广义双线性系统的最优控制

Optimal Control for Singular Bilinear Systems

最优控制是自动控制理论的重要研究分支,本文首次对广义双线性系统的最优控制问题进行研究。利用李雅普诺夫稳定性理论和广义李雅普诺夫方程的解来设计最优控制器,使得闭环系统全局渐近稳定且使广义二次性能指标最小。此外,还给出最优化控制器的设计方法,整个设计过程简单,具有较少的保守性,例子表明设计方法的有效性和合理性。

The optimal control is an important ramify of auto- control theory, the optimal control problem of Singular bilinear systems is studied in this paper firstly. The optimal controller is designed by using Lyapunov stability theory and the solution of generalized Lyapunov equations, to guarantee the closed- loop system is global asymptotically stable and that the generalized quadratic performance index is minimized. Furthermore, the designing method for optimal stabilizing controller is presented, which has simple designing process and less conservative, and it＇s effectiveness and rationality is illustrated by a numerical example.