Stochastic algebraic Riccati equations, a.k.a. rational algebraic Riccati equations, arising in linear-quadratic optimal control for stochastic linear time-invariant systems, were considered to be not easy to solve. The-state-of-art numerical methods most rely on differentiability or continuity, such as Newton-type method, LMI method, or homotopy method. In this paper, we will build a novel theoretical framework and reveal the intrinsic algebraic structure appearing in this kind of algebraic Riccati equations. This structure guarantees that to solve them is almost as easy as to solve deterministic/classical ones, which will shed light on the theoretical analysis and numerical algorithm design for this topic.
翻译:在线性赤道最佳控制线性线性线性线性时间变异系统中产生的Stochacti代数立方程式,a.k.a.a.a.理性代数立方程式,被认为是不容易解决的。最先进的数字方法最依赖差异性或连续性,如牛顿型方法、LMI方法或同质式方法。在本文中,我们将建立一个新颖的理论框架,并揭示出这种代数里立方程式中出现的内在代数结构。这种结构保证解决它们几乎与解决确定性/古典方法一样容易,这将为本专题的理论分析和数字算法设计提供启发。