Optimal tracing of harmonic signals in linear systems with noise in measurements (Q1595557)

Consider a vector linear differential equation \({d\over dt} x(t)= Ax(t)+ bu(t)+ f^0\phi_1(t)\) where \(y(t)\) is a linear combination of \(x(t)\) and \(\phi_2(t)\) while \(z(t)\) is a linear combination of \(x(t)\) and \(u(t)\). The external disturbances \(\phi_1(t)\), \(\phi_2(t)\) are assumed to be harmonic functions. The authors define a class \({\mathcal N}\) of (not necessarily linear) admissible regulators. An admissible regulator is called optimal if it provides a minimum of a certain mean square integral. Under reasonable assumptions it is shown that there exists an optimal universal regulator in \({\mathcal N}\) that is linear.