一类非线性奇异摄动系统的次优控制

Suboptimal Control for A Class of Nonlinear Singularly Perturbed Systems

研究一类非线性奇异摄动系统的线性二次型最优控制问题.基于奇异摄动的快慢分解理论,将系统分解为一个快子系统和一个降阶的非线性慢子系统.利用逐次逼近方法,得到了非线性慢子系统的最优控制律,进而结合快子系统的最优控制律得到了原系统的次优控制律.仿真算例表明了算法的有效性.

The linear quadratic optimal control problem for a class of nonlinear singularly perturbed systems is studied.Based on the slow-fast decomposition theory of singular perturbation,the system is decomposed into a fast subsystem and a nonlinear slow subsystem.The slow optimal control law is given by using the successive approximation approach,and the suboptimal control law of the original system is obtained via the optimal control laws of the two subsystems.Simulation examples show the validity of proposed algorithm.