Statistics for Spatial Data.

https://eprints.soton.ac.uk/65935/01/Forr_09.pdf

Recent advances in surrogate-based optimization

Feel lonely? What about reading books? Book is one of the greatest friends to accompany while in your lonely time. When you have no friends and activities somewhere and sometimes, reading book can be a great choice. This is not only for spending the time, it will increase the knowledge. Of course the b=benefits to take will relate to what kind of book that you are reading. And now, we will concern you to try reading modelling and control of robot manipulators as one of the reading material to finish quickly.

Modelling and Control of Robot Manipulators

Bartels---Stewart algorithm is an effective and widely used method with an O(n 3) time complexity for solving a static Sylvester equation. When applied to time-varying Sylvester equation, the computation burden increases intensively with the decrease of sampling period and cannot satisfy continuous realtime calculation requirements. Gradient-based recurrent neural network are able to solve the time-varying Sylvester equation in real time but there always exists an estimation error. In contrast, the recently proposed Zhang neural network has been proven to converge to the solution of the Sylvester equation ideally when time goes to infinity. However, this neural network with the suggested activation functions never converges to the desired value in finite time, which may limit its applications in realtime processing. To tackle this problem, a sign-bi-power activation function is proposed in this paper to accelerate Zhang neural network to finite-time convergence. The global convergence and finite-time convergence property are proven in theory. The upper bound of the convergence time is derived analytically. Simulations are performed to evaluate the performance of the neural network with the proposed activation function. In addition, the proposed strategy is applied to online calculating the pseudo-inverse of a matrix and nonlinear control of an inverted pendulum system. Both theoretical analysis and numerical simulations validate the effectiveness of proposed activation function.

Accelerating a Recurrent Neural Network to Finite-Time Convergence for Solving Time-Varying Sylvester Equation by Using a Sign-Bi-power Activation Function

This technical note presents theoretical analysis and simulation results on the performance of a classic gradient neural network (GNN), which was designed originally for constant matrix inversion but is now exploited for time-varying matrix inversion. Compared to the constant matrix-inversion case, the gradient neural network inverting a time-varying matrix could only approximately approach its time-varying theoretical inverse, instead of converging exactly. In other words, the steady-state error between the GNN solution and the theoretical/exact inverse does not vanish to zero. In this technical note, the upper bound of such an error is estimated firstly. The global exponential convergence rate is then analyzed for such a Hopfield-type neural network when approaching the bound error. Computer-simulation results finally substantiate the performance analysis of this gradient neural network exploited to invert online time-varying matrices.

Performance Analysis of Gradient Neural Network Exploited for Online Time-Varying Matrix Inversion

As inspired by revising (Zhang and Ge, 2003), the traditional gradient-based neural system (also termed analog computer (Manherz et al., 1968)) for matrix inversion is re-visited by examining different activation functions and various implementation errors. A general neural system for matrix inversion is thus presented which can be constructed by using monotonically-increasing odd activation functions. For superior convergence and robustness of such a system, the power-sigmoid activation function is preferred to be in use if the hardware permits. In addition to investigating the singular case, this paper also presents an application example on inverse-kinematic control of redundant manipulators via online pseudoinverse solution

Revisit the Analog Computer and Gradient-Based Neural System for Matrix Inversion

Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. However, during its model-tuning procedure, the GP implementation suffers from numerous covariance-matrix inversions of expensive O(N3) operations, where N is the matrix dimension. In this article, we propose using the quasi-Newton BFGS O(N2)-operation formula to approximate/replace recursively the inverse of covariance matrix at every iteration. The implementation accuracy is guaranteed carefully by a matrix-trace criterion and by the restarts technique to generate good initial guesses. A number of numerical tests are then performed based on the sinusoidal regression example and the Wiener–Hammerstein identification example. It is shown that by using the proposed implementation, more than 80% O(N3) operations could be eliminated, and a typical speedup of 5–9 could be achieved as compared to the standard maximum-likelihood-estimation (MLE) implementation commonly used in Gaussian process r...

Yunong Zhang

Papers

Revisit the Analog Computer and Gradient-Based Neural System for Matrix Inversion

O(N2)-Operation approximation of covariance matrix inverse in Gaussian process regression based on quasi-Newton BFGS method

Exploiting Hessian matrix and trust-region algorithm in hyperparameters estimation of Gaussian process

Log-det approximation based on uniformly distributed seeds and its application to Gaussian process regression

Efficient Gaussian process based on BFGS updating and logdet approximation