Control-theoretic data smoothing

The problem of recovering continuous time signals from a set of discrete measurements is ill-posed in a classical sense (non-uniqueness of solution). Our approach introduces generative models with inputs, states and outputs, and regularizes this problem by trading total fit-error against suitable penalty functionals of input and state. This enables us to apply techniques from optimal control and obtain solutions in a semi-analytical way. Using a modified version of Pontryagin´s maximum principle, this paper treats data smoothing as an optimal control problem. In addition to addressing data smoothing problems in Euclidean settings, our results are also applicable to problems arising in finite dimensional matrix Lie group settings. In particular, this paper discusses an example problem on SE(2), and exploits symmetry and reduction to an integrable Hamiltonian system as means to data smoothing.