Criterion for the convergence of the solution of the Riccati differential equation
Criterion for the convergence of the solution of the Riccati differential equation
复制标题
Riccati 微分方程解的收敛准则
DOI：
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发表时间：
1981
期刊：
影响因子：
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通讯作者：
J. Willems
中科院分区：
文献类型：
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作者：
F. Callier;J. Willems
对于具有二次代价函数的线性系统的最优控制问题，将其转化为矩阵Riccati方程。研究了当时间间隔增加时，该方程的解作为最终状态惩罚矩阵的函数的收敛问题。在代价函数中的输出不可检测的情况下，给出了系统可镇定的充要条件。给出了一种确定代数Riccati方程对称半正定解的极限值的算法。给出了收敛和不收敛的例子。还讨论了Riccati微分方程解到代数Riccati方程的任何实对称(不一定是半正定)解的收敛性质。
The optimal control problem for a linear system with a quadratic cost function leads to the matrix Riccati differential equation. The convergence of the solution of this equation for increasing time interval is investigated as a function of the final state penalty matrix. A necessary and sufficient condition for convergence is derived for stabilizable systems, even if the output in the cost function is not detectable. An algorithm is developed to determine the limiting value of the solution, which is one of the symmetric positive semidefinite solutions of the algebraic Riccati equation. Examples for convergence and nonconvergence are given. A discussion is also included of the convergence properties of the solution of the Riccati differential equation to any real symmetric (not necessarily positive semidefinite) solution of the algebraic Riccati equation.