We introduce and discuss new accelerated algorithms for linear discriminant analysis (LDA) in unimodal multiclass Gaussian data. These algorithms use a variable step size, optimally computed in each iteration using (i) the steepest descent, (ii) conjugate direction, and (iii) Newton-Raphson methods in order to accelerate the convergence of the algorithm. Current adaptive methods based on the gradient descent optimization technique use a fixed or a monotonically decreasing step size in each iteration, which results in a slow convergence rate. Furthermore, the convergence of these algorithms depends on appropriate choices of the step sizes. The new algorithms have the advantage of automatic optimal selection of the step size using the current data samples. Based on the new adaptive algorithms, we present self-organizing neural networks for adaptive computation of −1/2 and use them in cascaded form with a PCA network for LDA. Experimental results demonstrate fast convergence and robustness of the new algorithms and justify their advantages for on-line pattern recognition applications with stationary and non-stationary multidimensional input data.

Impedance control is a compliance control strategy capable of accommodating both unconstrained and constrained motions. The performance of impedance controllers depends heavily upon environment dynamics and the choice of target impedance. To maintain performance for a wide range of environments, target impedance needs to be adjusted adaptively. In this paper, a geometric view on impedance control is developed for stiff environments, resulting in a "static-optimized" controller that minimizes a combined generalized position and force trajectory error metric. To incorporate the dynamic nature of the manipulator-environment system, a new cost function is considered. A classic quadratic optimal control strategy is employed to design a novel adaptive compliance controller with control parameters adjusted based upon environment stiffness and damping. In steady state, the proposed controller ultimately implements the static-optimized impedance controller. Simulation and experimental results indicate that the proposed optimal controller offers smoother transient response and a better trade-off between position and force regulation.

Purpose -The purpose of this paper is to solve an unsteady nonlinear convective-radiative equation and a nonlinear convective-radiative-conduction equation containing two small parameters of 1 1 and 1 2 by variational homotopy perturbation method. Design/methodology/approach -The heat transfer equations are described. The variational homotopy perturbation method as a powerful method for solving linear and nonlinear equations is applied to find the solutions of our model equations.Findings -The solutions of heat transfer equations are calculated in the form of convergent series with easily computable components. Two examples are solved as illustrations, using symbolic computation. Originality/value -The results show that the suggested method is easy to implement and has high level of accuracy. The method introduces a reliable tool for solving many linear and nonlinear differential equations. Nomenclature

In a recent paper, Abassy et al. (J. Comput. Appl. Math. 207:137-147, 2007) proposed a modified variational iteration method (MVIM) for a special kind of nonlinear differential equations. In this paper, we consider variational iteration method (VIM) and MVIM (proposed in Abassy et al., J. Comput. Appl. Math. 207:137-147, 2007) to obtain an approximate series solution to the generalized Fisher's equation which converges to the exact solution in the region of convergence. It is also shown that the application of VIM to the generalized Fisher's equation leads to calculation of unneeded terms for series solution. Therefore, we use MVIM to overcome this disadvantage. Comparison of error between VIM and MVIM is made. The results show that the MVIM is more effective than the VIM.

SUMMARYIn this paper, we introduce a new analytic technique for a class of nonlinear optimal control problems and present a theorem of convergence of the method. In this scheme, first, the original optimal control problem is transformed into a nonlinear two‐point boundary value problem via the Pontryagin's maximum principle, and then, we apply a new method for solving two‐point boundary value problem. The proposed modification is made by introducing He's polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for using in these problems. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. Copyright © 2013 John Wiley & Sons, Ltd.