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??We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and L\'{e}vy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation.     

带注资的二维复合泊松模型的最优分红

研究建立两类理赔关系的二维复合泊松模型的最优分红与注资问题,目标为最大化分红减注资的折现. 该问题由随机控制问题刻画, 通过解相应的哈密尔顿-雅克比-贝尔曼(HJB)方程,得到了最优分红策略,并在指数理赔时明确地解决该问题.     

具外部扰动的变时滞不确定奇异系统的滑动模态控制

研究了含有多个变时滞的不确定奇异系统的滑动模态问题.该系统相比文献中已研究的系统更为复杂,具有多个变时滞,且分别含有匹配和不匹配的外部扰动项.通过对系统进行等价分解化为两个子系统,对分解后的系统进行切换函数的设计,再通过定义Lyapunov函数得到使得系统的滑模运动渐近稳定的充分条件.由此证明了所设计的滑模控制率能够保证状态轨迹在优先时间内被驱动到指定的切换面上且保持运动.设计过程简单,且结果以线性矩阵不等式呈现,相比文献中已有的结论更易于实现.最后通过例子验证结论的正确性.     

Controllability of delay systems with restrained controls

Using a geometric growth condition, we characterize both the function space and Euclidean controllability of a nonlinear delay system which has a compact and convex control set. This extends analogous results for ordinary differential systems, and it yields conditions under which perturbed nonlinear delay controllable systems are controllable.This research was supported by the National Aeronautics and Space Administration under Contract No. NSG 1445Now on leave of absence as Professor, Department of Mathematics, University of Jos, Jos, Nigeria.     

Numerical solution of a time-optimal parabolic boundary-value control problem

A special time-optimal parabolic boundary-value control problem describing a one-dimensional heat-diffusion process is solved numerically. Using a bang-bang principle recently proved by Lempio, this problem can be transformed in such a way that the variables are jumps of bang-bang controls. A discretization is performed in two steps, and the convergence of the approximate solutions is proved. Finally, an algorithm to solve the discrete problem is developed and some numerical results are discussed.The author would like to thank Prof. F. Lempio, who pointed out this problem to him, and Prof. K. Glashoff for many helpful comments and suggestions.     

Optimal control of systems with multiple criteria when disturbances are present

Optimal control problems with a vector performance index and uncertainty in the state equations are investigated. Nature chooses the uncertainty, subject to magnitude bounds. For these problems, a definition of optimality is presented. This definition reduces to that of a minimax control in the case of a scalar cost and to Pareto optimality when there is no uncertainty or disturbance present. Sufficient conditions for a control to satisfy this definition of optimality are derived. These conditions are in terms of a related two-player zero-sum differential game and suggest a technique for determining the optimal control. The results are illustrated with an example.This research was supported by AFOSR under Grant No. 76-2923.     

高阶非完整系统的适应调节

通过综合利用“加幂积分器”的方法、“不连续投影”技巧和state scaling技巧构造出了一个不连续的动态适应控制律,解决了一类高阶参数非完整系统的适应调节问题．且所求控制律能确保未知参数的估值在一个预先给定范围内．     

一类不确定非线性系统的适应H-infinity控制

主要讨论了一类具有不确定参数的非线性系统的通过适应输出反馈达到干扰衰减的问题．通过构造降维观测器,利用Backstepping方法设计输出反馈控制器,使闭环系统具有不确定参数的标准的增益问题可解,并使系统达到内稳定．     

参数激励Duffing-VanderPol振子的动力学响应及反馈控制

研究了Duffing-Van der Pol振子的主参数共振响应及其时滞反馈控制问题．依平均法和对时滞反馈控制项Taylor展开的截断得到的平均方程表明,除参数激励的幅值和频率外,零解的稳定性只与原方程中线性项的系数和线性反馈有关,但周期解的稳定性还与原方程中非线性项的系数和非线性反馈有关．通过调整反馈增益和时滞,可以使不稳定的零解变得稳定．非零周期解可能通过鞍结分岔和Hopf分岔失去稳定性,但选择合适的反馈增益和时滞,可以避免鞍结分岔和Hopf分岔的发生．数值仿真的结果验证了理论分析的正确性．     

挖坑机钻头主轴纵向振动系统模型的建立与控制

首先利用弹性杆理论和H am ilton变分原理建立了挖坑机钻头主轴及钻尖在工作过程中由于外激励的作用使钻尖与土壤互相作用而产生纵向振动的动力学模型,同时给出边界条件和初始条件.其次通过把系统外激励函数当作控制变量,利用Banach空间几何性质证明了此系统存在唯一最优控制元.