Tracking controllability for finite-dimensional linear systems (2407.18641v2)

Abstract: In this work, we present a functional analytic framework for tracking controllability in finite-dimensional linear systems. By leveraging the Hilbert Uniqueness Method (HUM) and duality principles, we rigorously characterize tracking controllability through a non-standard observability inequality for the adjoint system. This enables the synthesis of minimum-norm tracking controls while revealing novel regularity requirements that depend intricately on system structure and the projection operator. Our approach generalizes classical concepts, embedding them in an energy-minimization context that extends functional output controllability and invertibility. Explicit control constructions in the scalar case illustrate these principles, and numerical experiments validate the approach for both smooth and non-smooth targets.