非线性最优控制系统的时程精细计算研究

针对非线性最优控制问题 ,通过一阶 Taylor级数展开 ,得到线性化的动力学方程 ,进而在方程原变量的基础上 ,引入对偶向量 (Lagrange乘子向量 ) ,将动力学方程从 Lagrange体系引入到了 Hamilton体系 ,在全状态下 ,从一个新的角度对非线性最优控制问题进行了描述 ,进一步基于时程精细积分理论 ,对其方程进行了有效的精细求解 。

基于部件模态的多柔体系统非约束频率估计

基于部件模态建立多柔体系统的线性化动力学方程,通过特征分析及与ANSYS有限元分析软件计算结果相比较,表明结果是可行的。在此基础上,研究了中心刚体和柔性附件的相对质量特性对多柔体系统非约束固有频率的影响。

Velocity of a Liquid Drop with a Sorption-Controlled Surfactant

The terminal velocity of a liquid droplet settling in a sulfactant solution has been studied for the non-linear adsorption Langmuir frameworks accounting for monolayer saturation and non-ideal surfactant interactions. Most prior research uses a linear adsorption model which cannot capture these effects, The Maragoni migration of a liquid drop settling through a surfactant solution is examined by using Langmuir framework. The solution concentration Ceq is assumed large enough for the surfactant mass transfer to be adsorption-controlled. Langmuir model generates non-linear Marangoni stresses which diverge in the limit of approaching ∝, strongly retarding U'.

Collective Directional Transport in Symmetric Periodic Potentials by Breaking the Coupling Symmetry

Collective unidirectional motion of an asymmetrically coupled array of oscillators in symmetric periodic potentials is studied. A directed current is observed when the drift coupling is presented, while no external biased force is applied. Negative directed current is found when varying system parameters. An addition of a periodic rocking force may enhance the efficiency of directed transport. Resonant steps of the current are found and interpreted as the mode locking between the array and the ac force. Noise-assisted transport is observed, and an optimal noise intensity can give rise to a most efficient transport. The directed transport thus can be optimized and furthermore controlled by suitably adjusting the parameters of the system.

Can coordination variability identify performance factors and skill level in competitive sport? The case of race walking

Background:Marginal changes in the execution of competitive sports movements can represent a significant change for performance success.However,such differences may emerge only at certain execution intensities and are not easily detectable through conventional biomechanical techniques.This study aimed to investigate if and how competition standard and progression speed affect race walking kinematics from both a conventional and a coordination variability perspective.Methods:Fifteen experienced athletes divided into three groups(elite,international,and national) were studied while race walking on a treadmill at two different speeds(12.0 and 15.5 km/h).Basic gait parameters,the angular displacement of the pelvis and lower limbs,and the variability in continuous relative phase between six different joint couplings were analyzed.Results:Most of the spatio-temporal,kinematic,and coordination variability measures proved sensitive to the change in speed.Conversely,non-linear dynamics measures highlighted differences between athletes of different competition standard when conventional analytical tools were not able to discriminate between different skill levels.Continuous relative phase variability was higher for national level athletes than international and elite in two couplings(pelvis obliquity—hip flex/extension and pelvis rotation—ankle dorsi/plantarflexion) and gait phases(early stance for the first coupling,propulsive phase for the second) that are deemed fundamental for correct technique and performance.Conclusion:Measures of coordination variability showed to be a more sensitive tool for the fine detection of skill-dependent factors in competitive race walking,and showed good potential for being integrated in the assessment and monitoring of sports motor abilities.

Time Evolution,Dynamical Quantum Fluctuation and High-Order Squeezing Feature in Polariton System——Ⅰ

We have set up a new reduced model Hamiltonian for the polariton system, in which the nonlinear interaction contains the rotating term k l （ a ＋ b ＋ ab＋） and the attractive two-mode squeezed coupling - k2 （ a ＋ b＋ ＋ ab ） . The dynamical evolution of this system has been solved and the nonclassical features relevant to the second-order and high-order squeezing have been obtained in an analytical form. For the first time, in contrast to the existing result, we have confirmed for the phonon field that the attractive two-mode squeezed interaction will not only result in the second-order and high-order squeezing in X-component with the time evolution, but also in time average. Furthermore, the phenomena of collapse and revival of inversion will occur as well in the time evolution of the average number of photon and phonon, as also in the second-order and high-order squeezing of photon field, particularly, in the high-order squeezing of phonon field.

Improved control of intelligent excavator using proportional-integral-plus gain scheduling

Consider the design and implementation of an electro-hydraulic control system for a robotic excavator, namely the Lancaster University computerized and intelligent excavator (LUCIE). The excavator was developed to autonomously dig trenches without human intervention. One stumbling block is the achievement of adequate, accurate, quick and smooth movement under automatic control, which is difficult for traditional control algorithm, e.g. PI/PID. A gain scheduling design, based on the true digital proportional-integral-plus (PIP) control methodology, was utilized to regulate the nonlinear joint dynamics. Simulation and initial field tests both demonstrated the feasibility and robustness of proposed technique to the uncertainties of parameters, time delay and load disturbances, with the excavator arm directed along specified trajectories in a smooth, fast and accurate manner. The tracking error magnitudes for oblique straight line and horizontal straight line are less than 20 mm and 50 mm, respectively, while the velocity reaches 9 m/min.

Modeling Evolution of Weighted Clique Networks

We propose a weighted clique network evolution model, which expands continuously by the addition of a new clique （maximal complete sub-graph） at. each time step. And the cliques in the network overlap with each other. The structural expansion of the weighted clique network is combined with the edges＇ weight and vertices＇ strengths dynamical evolution. The model is based on a weight-driven dynamics and a weights＇ enhancement mechanism combining with the network growth. We study the network properties, which include the distribution of vertices＇ strength and the distribution o~ edges＇ weight, and find that both the distributions follow the scale-free distribution. At the same time, we also find that the relationship between strength and degree of a vertex are linear correlation during the growth of the network. On the basis of mean-field theory, we study the weighted network model and prove that both vertices＇ strength and edges＇ weight of this model follow the scale-free distribution. And we exploit an algorithm to forecast the network dynamics, which can be used to reckon the distributions and the corresponding scaling exponents. Furthermore, we observe that mean-field based theoretic results are consistent with the statistical data of the model, which denotes the theoretical result in this paper is effective.

Effect of Ultraviolet Aging on Asphalt Rheological Properties

This paper simulated the ultraviolet aging process of asphalt and used dynamic mechanic analysis （DMA） method to evaluate the effect of ultraviolet aging on the asphalt theological properties. After having experienced ultravio- let aging, the low temperature performance of asphalt binder decreased significantly, with its complex modulus increased and phase angle decreased along with changing rheological properties as compared to the performance of original asphalt binder. The ultraviolet aging process would make asphalt binder more sensitive to brittle and fatigue failure. On the basis of the time-temperature superposition principle （TTSP）, the viscoelastic transition frequency （coT） is proposed to evaluate the effect of ultraviolet aging. It is found that with the increase in ultraviolet aging time, the cox moves to the lower frequency range gradually. Since the viscoelastic transition frequency is sensitive to the effect of aging, it can be used as an indicator of ultraviolet aging.

空间机器人最优能耗捕获目标的自适应跟踪控制

提出了一种能够引导末端执行器以期望速度跟踪目标的轨迹规划方法。该方法可以实现避障并满足关节限制要求。基于轨迹规划方法,设计了一种利用自由飘浮空间机器人跟踪与捕获章动自旋卫星的自适应控制策略。此外,该控制策略还考虑了最优能耗、测量误差和优化误差。首先,为了使执行器的跟踪误差和机械臂的能耗最小,将空间机器人的控制策略描述为一个关于关节速度、力矩和避障距离的不等式约束优化问题。然后,推导出一个系数为下三角矩阵的显式状态方程,并对目标函数进行解耦和线性化。设计了一种关节速度和力矩分段优化方法去代替传统的凸二次规划方法求解最优问题,这种方法具有较高的计算效率。最后,利用李雅普诺夫稳定性理论验证了所提控制方法的收敛性。

Breather-Type Periodic Soliton Solutions for (1+1)-Dimensional Sinh-Poisson Equation

In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonlinear evolution equation has rich dynamical behavior even if it is (1+1)-dimensional.

Linear Unsteady Aerodynamic Forces on Vibrating Annular Cascade Blades

The paper presents the formulation to compute numerically the unsteady aerodynamic forces on the vibrating annular cascade blades.The formulation is based on the finite volume method.By applying the TVD scheme to the linear unsteady calculations,the precise calculation of the peak of unsteady aerodynamic forces at the shock wave location like the delta function singularity becomes possible without empirical constants.As a further feature of the present paper,results of the present numerical calculation are compared with those of the double linearization theory(DLT),which assumes small unsteady and steady disturbances but the unsteady disturbances are much smaller than the steady disturbances.Since DLT requires far less computational resources than the present numerical calculation,the validation of DLT is quite important from the engineering point of view.Under the conditions of small steady disturbances,a good agreement between these two results is observed,so that the two codes are cross-validated.The comparison also reveals the limitation on the applicability of DLT.

Nonlinear dynamical behavior of Xenon atoms along dislocation lines in UO_(2+x) nuclear fuel

Experimental results showed that there are a few Xenon atom bubbles connected by the dislocation line in the UO2+x nuclear fuel, and the largest radius of bubbles is about 45 nm. This phenomenon is in contrast to traditional bubble formation mechanism. This phenomenon is very important in understanding the properties of nuclear fuel. In this work, we apply a time- dependent microscopic atom transport equation and take into account stress coherent potential in the boundary of the dislocation. Using the equation, we numerically solved the stress coherence effect and studied the transfer properties of Xenon atoms along the dislocation line. Our numerical results show that the transport of the Xenon atoms along the dislocation changes nonlinearly with the external driving energy, and reaches at the saturation values. It explains the growth limit of Xenon atom bubbles that is in agreement with the experiment results.

GLOBAL ASYMPTOTIC STABILITY FOR A TWO-SPECIES DISCRETE RATIO-DEPENDENT PREDATOR-PREY SYSTEM

The dynamical behaviors of a two-species discrete ratio-dependent predator-prey sys- tem are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization method. Further, we also obtain a new sufficient condition to ensure that the positive equilibrium is globally asymptotically stable by using an iteration scheme and the comparison principle of difference equations, which generalizes what paper [G. Chen, Z. Teng and Z. Hu, Analysis of stability for a discrete ratio-dependent predator-prey system, Indian J. Pure Appl. Math. 42（1） （2011） 1-26] has done. The method given in this paper is new and very resultful comparing with papers [H. F. Huo and W. T. Li, Existence and global stability of periodic solutions of a discrete predator--prey system with delays, Appl. Math. Comput. 153 （2004） 337-351; X. Liao, S. Zhou and Y. Chen, On permanence and global stability in a general Gilpin- Ayala competition predator prey discrete system, Appl. Math. Comput. 190 （2007） 500-509] and it can also be applied to study the global asymptotic stability for general multiple species discrete population systems. At the end of this paper, we present an open question.