【摘要】 本文讨论了无限时间自由终端随机最优调节器问题和其相应的广义代数R iccati方程解之间的关系.具体而言,本文证明了无限时间自由终端随机最优调节器对应着广义代数R iccati方程的最小非负解,该最小解的核空间等于随机系统的精确不能观子空间.另外本文指出了以往文献中关于广义代数R iccati方程最大解存在性的一个证明错误,并对错误进行了分析.更多还原

【Abstract】 This paper discusses the relation between the infinite horizon free endpoint regulator of stochastic systems and the solution of the corresponding generalized algebraic Riccati equation.It is shown that an infinite horizon optimal regulator with free endpoint corresponds to a minimal nonnegative solution of the generalized algebraic Riccati equation.Moreover,the kernel space of this minimal solution equals to the exact unobservable subspace of the stochastic systems.In addition,an error in earlier literature in proving the existence of a maximal solution of the generalized algebraic Riccati equation is pointed out and analyzed.更多还原