自适应光学波面传感器的研究

在讨论几种波面传感器的基础上,介绍了一种新型的自适应光学波面传感器。实验结果表明,软刀口型波面传感器具有良好的实际应用前景。给出了它的工作原理,并介绍了各种传感器的优点。     

自适应光学系统的最优斜率复原算法

分析了自适应光学系统的波前斜率校正效果，综合大气湍流扰动和测量噪声的统计特性，在最小二乘复原算法的基础上推导得出一种形式简洁、易于实际操作的最优斜率复原算法。在大气湍流波前扰动条件下，对这种最优斜率复原算法的补偿效果和工作稳定性进行了计算研究。     

激光导引星大气湍流波前非等晕性误差的像差模式分解

激光导引星概念解决了自适应光学技术的信标问题，同时带来了无法克服的非等晕性误差。将高度聚焦非等晕性误差和角度等晕性误差统一起来考虑，分析激光导引星的大气湍流波前各阶模式的非等晕性误差，并给出了解析模型。同时分析了瑞利导星和纳导星的大气湍流波前的模式非等晕性相对误差，在没有角度偏离的情况下，90km的钠导星的模式非等晕性误差明显小于15km的瑞利导星，但是它对角度的敏感程度却远远大于端利导星。采用激光导引星的自适应光学系统用于大气湍流的校正，选择较低阶的模式校正就可以达到较好的效果，而且即使目标与导引星的偏角大于等晕角，选择低阶模式也可以达到有效的部分校正效果。     

Assessment of adaptive and heuristic time stepping for variably saturated flow

The performance of improved initial estimates and ‘heuristic’ and ‘adaptive’ techniques for time step control in the iterative solution of Richards equation is evaluated. The so‐called heuristic technique uses the convergence behaviour of the iterative scheme to estimate the next time step whereas the adaptive technique regulates the time step on the basis of an approximation of the local time truncation error. The sample problems used to assess these various schemes are characterized by nonuniform (in time) boundary conditions, sharp gradients in the infiltration fronts, and discontinuous derivatives in the soil hydraulic properties. It is found that higher order initial solution estimates improve the convergence of the iterative scheme for both the heuristic and adaptive techniques, with greater overall performance gains for the heuristic scheme, as could be expected. It is also found that the heuristic technique outperforms the adaptive method under strongly nonlinear conditions. Previously reported observations suggesting that adaptive techniques perform best when accuracy requirements on the numerical solution are very stringent are confirmed. Overall both heuristic and adaptive techniques have their limitations, and a more general or mixed time stepping strategy combining truncation error and convergence criteria is recommended for complex problems. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive VOF with curvature‐based refinement

Adaptive refinement is implemented in the context of the volume‐of‐fluid (VOF) methodology in order to study the efficacy of resolving interfaces adaptively based on the local value of curvature. The usual uniform mesh VOF implementation is modified slightly to ensure accurate advection of fluxes between cells at different resolutions. Normals and curvatures are calculated accurately via height functions. Results of a series of tests indicate that in most instances the use of adaptive refinement (when compared to uniform refinement with a similar number of cells) leads to more accurate VOF advection. The results also clearly show that curvature‐based adaptive refinement leads to a distribution of errors along an interface that is nearly independent of curvature. Copyright © 2007 John Wiley & Sons, Ltd.     

A Distal Model of Congenital Nystagmus as Nonlinear Adaptive Oscillations

Congenital nystagmus (CN) is an incurable pathological spontaneous oscillation of the eyes with an onset in the first few months of life. The pathophysiology of CN is mysterious. There is no consistent neurological abnormality, but the majority of patients have a wide range of unrelated congenital visual abnormalities affecting either the cornea, lens, retina or optic nerve. In this theoretical study, we show that these eye oscillations could develop as an adaptive response to maximize visual contrast with poor foveal function in the infant visuomotor system, at a time of peak neural plasticity. We argue that in a visual system with abnormally poor high spatial frequency sensitivity, image contrast is not only maintained by keeping the image on the fovea (or its remnant) but also by some degree of image motion. Using the calculus of variations, we show that the optimal trade-off between these conflicting goals is to generate oscillatory eye movements with increasing velocity waveforms, as seen in real CN. When we include a stochastic component to the start of each epoch (quick-phase inaccuracy) various observed waveforms (including pseudo-cycloid) emerge as optimal strategies. Using the delay embedding technique, we find a low fractional dimension as reported in real data. We further show that, if a velocity command-based pre-motor circuitry (neural integrator) is harnessed to generate these waveforms, the emergence of a null region is inevitable. We conclude that CN could emerge paradoxically as an ‘optimal’ adaptive response in the infant visual system during an early critical period. This can explain why CN does not emerge later in life and why CN is so refractory to treatment. It also implies that any therapeutic intervention would need to be very early in life.     

Adaptive methods for piecewise polynomial collocation for ordinary differential equations

Various adaptive methods for the solution of ordinary differential boundary value problems using piecewise polynomial collocation are considered. Five different criteria are compared using both interval subdivision and mesh redistribution. The methods are all based on choosing sub-intervals so that the criterion values have (approximately) equal values in each sub-interval. In addition to the main comparison it is shown by example that at least when accuracy is low then equidistribution may not give a unique solution. The main results that using interval size times maximum residual as criterion gives very much better results than using maximum residual itself. It is also shown that a criterion based on a global error estimate while giving very good results in some cases, is unsatisfactory in other cases. The other criteria considered are that given by De Boor and the last Chebyshev series coefficient. AMS subject classification (2000)  65L10, 65L50, 65L60     

Strong Consistency of Bayes Estimates in Stochastic Regression Models

Under minimum assumptions on the stochastic regressors, strong consistency of Bayes estimates is established in stochastic regression models in two cases: (1) When the prior distribution is discrete, the p.d.f.fof i.i.d. random errors is assumed to have finite Fisher informationI=∫^∞_−∞(f′)²/f dx<∞; (2) for general priors, we assumefis strongly unimodal. The result can be considered as an application of a theorem of Doob to stochastic regression models.     

Memory-augmented adaptive flocking control for multi-agent systems subject to uncertain external disturbances

This paper presents a novel flocking algorithm based on a memory-enhanced disturbance observer.To compensate for external disturbances,a filtered regressor for the double integrator model subject to external disturbances is designed to extract the disturbance information.With the filtered regressor method,the algorithm has the advantage of eliminating the need for acceleration information,thus reducing the sensor requirements in applications.Using the information obtained from the filtered regressor,a batch of stored data is used to design an adaptive disturbance observer,ensuring that the estimated values of the parameters of the disturbance system equation and the initial value converge to their actual values.The result is that the flocking algorithm can compensate for external disturbances and drive agents to achieve the desired collective behavior,including virtual leader tracking,inter-distance keeping,and collision avoidance.Numerical simulations verify the effectiveness of the algorithm proposed in the present study.     

基于神经网络的一类非线性时滞系统自适应控制器设计

针对一类带有扰动和未知时滞的非线性系统,通过反步方法设计一种鲁棒自适应控制器.提出了一种新的Lyapunov-Krasovskii泛函,补偿了未知时滞项的不确定性.引入一种合适的偶函数,避免了控制器的奇异性问题.通过Lyapunov直接方法,证明了所设计的控制器能保证闭环系统所有信号全局一致最终有界.