Lyapunov‐stable discrete‐time model reference adaptive control

Discrete‐time model reference adaptive control (MRAC) is considered with both least squares and projection algorithm parameter identification. For both cases complete Lyapunov proofs are given for stability and convergence. The results extend the approach of Johansson (Int. J. Control 1989; 50 (3):859–869) to include Lyapunov stability for MRAC when the normalized projection algorithm is used for parameter identification. Copyright © 2005 John Wiley & Sons, Ltd.     

Cellular neural network with trapezoidal activation function

This paper presents a cellular neural network (CNN) scheme employing a new non‐linear activation function, called trapezoidal activation function (TAF). The new CNN structure can classify linearly non‐separable data points and realize Boolean operations (including eXclusive OR) by using only a single‐layer CNN. In order to simplify the stability analysis, a feedback matrix W is defined as a function of the feedback template A and 2D equations are converted to 1D equations. The stability conditions of CNN with TAF are investigated and a sufficient condition for the existence of a unique equilibrium and global asymptotic stability is derived. By processing several examples of synthetic images, the analytically derived stability condition is also confirmed. Copyright © 2005 John Wiley & Sons, Ltd.     

Nonpathological Lyapunov functions and discontinuous Carathéodory systems

Differential equations with discontinuous right-hand side and solutions intended in Carathéodory sense are considered. For these equations, sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle is also proven.     

Adaptive tracking control of manipulators: Theory and experiments

This paper considers the trajectory tracking problem for uncertain robot manipulators and proposes two adaptive controllers as solutions to this problem. The first controller is derived under the assumption that the manipulator state is measurable, while the second strategy is developed for those applications in which only position measurements are available. The adaptive schemes are very general and computationally efficient since they do not require knowledge of either the mathematical model or the parameter values of the manipulator dynamics, and are implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategies ensure uniform boundedness of all signals in the presence of bounded disturbances, and that the ultimate size of the tracking errors can be made arbitrarily small. Experimental results are presented for a PUMA 560 manipulator and demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed controllers.     

Lyapunov analysis of the approximate motion equations of flexible structures

In this paper, the effectiveness of the approximate motion equations of a flexible structure, obtained by the RitzKantorovich method, is analysed by using Lyapunov functions. The analysis, which is restricted to the case of a single flexible beam for the sake of simplicity, is carried out under the assumption that a partial dissipation is present, affecting only the first degrees of freedom of the system. By means of suitable Lyapunov functions, an overbounding estimate of the quadratic approximation error is determined as a decreasing function of the approximation order. The analysis is completed by considering the two ‘extreme’ cases: the theoretical absence of dissipation and the presence of structural dissipation, affecting all the infinite degrees of freedom.     

Homogeneous Lyapunov function for homogeneous continuous vector field

The goal of this article is to provide a construction of a homogeneous Lyapunov function associated with a system of differential equations , under the hypotheses: (1) vanishes at x = 0 and is homogeneous; (2) the zero solution of this system is locally asymptotically stable. Moreover, the Lyapunov function tends to infinity with x, and belongs to , with as large as wanted. As application to the theory of homogeneous systems, we present two well known results of robustness, in a slightly extended form, and with simpler proofs.     

动态交通分配中一类转换率系统的稳定性

在假设交通很拥挤同时交通的转换率与路径费用成正比的前提下，构建了一个动态的转换率模型．为了获取转换率系统的全局渐近稳定，提出了一个普遍适用的Lyapunov函数方法，与此同时通过线性矩阵不等式方法，得到了保证转换率系统全局渐近稳定的充分条件．     

SOME NEW ASPECT OF LYAPUNOV TYPE THEOREMS FOR STOCHASTIC DIFFERENCE EQUATIONS WITH CONTINUOUS TIME

Some new Lyapunov type theorems for stochastic difference equations with continuous time are proven. It is shown that these theorems simplify an application of Lyapunov functionals construction method.     

用测井资料预测储层的润湿性

岩心电性及润湿性实验测量结果表明，润湿性对阿尔奇饱和度指数n有很大影响。通过引入相对润湿指数，发现阿尔奇饱和度指数n的对数与相润湿指数之间存在很好的线性关系，为利用饱和度指数预测储层的润湿性提供了依据。同时使用电磁波传播测井和微球形聚焦电阻率测井求出饱和度指数随地层深度的变化曲线，预测储层的润湿性。现场井资料处理结果表明，该方法能快速直观显示不同深度处储层润湿性的变化。     

Convergence of self-tuning Riccati equation with correlated noises

For the linear discrete time-invariant stochastic system with correlated noises,and with unknown model parameters and noise statistics,substituting the online consistent estimators of the model paramet...