Towards a representer theorem for identification of passive systems

A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this paper, we present first steps towards tackling this problem for passive systems. In particular, using ideas from the theory of reproducing kernel Hilbert spaces, we solve the problem of identifying a nonnegative input-output operator from data consisting of input-output trajectories of the system. We prove a representer theorem for this problem in the case where the input space is finite-dimensional. This provides a computationally tractable solution, which we show can be obtained by solving an associated semidefinite program.