摘要
应用常微分方程关于部分变元稳定性理论,研究了线性定常完全能控系统,以二次型为性能指标的最优反馈系统关于部分变元的稳定性问题。得到:当性能指标只能观测部分变元,或性能指标关于状态变元的加权矩阵部分变元正定时,最优反馈系统的零解关于部分变元在大范围渐近稳定。
By using the partial stability theory, this paper studies the partial stability of the trivial solution of the optimal feedback system, where the state equation is completely controllable autonomous system with a cost of quadratic form to be minimized. Two results are obtained, when (1): only partial variables can be observed through the cost, or(2): the weight matrix with state variables in the cost is partial positive definite, then the trivial solution of the optimal feedback system is of partial global asymptotical stability.
关键词
最优控制
可观性
正定矩阵
稳定性
optimal control
observability
positive definite matrix
stability
