微分求积法在悬臂梁结构非线性动力学中的应用研究

利用微分求积法对受横向载荷和轴向载荷联合作用的粘弹性悬臂梁的非线性动力学偏微分控制方程直接离散求解,并提出了一种新的边界条件施加方法处理悬臂梁的边界条件。在数值结果的基础上结合非线性动力学理论,利用分叉图,时间历程图,相图等对受横向载荷和轴向载荷联合作用的粘弹性悬臂梁的非线性动力学特性进行了分析。由以上图形得到的其非线性动力学性质是一样的,因而表明微分求积法以及施加边界条件的新方法能够有效地用来分析悬臂梁结构的非线性动力学性质。

Temperature control for thermal treatment of aluminum alloy in a large-scale vertical quench furnace

The temperature control of the large-scale vertical quench furnace is very difficult due to its huge volume and complex thermal exchanges. To meet the technical requirement of the quenching process, a temperature control system which integrates temperature calibration and temperature uniformity control is developed for the thermal treatment of aluminum alloy workpieces in the large-scale vertical quench furnace. To obtain the aluminum alloy workpiece temperature, an air heat transfer model is newly established to describe the temperature gradient distribution so that the immeasurable workpiece temperature can be calibrated from the available thermocouple temperature. To satisfy the uniformity control of the furnace temperature, a second order partial differential equation(PDE) is derived to describe the thermal dynamics inside the vertical quench furnace. Based on the PDE, a decoupling matrix is constructed to solve the coupling issue and decouple the heating process into multiple independent heating subsystems. Then, using the expert control rule to find a compromise of temperature rising time and overshoot during the quenching process. The developed temperature control system has been successfully applied to a 31 m large-scale vertical quench furnace, and the industrial running results show the significant improvement of the temperature uniformity, lower overshoot and shortened processing time.

Boundary Control of Coupled Nonlinear Three Dimensional Marine Risers

This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser＇s motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser＇s vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.

Stochastic Differential Game Model for Decentralized Power Control with Wisdom Regulation Factor in Wearable Audio-Oriented BodyNets

In this study, aiming at the characteristics of randomness and dynamics in Wearable Audiooriented BodyNets （WA-BodyNets）, stochastic differential game theory is applied to the investigation of the problem of transmitted power control inconsumer electronic devices. First, astochastic differential game model is proposed for non-cooperative decentralized uplink power control with a wisdom regulation factor over WA-BodyNets with a onehop star topology.This model aims to minimize the cost associated with the novel payoff function of a player, for which two cost functions are defined： functions of inherent power radiation and accumulated power radiation darmge. Second, the feedback Nash equilibrium solution of the proposed model and the constraint of the Quality of Service （QoS） requirement of the player based on the SIR threshold are derived by solving the Fleming-Bellman-Isaacs partial differential equations. Furthermore, the Markov property of the optimal feedback strategies in this model is verified.The simulation results show that the proposed game model is effective and feasible for controlling the transmitted power of WA-BodyNets.

From phenomena of synchronization to exact synchronization and approximate synchronization for hyperbolic systems

In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations,and will be connected with the control theory via boundary controls in a finite time interval. More precisely,various kinds of exact boundary synchronization and approximate boundary synchronization will be introduced and realized by means of fewer boundary controls for a coupled system of wave equations with Dirichlet boundary controls. Moreover, as necessary conditions for various kinds of approximate boundary synchronization, criteria of Kalman's type are obtained. Finally, some prospects will be given.

OPTIMAL BIRTH CONTROL FOR AN AGE-DEPENDENT COMPETITION SYSTEM OF N SPECIES

In this paper, we investigate optimal policies for an age-dependent n-dimensional competition system, which is controlled by fertility. By using Dubovitskii-Milyutin＇s general theory, the maximum principles are obtained for the problems with free terminal states, infinite horizon, and target sets, respectively.

OPTIMAL INVERSE LQG CONTROL FOR CERTAIN ODE AND PDE STATIONARY PROCESSES

Following work carried out earlier on linear-quadratic optimal control for linear finitedimensional stationary systems we report,in this article,on extension of some of those results to certaininfinite dimensional systems;in particular a class of PDE systems of elliptic type.These systems arestudied in the now familiar framework developed by J.L.Lions and E.Magenes,specialized to asubclass of such systems important in a variety of applications.As an extended example this paperstudies an optimal redistribution problem in a groundwater flow system governed by Darcy's equation,presenting both analytic and computational work related to such problems.

Mathematical study for peristaltic flow of Williamson fluid in a curved channel

In this paper, we have investigated the peristaltic flow of Williamson fluid in a curved channel. The governing equations of Williamson fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equa- tions are simplified by using the wave frame transformation, long wavelength and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity profile and stream functions.

OPTIMAL CONTROL FOR A NONLINEAR n-DIMENSIONAL COMPETING SYSTEM WITH AGE-STRUCTURE

This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland＇s variational principle, the existence and unique char- acterization of the optimal control strategy are established. The optimality conditions for the control problem are obtained by the concept of the normal cone.