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Classical solutions of nonautonomous Riccati equations arising in parabolic boundary control problems. II. (English) Zbl 0952.49029
The authors consider an abstract linear-quadratic regulator problem associated with linear nonautonomous parabolic systems with boundary controls. The paper mostly is devoted to the proof of differentiability (with respect to the time parameters \(s\), \(t\)) of the optimal state operator, which to a given initial value at a time \(s\) assigns the optimal state at the time \(t\).
[See also Part I in Appl. Math. Optimization 39, No. 3, 361-409 (1999; Zbl 0926.49019)].

49N10 Linear-quadratic optimal control problems
49K20 Optimality conditions for problems involving partial differential equations
49K27 Optimality conditions for problems in abstract spaces
35B37 PDE in connection with control problems (MSC2000)
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