拟不可积Hamilton系统响应的随机最优控制  

STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS

作　　者：邓茂林[1] 洪明潮[2] 朱位秋[3] 

机构地区：[1]浙江大学生物医学工程系,杭州310027 [2]浙江大学计算中心,杭州310027 [3]浙江大学力学系,杭州310027

出　　处：《固体力学学报》2004年第1期1-6,共6页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金 ( 19972 0 5 9)资助

摘　　要：提出了一种基于拟不可积Hamilton系统随机平均法和随机动态规划原理的控制策略 .它可以对受高斯白噪声激励的拟不可积Hamilton系统进行非线性随机最优控制 ,以使系统的响应最小化 .利用拟不可积Hamilton系统随机平均法可以将受控的拟不可积Hamilton系统降维成一维的It 随机微分方程 .利用随机动态规划原理可以为系统响应最小化问题建立动态规划方程 .在控制力为有界的条件下 ,从动态规划方程中可以确定出最优控制规律 .受控系统的响应是通过求解与It 随机微分方程相联系的FPK方程得到的 ,用一个例子阐述了这一随机最优控制策略的实施过程 .A strategy is proposed based on the stochastic averaging method for quasi non-integrable Hamiltonian systems and the stochastic dynamical programming principle. The proposed strategy can be used to design nonlinear stochastic optimal control to minimize the response of quasi non-integrable Hamiltonian systems subject to gauss white noise excitation. By using the stochastic averaging method for quasi non-integrable Hamiltonian systems the equations of motion of a controlled quasi non-integrable Hamiltonian system is reduced to an one-dimensional averaged It stochastic differential equation. By using the stochastic dynamical programming principle the dynamical programming equation for minimizing the response of the system is formulated. The optimal control law is derived from the dynamical programming equation and the bounded control constraints. The response of optimally controlled systems is predicted through solving the FPK equation associated with It stochastic differential equation. An example is worked out in detail to illustrate the application of the proposed control strategy.

关 键 词：拟不可积Hamilton系统 系统响应 随机最优控制 随机平均法 动态规划 动态规划方程 

分 类 号：O231[理学—运筹学与控制论]