非线性调节器和L_2增益最优控制  

Design of Nonlinear Optimal Regulator and L_(2)-Gain Optimal Controller

作　　者：谢世杰[1] 徐德民[1] 于茜[1] 王晓利[1] 

机构地区：[1]西北工业大学航海工程学院，陕西 西安 710072

出　　处：《西北工业大学学报》2000年第4期625-628,共4页Journal of Northwestern Polytechnical University

基　　金：国防科技重点实验室基金资助(99JS26.7.1.ZS2604)

摘　　要：利用返回差条件和 Hamilton- Jacobi方程 ,借助“配方”方法讨论非线性系统达到最优调节所必须满足的条件 ,获得最优调节和 L2 增益最优控制的统一结果。同时讨论了在满足一定条件时 ,这种设计方法对模型误差具有较强的鲁棒性 。Recent interest and advances in L 2 gain optimal controller made it possible to design nonlinear optimal regulator and L 2 gain optimal controller. We considered the smooth affine nonlinear system described by eqs.(1) and (2). Using return difference condition and Hamilton Jacobi equation, and taking the generally accepted assumptions, we gave eqs.(3) through (6) for the determination of u in eq.(11), which is needed for our design. Theorem 1 states that the control law is the same for optimal regulator and L 2 gain optimal controller. We considered the perturbed smooth affine nonlinear system described by eqs.(9) through (11). Eqs.(3) through (6) can still be used to determine u in eq.(9). Theorem 1 still holds true under certain conditions given in Theorem 2. “Completion of the squares” is the main method used in the proofs given for Theorems 1 and 2. Of coures, u determined for the perturbed system ensures its robustness. Simulation results given in Figs. 1a and 1b show preliminarily the validity of our design method.

关 键 词：返回差条件 HAMILTON-JACOBI方程 非线性调节器 L2增益 最优控制 

分 类 号：TP214.2[自动化与计算机技术—检测技术与自动化装置]