TY - JOUR

T1 - A Kleinman–Newton construction of the maximal solution of the infinite-dimensional control Riccati equation

AU - Curtain, Ruth F.

AU - Zwart, Hans

AU - Iftime, Orest V.

PY - 2017/9/15

Y1 - 2017/9/15

N2 - Assuming only strong stabilizability, we construct the maximal solution of the algebraic Riccati equation as the strong limit of a Kleinman–Newton sequence of bounded nonnegative operators. As a corollary we obtain a comparison of the solutions of two algebraic Riccati equations associated with different cost functions. We show that the weaker strong stabilizability assumptions are satisfied by partial differential systems with collocated actuators and sensors, so the results have potential applications to numerical approximations of such systems. By means of a counterexample, we illustrate that even if one assumes exponential stabilizability, the Kleinman–Newton construction may provide a solution to the Riccati equation that is not strongly stabilizing.

AB - Assuming only strong stabilizability, we construct the maximal solution of the algebraic Riccati equation as the strong limit of a Kleinman–Newton sequence of bounded nonnegative operators. As a corollary we obtain a comparison of the solutions of two algebraic Riccati equations associated with different cost functions. We show that the weaker strong stabilizability assumptions are satisfied by partial differential systems with collocated actuators and sensors, so the results have potential applications to numerical approximations of such systems. By means of a counterexample, we illustrate that even if one assumes exponential stabilizability, the Kleinman–Newton construction may provide a solution to the Riccati equation that is not strongly stabilizing.

KW - Infinite-dimensional systems

KW - Kleinman–Newton method

KW - Maximal solution

KW - Riccati equations

KW - Strong stabilizability

UR - http://www.scopus.com/inward/record.url?scp=85029415062&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2017.08.030

DO - 10.1016/j.automatica.2017.08.030

M3 - Article

AN - SCOPUS:85029415062

SN - 0005-1098

VL - 86

SP - 147

EP - 153

JO - Automatica

JF - Automatica

ER -