H2-optimal rejection with preview in the continuous-time domain

The synthesis of a feedforward unit for H2-optimal rejection of previewed signals in continuous time-invariant linear systems is considered. The H2-optimal compensator herein devised consists of a finite impulse response system working in connection with a standard dynamic unit. The design strategy is based on a simple interpretation of the H2-optimal rejection problem with preview as a compound optimal control problem, i.e. as a problem consisting of a finite-horizon LQ control problem with constrained final state, an infinite-horizon LQ control problem, and the problem of minimizing the global cost functional. An explicit description of the compensator is derived by exploiting some results on the parameterization of the solutions of the associated autonomous Hamiltonian system.