. By using the delay- and parameter-dependent multiple Lyapunov–Krasovskii functional approach, sufficient criteria on uniform H∞ finite-time stabilization via observer-based state feedback are presented for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the validity of the proposed theoretical results.  相似文献   

12.
This paper investigates the H∞ performance of two-dimensional (2-D) switched system represented by Fornasini–Marchesini local state-space (FMLSS) model with maximum and minimum dwell time approach. By using the multiple Lyapunov function approach, and designing a set of switching signals subject to maximum and minimum dwell time characteristic, respectively, for all stable subsystems or both stable and unstable subsystems exist, we give the sufficient condition on exponential stability of the given switched system, and propose the sufficient condition which can guarantee that the given switched system is exponentially stable and has a specified H∞ disturbance attenuation level γ. All the results obtained are on normal noise attenuation index of strictly non-weighted form, which are better than the existing results on weak one of weighted form from the physical point of view. Finally, numerical examples are presented to display the effectiveness of the proposed results.  相似文献   

13.
In this paper, the problem of H∞ filtering for neutral systems with mixed time-varying delays and nonlinear perturbations is investigated. Some new delay-dependent sufficient conditions are presented to ensure that the filtering error system is asymptotically stable with a prescribed level of H∞ noise attenuation. In addition, the design procedures for the existence of such filter are presented in terms of a set of linear matrix inequalities (LMIs). Slack variables and convex combination technique are adopted to reduce the conservatism of obtained results. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method.  相似文献   

14.
This paper presents an adaptive robust control strategy based on a radial basis function neural network (RBFNN) and an online iterative correction method (OICM) for a planar n-link underactuated manipulator with a passive first joint to realize its position control objective. An uncertain model of the planar n-link underactuated manipulator is built, which contains the parameter perturbation and the external disturbance. The adaptive robust controllers based on the RBFNN are designed to realize the model reduction, which makes the system reduce to a planar virtual three-link underactuated manipulator (PVTUM) and simplifies the complexity of the system control. An online differential evolution (DE) algorithm is used to calculate the target angles of the PVTUM based on the nominal model parameters. The control of the PVTUM is divided into two stages, and the adaptive robust controllers are still employed to realize the control objective of each stage. Then, the OICM is used to correct the deviations of all link angles of the PVTUM caused by the parameter perturbation, which makes the end-point of the system gradually approach to its target position. Finally, simulation results of a planar four-link underactuated manipulator demonstrate the effectiveness of the proposed adaptive robust control strategy.  相似文献   

15.
This paper investigates the finite-time control problems for a class of discrete-time nonlinear singular systems via state undecomposed method. Firstly, the finite-time stabilization problem is discussed for the system under state feedback, and a finite-time stabilization controller is obtained. Then, based on which, the finite-time H∞ boundedness problem is studied for the system with exogenous disturbances. Finally, an example of population distribution model is presented to illustrate the validity of the proposed controller. Because there is no any constraint for singular matrix E in the paper, controllers can be designed for more discrete-time nonlinear singular systems.  相似文献   

16.
A numerical modeling of natural convection under the influence of either axial (Bz) or radial (Br) magnetic field in a cylindrical configuration filled with a low-Prandtl number electrically conducting fluid, is studied. The finite volume method is used to discretize the equations of continuity, Navier Stokes and energy. A computer program based on the SIMPLER algorithm is developed. The flow and temperature fields are presented by stream function and isotherms, respectively. Stability diagrams are established according to the numerical results of this investigation. These diagrams put in evidence the dependence of the critical Grashof number, Grcr with the increase of the Hartmann number, Ha. The strongest stabilization of the convective flows occurs when the magnetic field is applied in the radial direction. This study confirms the possibility of stabilization of a liquid metal flow in natural convection by application of a radial magnetic field.  相似文献   

17.
In this paper, a new approach to non-parametric signal detection with independent noise sampling is presented. The present approach is based on the locally asymptotically optimum (LAO) methodology, which is valid for vanishingly small signals and very large sample sizes, and on semi-parametric statistics. Its unique feature and essential difference from other techniques is that LAO non-parametric detectors are optimum according to the Neyman-Pearson criterion by being asymptotically uniformly most powerful at false alarm level α (AUMP (α)) and adaptive in the sense that no loss in Fisher's information number is incurred when the underlying noise process is no longer parametrically defined. Accordingly, they are robust against deviations from the postulated noise model and, unlike other non-parametric detectors, are distribution-free under both hypotheses H0 (“noise only present”) and H1 (“signal and noise present”). Non-parametric LAO detectors are derived from an asymptotic stochastic expansion of the log-likelihood ratio for coherent and narrowband incoherent “on-off” signals. Moreover, under the present framework it is shown that, in direct contrast to already known results, the non-parametric sign detector is AUMP (α) and adaptive even for non-constant signal samples.  相似文献   

18.
In this paper, an analytic solution of nonlinear H∞ robust controller is first proposed and used in a complete six degree-of-freedom nonlinear equations of motion of flight vehicle system with mass and moment inertia uncertainties. A special Lyapunov function with mass and moment inertia uncertainties is considered to solve the associated Hamilton-Jacobi partial differential inequality (HJPDI). The HJPDI is solved analytically, resulting in a nonlinear H∞ robust controller with simple proportional feedback structure. Next, the control surface inverse algorithm (CSIA) is introduced to determine the angles of control surface deflection from the nonlinear H∞ control command. The ranges of prefilter and loss ratio that guarantee stability and robustness of nonlinear H∞ flight control system implemented by CSIA are derived. Real aerodynamic data, engine data and actuator system of F-16 aircraft are carried out in numerical simulations to verify the proposed scheme. The results show that the responses still keep good convergence for large initial perturbation and the robust stability with mass and moment inertia uncertainties in the permissible ranges of the prefilter and loss ratio for which this design guarantees stability give same conclusion.  相似文献   

19.
In this paper, the issue about the stationary distribution for hybrid multi-stochastic-weight coupled networks (HMSWCN) via aperiodically intermittent control is investigated. Specially, when stochastic disturbance gets to zero, the exponential stability in pth moment for hybrid multi-weight coupled networks (HMWCN) is considered. Under the framework of the Lyapunov method, M-matrix and Kirchhoff’s Matrix Tree Theorem in the graph theory, several sufficient conditions are derived to guarantee the existence of a stationary distribution and exponential stability. Different from previous work, the existing area of a stationary distribution is not only related to the topological structure of coupled networks, but also aperiodically intermittent control (the rate of control width and control duration). Subsequently, as an application to theoretical results, a class of hybrid multi-stochastic-weight coupled oscillators is studied. Ultimately, numerical examples are carried out to demonstrate the effectiveness of theoretical results and effects of the control schemes.  相似文献   

20.
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   

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