RKH space methods for low level monitoring and control of nonlinear systems

A monitor or controller is smart provided that the device is equipped with local computational resources for analyzing data, detecting changes, and making decisions. The problem for the monitoring function is to design algorithms to flag model shifts for dynamic systems in a context requiring many interacting system components and system reconfigurations. The problem for the control function is to improve system performance by updating control feedbacks after the model shift has been detected. Therefore it is desirable that smart monitors and controllers be adaptive and update with minimal intervention from a central director. We present here an approach to designing smart monitoring and control devices based on a stochastic linearization of the system whose dynamics is noisy and unknown. This linearization is obtained by factoring the discrete system covariance matrix, estimated from observations, and applying reproducing kernel Hilbert space techniques. The method is nonparametric which allows the smart devices to operate with only a low level logic.