In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied tho...In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.展开更多
This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in It?Markov jump systems.A new iterative algorithm is developed by using the latest estimation information and introdu...This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in It?Markov jump systems.A new iterative algorithm is developed by using the latest estimation information and introducing a tuning parameter.The iterative solution obtained by the proposed algorithm with zero initial conditions converges to the unique positive definite solution of the considered equations.The convergence rate of the algorithm is dependent on the adjustable parameter.Furthermore,a numerical example is provided to show the effectiveness of the presented algorithms.展开更多
文摘In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.
基金supported by the Shenzhen Municipal Basic Research Project for Discipline Layout(Grant No.JCYJ20170811160715620)the National Natural Science Foundation of China for Excellent Young Scholars(Grant No.61822305)+1 种基金the Shenzhen Municipal Project for International Cooperation(Grant No.GJHZ20180420180849805)the Guangdong Natural Science Foundation(Grant No.2017A030313340)。
文摘This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in It?Markov jump systems.A new iterative algorithm is developed by using the latest estimation information and introducing a tuning parameter.The iterative solution obtained by the proposed algorithm with zero initial conditions converges to the unique positive definite solution of the considered equations.The convergence rate of the algorithm is dependent on the adjustable parameter.Furthermore,a numerical example is provided to show the effectiveness of the presented algorithms.
