非线性控制系统稳定化中一类非光滑优化问题的求解

Analysis and Computation of A Class of Nonsmooth Optimization Problem in the Stabilization for Control Systems

本文对控制系统稳定化设计中的投影问题的求解和计算进行了研究,首先构建投影问题的非光滑优化模型,然后利用K-T条件和非线性互补函数将其转化为非光滑方程组,并分别用广义牛顿法和光滑化阻尼牛顿法求解此非光滑方程组.一维控制系统的数值实验验证了两种方法的可行性和有效性。

The analysis and computation of a projection problem which arises from the stabilization for control systems is studied. First, a nonsmooth optimization model for the projection problem and then the model is transformed into an equivalent system of nonsmooth equations based on the K - T optimality conditions and the Fischer - Burmeister NCP function. Finally, the generalized Newton method and the smoothing damped Newton method are applied to solving the equations. The feasibility and validity of the two methods is verified through the Numerical experiments