基于BMI的一类不确定分段线性系统的最优控制设计

Optimal Control of a Class of Uncertain Piecewise Linear Systems Based on BMI

摘要: 将不确定分段线性系统的最优控制问题转化成最优控制性能界的优化问题．其中性能上界的优化是以反馈增益为寻优参数的一组双线性矩阵不等式（BMI）问题，对此将遗传算法和内点法结合，设计了一种混合算法进行求解．最后的算例表明控制律的设计及其求解算法的有效性．

Abstract: The optimal control of uncertain piecewise linear systems is converted to the optimization of upper and lower bounds of the cost function.The optimization of upper bound can be cast as a bilinear matrix inequality(BMI)problem in which the feedback gain is a set of optimization parameters,and a mixed algorithm that combines genetic algorithm and interior point method is designed for the BMI problem.The results from numerical example illustrate the effectiveness of the design and calculation approach for the control law.