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Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data

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    * Corresponding author 
The authors gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft through the Collaborative Research Center 901 "Control of self-organizing nonlinear systems: Theoretical methods and concepts of application" (projects A2, A8).
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  • For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert–Schmidt operators existence of solutions is studied. An existence result known for algebraic Riccati equations is generalized and used to obtain the existence of a solution to the approximation of the problem via a backward Euler scheme. Weak and strong convergence of the sequence of approximate solutions is established permitting a large class of right-hand sides and initial data.

    Mathematics Subject Classification: Primary: 47J35, 35K58, 65J15, 65M12; Secondary: 34H05, 49J99.


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