分段线性微分包含系统的最优控制设计

Optimal control of piecewise linear differential inclusions

针对分段线性微分包含系统,根据Hamilton-Jacobi-Bellman(H-J-B)不等式将最优控制设计问题转化成最优控制性能上界的优化问题及性能下界的求取问题.其中性能上界的优化是一组以反馈增益为寻优参数的双线性矩阵不等式(bilinear matrix inequalities,BMI)问题,而性能下界是一组基于线性矩阵不等式(linear matrixinequalities,LMI)的半正定规划问题.结合遗传算法和内点法设计了一种混合算法对BMI问题进行求解.算例表明方法的有效性.

Based on Hamihon-Jacobi-Bellman inequalities, the optimal control of piecewise linear differential inclusions is converted to the problem of seeking upper and lower bounds of the cost function. The design of upper bound can be cast as a bilinear matrix inequalities （BMI） problem in which the feedback gain is a set of optimization parameters, and the lower bound computation can be solved as a semidefinite programming problem based on linear matrix inequalities （LMI）. A mixed algorithm that combines genetic algorithm and interior-point method is designed to solve the BMI problem. The results from numerical examples illustrate the effectiveness of the proposed method.