Quadratic optimal control of stable systems through spectral factorization
The quadratic cost minimization problem had been solved using Wiener-Hopf factorization theory. The stable input-output system \(y(t)= (\gamma * u) (t)+ f(t)\), \(t\in \overline {\mathbb{R}}^+\), \(u(t)= \varphi (t)\), \(t\in \mathbb{R}^-\) is studied. Here \(\gamma\) represents the impulse response of the system. Some realizations of this system are analyzed. The difficulty with unbounded control and observation operators is replaced by the difficulty of performing the spectral factorization. The used technique essentially differs from the usual one and doesn't use state-space theory to get the feedback operator and the Riccati operator.
scientific article; zbMATH DE number 840223
scientific article