Kernel-Based Identification of Positive Systems

In this paper, we introduce a novel method for identification of internally positive systems. In this regard, we consider a kernel-based regularization framework. For the existence of a positive realization of a given transfer function, necessary and sufficient conditions are introduced in the realization theory of the positive systems. Utilizing these conditions, we formulate a convex optimization problem by which we can derive a positive system for a given set of input-output data. The optimization problem is initially introduced in reproducing kernel Hilbert spaces where stable kernels are used for estimating the impulse response of system. Following that, employing theory of optimization in function spaces as well as the well-known representer theorem, an equivalent convex optimization problem is derived in finite dimensional Euclidean spaces which makes it suitable for numerical simulation and practical implementation. Finally, we have numerically verified the method by means of an example and a Monte Carlo analysis.