Original title: Taylor-Informed Indirect Adaptive Predictive Control Using Jacobian-Frozen Affine Predictors
Tam W. Nguyen · September 2026
Controlling complex, nonlinear machines is hard because their behavior changes constantly. Researchers created a new adaptive control method to solve this. First, they approximate the system's behavior using a math tool called a Taylor expansionA mathematical approximation that represents a complex function as a sum of polynomial terms., which turns complex curves into polynomials. An online algorithm called recursive least squares constantly learns these polynomial numbers in real time. To keep the math simple, the team trimmed unnecessary parts using system symmetry and forward-Euler structure. At each step, they take the system's rate of change, freeze it over a short future window, and make an affine prediction to plan the controls. Tests on an unstable benchmark showed that higher-order Taylor models tracked targets better far from the starting point without requiring more control effort.
Imagine trying to park a car in a tight spot while it's on a slippery road. When you turn the steering wheel, the car's response depends on its current speed and angle, which keep changing. If those conditions shift rapidly, your adjustments might not work as expected. In this paper, the controller captures the car's turning behavior at each moment and holds it fixed briefly to plan its next move, making control more reliable even when the car is unstable.
Engineers and operators working with unpredictable machines, like in aerospace or robotics, need safer control. This method improves accuracy when systems behave far from their usual conditions, without requiring more energy.
The method is validated only through numerical simulations on a specific benchmark, not on physical hardware. It relies on polynomial approximations that might not capture all types of nonlinear behavior. The freezing of the Jacobian assumes the system's behavior doesn't change too rapidly over the prediction horizon.
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Taylor-Informed Indirect Adaptive Predictive Control Using Jacobian-Frozen Affine Predictors — Tam W. Nguyen
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.