摘要
对于LQR(具有二次型性能指标的线性最优调节器)问题,求解最优控制律的关键在于求解黎卡堤方程.但对于时变系统,其求解变得相当复杂,从而影响了它的实际应用.本文提出用移位雅可比正交多项式求解,通过直接计算最优反馈律K(t)所需的状态转移矩阵,获得了一个计算K(t)的新方法,它将一个增广型的状态方程转化为一个简单的矩阵代数方程,从而避开了黎卡堤方程求解的困难,并使计算大为简化。
For LQR(Linear Quadritic Optimal Regulator)problem, the key to solve optimal control law is to solve Riccati equation. Because the solving process will be very complicated for time-varying systems, this method is difficultly used for practical systems. Shifted Jacobi orthogonal polynomial is used to directly solve the state transition matrix which is necessary to calculate optimal feedback law K(t), so a new calculating method for K ( t ) is obtained. It transformes the extended state equation into a simple matrix algebra equation. Therefore,the complex Riccati equation may be avoided and the calculation is simplified enormously.
关键词
最优控制
线性时变系统
解法
Optimal control
Linear systems
Time varying
Time-dependency systems
Jacobi polynomial
Solution
