Numerically Implementing the API Based Solution to Learn a Plant Dynamics for Stochastic Control Concurrently

This paper considers the case of filters acting in a control system subject to a priori parameter uncertainty and abrupt changes. The Original (theoretical) Performance Index (OPI), which is the mean-squared state prediction error, is originally inapplicable: it cannot be calculated in practice for filter optimization purposes. Meeting the challenges, we construct the Auxiliary Performance Index (API) with the following advantages: 1) it can be calculated from the available data; 2) it has the same minimizer as the original criterion. Having the same minimizer is called "equimodality" between OPI and API. Such a solution makes it possible to apply all the practical methods of optimization to find a minimum of the OPI by calculating the minimum of API. Essentially, that it does this job with no bias in parameter estimates. The API-based solution is critically distinct from the well-known Minimum Prediction Error identification approach because the latter defines the minimized prediction error as the difference between the system (noisy) output and predictor output, and it is not what the OPI means at all.