一类线性时变大系统的运动稳定性

本文运用向量李雅普诺夫函数和比较原理的方法研究一类线性时变大系统的运动稳定性同时扩大了文[1]所研究的n阶常系数线性方程组和文[2]所研究的一类时变大系统的参数稳定性区域。     

An all-coefficient adaptive control method for a class of nonlinear time-varying systems

In this paper, the extension of the all-coefficient adaptive control method to nonlinear time-varying systems is studied. A novel discretizing method is first proposed to derive the discrete-time model for a class of nonlinear time-varying systems. The characteristics of the coefficients of the discrete-time model are derived by this method, based on which the all-coefficient adaptive control method is given for the class of nonlinear time-varying systems. Sufficient conditions on the closed-loop stability ...     

Inequality-Based Properties of Detectability and Stabilizability of Linear Time-Varying Systems in Discrete Time

Well-known properties of uniform detectability and uniform stabilizability are sharpened in terms of Lyapunov and Riccati inequalities for discrete-time linear time-varying systems. In particular, it is shown that the stabilizing output injection law can be taken to depend solely on a finite path of past and present system coefficients and the stabilizing state feedback law solely on a finite-path of present and future coefficients. These results are applied to time-varying systems where the system coefficients vary among a finite set, and lead to precise and computable convex conditions for the stability and dynamic-output-feedback stabilizability of such systems.      

控制方向未知的时变非线性系统鲁棒控制

针对一类具有未知时变控制方向、不确定时变参数以及未知时变有界干扰的严反馈非线性系统,给出一种带有死区修正算法的鲁棒控制方法.在控制系数符号未知的情况下,通过在反步法中引入Nussbaum增益和死区修正技术,得到一种修正的鲁棒反步设计方法.该方法不需要未知时变控制系数的上下界先验知识以及不确定参数和外界干扰的上界信息.算法保证了闭环系统所有信号的有界性,同时使得跟踪误差收敛于零的任意小邻域内.     

A neural network solution for fixed-final time optimal control of nonlinear systems

In this paper, fixed-final time optimal control laws using neural networks and HJB equations for general affine in the input nonlinear systems are proposed. The method utilizes Kronecker matrix methods along with neural network approximation over a compact set to solve a time-varying HJB equation. The result is a neural network feedback controller that has time-varying coefficients found by a priori offline tuning. Convergence results are shown. The results of this paper are demonstrated on an example.     

Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients

Presents a robust adaptive control approach for a class of time-varying uncertain nonlinear systems in the strict feedback form with completely unknown time-varying virtual control coefficients, uncertain time-varying parameters and unknown time-varying bounded disturbances. The proposed design method does not require any a priori knowledge of the unknown coefficients except for their bounds. It is proved that the proposed robust adaptive scheme can guarantee the global uniform ultimate boundedness of the closed-loop system signals and disturbance attenuation.     

Recursive design of finite-time convergent observers for a class of time-varying nonlinear systems

This paper considers the problem of designing globally finite-time convergent observers for a class of nonlinear systems with time-varying and output-dependent coefficients, which make the existing design approaches inapplicable. To solve this problem, a bottom-up design approach is first employed to recursively construct a finite-time convergent observer with time-varying coefficients for the nominal system. Then, using the homogeneous domination approach, we scale the finite-time convergent observer with an appropriate choice of gain for the original nonlinear system satisfying a Hölder condition. In addition, we show that the Hölder condition imposed on the nonlinearities can be removed for nonlinear systems with bounded trajectories.     

Time-varying reactivity reconstruction via Walsh functions

The problem of computing and reconstructing the time-varying reactivity input of nuclear reactor systems by using neutron level data records is considered. The integral equation representation of the nuclear reactor is used, and an expansion of the reactivity in a Walsh function series is made. The method provides simple formulas for computing the coefficients of this series. By using these coefficients and the Walsh functions provided by existing generators the time-varying reactivity can be easily reconstructed in a step-like form. A simple example shows the effectiveness of the method.     

Gabor transform of time-varying systems: exact representation andapproximation

Approximate modeling of discrete-time linear time-varying systems is studied based on a representation of linear systems in the Gabor time-frequency space. The time-varying system is assumed to be given in input-output or kernel representation. This representation has previously received attention because of its applicability in frozen-time analysis and design of optimal control for time-varying systems but requires a large number of coefficients. Motivated by its application to signal analysis, the Gabor transform is considered as a tool for the representation and approximation of linear time-variant systems. In order to show the main results, the class of systems considered is restricted to the one usually considered in the frozen-time approach. An example is included to illustrate the potential application of the technique     

Reply to remarks on the paper ‘A direct method for computing optimal feedback control for linear systems’

The method or generalized orthogonal polynomials (GOP) is applied to the analysis and optimal control of time-varying systems. The proposed GOP can represent all kinds of individual orthogonal-polynomial and non-orthogonal Taylor series. The operational matrix for the forward and backward integration of the generalized orthogonal polynomials, and the operational matrix of the product of r' and the generalized orthogonal-polynomial vector are derived and applied to time-varying systems. By using these three kinds of operational matrices, the computational algorithm for calculating the expansion coefficients is very simple and effective. Three satisfactory examples illustrate the usefulness of the method.     

Adaptive neural control for MIMO nonlinear systems with state time-varying delay

In this paper,adaptive neural control is proposed for a class of multi-input multi-output(MIMO)nonlinear unknown state time-varying delay systems in block-triangular control structure.Radial basis function(RBF)neural networks (NNs)are utilized to estimate the unknown continuous functions.The unknown time-varying delays are compensated for using integral-type Lyapunov-Krasovskii functionals in the design.The main advantage of our result not only efficiently avoids the controller singularity,but also relaxes the restriction on unknown virtual control coefficients.Boundedness of all the signals in the closed-loop of MIMO nonlinear systems is achieved,while The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories.The feasibility is investigated by two simulation examples.     

The exact model-matching problem for linear time-varying systems: an algebraic approach

The exact model-matching problem is formulated and solved for linear time-varying systems. The condition for the existence of a proper solution, which is well known in the time-invariant case, is proven here to still be valid in the time-varying case. The properness is characterized using the Smith-MacMillan form at infinity, recently defined by the authors for the transfer matrices with time-varying coefficients.     

Localization and parametrization of linear multidimensional control systems

We study the link existing between the parametrization of differential operators by potential-like arbitrary functions and the localization of differential modules, while applying these results to the parametrization of linear multidimensional control systems. We show that the localization of differential modules is a natural way to generalize some well-known results on transfer matrix, classically obtained by using Laplace transform, to time-varying ordinary differential control systems and to partial differential control systems with variable coefficients. In particular, we show that the parametrizations obtained by localization are simpler than those obtained by formal duality but are worse in the sense of Palamodov–Kashiwara's classification of differential modules.     

广义正交多项式用于时变延时线性系统的参数辨识

应用广义正交多项式(GOP)的展开式估计时变延时线性系统的参数.其基本思想是状 态函数和控制函数分别用有限多项广义正交多项式表示,利用GOP的运算矩阵,将时变延时 微分方程转化为用展开系数表示的线性方程组,通过输入输出数据,参数能够辨识.     

Implementation of an online DCT based time-varying delay estimator using systolic arrays

Time-delay estimation process is developed in the transform domain where discrete cosine transform (DCT) coefficients of time-varying delay signals are estimated. The DCT is very efficient in compacting the signal energy in a small number of coefficients. Hence, estimation of time-varying delay is obtained through calculation of small number of DCT coefficients. Online maximum likelihood estimator of time-varying delay is developed in which coefficients of the transformed delay signal are obtained by maximizing the likelihood function in terms of these DCT coefficients. A systolic array architecture is designed to implement the developed algorithm.     

Fixed-Final-Time-Constrained Optimal Control of Nonlinear Systems Using Neural Network HJB Approach

In this paper, fixed-final time-constrained optimal control laws using neural networks (NNS) to solve Hamilton-Jacobi-Bellman (HJB) equations for general affine in the constrained nonlinear systems are proposed. An NN is used to approximate the time-varying cost function using the method of least squares on a predefined region. The result is an NN nearly -constrained feedback controller that has time-varying coefficients found by a priori offline tuning. Convergence results are shown. The results of this paper are demonstrated in two examples, including a nonholonomic system.     

Parameter estimation of time-varying systems via Chebyshev polynomials of the second kind

A new method for the parameter estimation of linear time-varying systems using Chebyshev polynomials of the second kind is presented. The systems are characterized by linear differential equations with time-varying coefficients that are in the form of polynomials in the time variable. The operational matrices of integration and time-variable multiplication of Chebyshev polynomials of the second kind play key roles in the derivation of the algorithm. Least-squares estimation of overdetermined linear algebraic equations obtained from polynomial approximations of the systems is used to estimate the unknown parameters. Illustrative examples give satisfactory results     

Global output-feedback stabilization for a class of uncertain time-varying nonlinear systems

This paper investigates the global output-feedback stabilization for a class of uncertain time-varying nonlinear systems. The remarkable structure of the systems is the presence of uncertain control coefficients and unmeasured states dependent growth whose rate is inherently time-varying and of unknown polynomial-of-output, and consequently the systems have heavy nonlinearities, serious uncertainties/unknowns and serious time-variations. This forces us to explore a time-varying plus adaptive methodology to realize the task of output-feedback stabilization, rather than a purely adaptive one. Detailedly, based on a time-varying observer and transformation, an output-feedback controller is designed by skillfully combining adaptive technique, time-varying technique and well-known backstepping method. It is shown that, with the appropriate choice of the design parameters/functions, all the signals of the closed-loop system are bounded, and furthermore, the original system states globally converge to zero. It is worth mentioning that, the heavy nonlinearities are compensated by an updating law, while the serious unknowns and time-variations are compensated by a time-varying function. The designed controller is still valid when the system has an additive input disturbance which, essentially different from those studied previously, may not be periodic or bounded by any known constant.     

Automation of a hydroelectric power station using variable-structure control systems

This article presents the basis and conception of, and some experimental results obtained from, the automation of a hydroelectric power station. The principle of this automation, the purpose of which was to maximize the active power supplied by the station, requires a detailed analysis of the automatic water-gate control systems for the turbo-alternator sets. Because identification of these watergate systems proved tricky in view of the utilization conditions, their representation by a linear differential equation with widely time-varying coefficients emerges as a solution which is both realistic and convenient. In order to satisfy the constraints imposed, the controls for these systems may be synthetized by using the principles of variable-structure systems, the essential property of which is the insensitivity of performance to variations in the parameters of the controlled section. The general principles of variable structure control systems are presented and a procedure is given for the control law synthesis when the control action is restricted. Some experimental results of an automation system based on these algorithms are presented at the end of the article.     

控制方向未知的高次非线性系统的鲁棒自适应控制

研究了一类具有不可控不稳定线性化的非线性系统的自适应控制问题.该类系统的控制方向未知且含有不确定时变非线性参数.应用Nussbaum-type增益技术和adding a power integrator递推设计方法,设计了一种鲁棒自适应状态反馈控制器.所设计的控制器能够保证闭环系统的所有信号全局一致有界,且系统的状态渐近趋于零.除了假设未知参数及不确定性有界外,所设计的控制策略不需要控制系数的任何先验知识.仿真例子验证了算法的有效性.