周期係数をもつある種の Riccati 方程式における周期解の存在と解の漸近的振舞い

DOI Web Site Web Site

書誌事項

タイトル別名
  • On the Existence of a Periodic Solution and the Asymptotic Behavior of Solutions of a Certain Riccati Equation with Periodic Coefficients
  • シュウキ ケイスウ オ モツ アルシュ ノ Riccati ホウテイシキ ニ

この論文をさがす

抄録

This paper deals with a certain type of matrix Riccati equation with periodic coefficients, that is, a slightly generalized equation with the addition of a linear positive operator Π (t, ·) to the linear terms of the standard Riccati equation.<br>Such an equation arises, for example, in the quasi-steady state optimal control problem of a linear periodic system with a state-dependent noise, which is a natural generalization of the steady state optimal control problem of a linear time-invariant system.<br>In this paper, we discuss the existence of a periodic solution of the Riccati equation of this type and the asymptotic behavior of the solutions in connection with the periodic solution.<br>As a result, it is verified that under certain conditions of the coefficients (i. e.“stabilizability” and“detectability”), there exists a periodic solution to the above equation, if the coefficients Di(t), which form the positive operator Π (t, ·), are not too large. Moreover, we can see that under almost the same conditions, any solution of the Riccati equation converges to the above periodic solution in a certain sense as t goes to minus infinity. Then it is made sure that those results which have been obtained by G. A. Hewer et al. can be generalized to this case.<br>In the proofs quasi-linearlization methods and succesive approximation procedures are used effectively, so that the discussion becomes rather similar to the one which was adopted by W. M. Wonham.<br>Finally, we present one concrete example and apply the derived results to it.

収録刊行物

詳細情報 詳細情報について

問題の指摘

ページトップへ