RKH Space Methods for Low Level Monitoring and Control of Nonlinear Systems II. A Vector-Case Example: The Lorenz System

By using techniques from the theory of reproducing kernel Hilbert (RKH) spaces, we continue the exploration of the stochastic linearization method for possibly unknown and/or noise corrupted nonlinear systems. The aim of this paper is twofold: (a) the stochastic linearization formalism is explicitly extended to the vector case; and (b) as an illustration, the performance of the stochastic linearization for monitoring and control is assessed in the case of the Lorenz system for which the dynamic behavior is known independently.