Finite-time Convergent Neural Networks With Its Relevant Aplications

Neural networks have the ability of high-speed parallel processing and real-time computing, that the method is effective when solving the matrix equations with high computational complexity. The dynamic neural networks mostly adopt the asymptotic features. Compared with the asymptotic convergence performance, terminal convergent dynamics feature the finite-time convergent characteristics, and it can not only accelerate the convergent rate, but also enhance the accuracy of convergence.Solving matrix equations is an important class of matrix calculation, and it has a widely applicable background. As for various forms of matrix equations, the problem can be expanded to solve time-varying matrix inversion, quadratic programming and so forth. Owing to the essence of the conventional processing, a large number of well-accepted numerical algorithms when solving the matrix equations with high computational complexity may not be efficient enough. Based on terminal convergent features, this thesis proposes a variety of finite-time convergent neural networks, and uses these networks to solve the time-varying matrix inversion, quadratic programming, and trajectory planning of redundant manipulators. The simulation results are presented to verify the effectiveness of such neural networks.The main work of this thesis is summarized as follows:1. Based on finite-time attractive law, this thesis proposes several finite-time convergent neural networks as well as the accelerated forms, then we establish the convergence and stability conditions of these networks.2. Facing the problem of matrix inversion, in order to speed up the convergence rate of target matrix which converges to desired matrix, detailed solving process of this problem is given when using several finite-time convergent neural networks, then we analyze and validate the effectiveness of finite-time convergent neural networks while solving the problem of time-varying matrix inversion. Furthermore, we build the simulation model based on solving equation and show two simulation examples when using several finite-time convergent neural networks.3. In order to speed up the convergence rate of performance index which converges to zero, several finite-time convergent neural networks are applied to solve quadratic programming problem which is subject to the time-varying linear-equality constraints, then analyze the system states and the performance index of quadratic programming, finally we show two simulation examples of these networks.4. Based on the problem of repeatable motion planning of redundant manipulators, the detailed solving process of this problem is given when using several finite-time convergent neural networks. We analyze the periodic features of joint variables, including their angular velocity, and the convergence of performance index with different tracking task of whether the initial position on the circle or not, then shows the simulation of the finite-time convergent neural networks.