Multi-Innovation Gradient Iterative Locally Weighted Learning Identification for A Nonlinear Ship Maneuvering System

This paper explores a highly accurate identification modeling approach for the ship maneuvering motion with fullscale trial. A multi-innovation gradient iterative(MIGI) approach is proposed to optimize the distance metric of locally weighted learning(LWL), and a novel non-parametric modeling technique is developed for a nonlinear ship maneuvering system. This proposed method’s advantages are as follows: first, it can avoid the unmodeled dynamics and multicollinearity inherent to the conventional parametric model; second, it eliminates the over-learning or underlearning and obtains the optimal distance metric; and third, the MIGI is not sensitive to the initial parameter value and requires less time during the training phase. These advantages result in a highly accurate mathematical modeling technique that can be conveniently implemented in applications. To verify the characteristics of this mathematical model, two examples are used as the model platforms to study the ship maneuvering.

Improved gradient iterative algorithms for solving Lyapunov matrix equations

In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared with the GI algorithm, the improved algorithm reduces computational cost and storage. Finally, the algorithm is tested with GI several numerical examples.

Spline adaptive filtering algorithm based on different iterative gradients:Performance analysis and comparison

Two novel spline adaptive filtering(SAF)algorithms are proposed by combining different iterative gradient methods,i.e.,Adagrad and RMSProp,named SAF-Adagrad and SAF-RMSProp,in this paper.Detailed convergence performance and computational complexity analyses are carried out also.Furthermore,compared with existing SAF algorithms,the influence of step-size and noise types on SAF algorithms are explored for nonlinear system identification under artificial datasets.Numerical results show that the SAF-Adagrad and SAFRMSProp algorithms have better convergence performance than some existing SAF algorithms(i.e.,SAF-SGD,SAF-ARC-MMSGD,and SAF-LHC-MNAG).The analysis results of various measured real datasets also verify this conclusion.Overall,the effectiveness of SAF-Adagrad and SAF-RMSProp are confirmed for the accurate identification of nonlinear systems.

Comparison between iterative wavefront control algorithm and direct gradient wavefront control algorithm for adaptive optics system

Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n2) ～ O(n3) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ～(O(n)3/2), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits.

An iterative Wiener filtering method based on the gravity gradient invariants

How to deal with colored noises of GOCE （Gravity field and steady - state Ocean Circulation Explorer） satellite has been the key to data processing. This paper focused on colored noises of GOCE gradient data and the frequency spectrum analysis. According to the analysis results, gravity field model of the optima] degrees 90-240 is given, which is recovered by COCE gradient data. This paper presents an iterative Wiener filtering method based on the gravity gradient invariants. By this method a degree-220 model was calculated from GOCE SGG （Satellite Gravity Gradient） data. The degrees above 90 of ITG2010 were taken as the prior gravity field model, replacing the low degree gravity field model calculated by GOCE orbit data. GOCE gradient colored noises was processed by Wiener filtering. Finally by Wiener filtering iterative calculation, the gravity field model was restored by space-wise harmonic analysis method. The results show that the model＇s accuracy matched well with the ESA＇s （European Space Agency） results by using the same data,

A Gradient Iteration Method for Functional Linear Regression in Reproducing Kernel Hilbert Spaces

We consider a gradient iteration algorithm for prediction of functional linear regression under the framework of reproducing kernel Hilbert spaces.In the algorithm,we use an early stopping technique,instead of the classical Tikhonov regularization,to prevent the iteration from an overfitting function.Under mild conditions,we obtain upper bounds,essentially matching the known minimax lower bounds,for excess prediction risk.An almost sure convergence is also established for the proposed algorithm.

New Results on Discrete-time Delay Systems Identification

A new approach for simultaneous online identification of unknown time delay and dynamic parameters of discrete-time delay systems is proposed in this paper.The proposed algorithm involves constructing a new generalized regression vector and defining the time delay and the rational dynamic parameters in the same vector.The gradient algorithm is used to deal with the identification problem.The effectiveness of this method is illustrated through simulation.