Data modeling predictive control theory for deriving real-time models from simulations

This paper presents the mathematical framework and procedure for extracting differential equation based models from High-Fidelity Real-Time and Non Real-Time models for use in hyper-real-time simulation. Our approach captures a series of input/output scenario frames and derives analytical transfer function models from these examples. The result is a coupled set of differential equations that are integrated in real-time or analytically solved into polynomial form for Volterra type solution in real-time. The resulting model numerically yields the same answer on training inputs as the model was derived from, and yields nonlinear interpolated transfer functions in frequency space for off-nominal cases. Since the upper and lower error bounds and their variance are predictable, the derived model can maintain accreditation without implicit caveats. This allows the derived model to be executed in freeform when departures from intended uses are necessary but accreditation boundaries must not be violated.