Control of Unknown Nonlinear Systems with Linear Time-Varying MPC
This work addresses safety-critical control for unknown nonlinear systems, which is an incremental improvement over existing linearization-based MPC methods.
The authors tackled the problem of controlling unknown nonlinear systems by developing a robust Model Predictive Control (MPC) strategy that uses data-driven estimation and linearization with error bounds, demonstrating effectiveness in a nonlinear example where standard methods fail.
We present a Model Predictive Control (MPC) strategy for unknown input-affine nonlinear dynamical systems. A non-parametric method is used to estimate the nonlinear dynamics from observed data. The estimated nonlinear dynamics are then linearized over time varying regions of the state space to construct an Affine Time Varying (ATV) model. Error bounds arising from the estimation and linearization procedure are computed by using sampling techniques. The ATV model and the uncertainty sets are used to design a robust Model Predictive Control (MPC) problem which guarantees safety for the unknown system with high probability. A simple nonlinear example demonstrates the effectiveness of the approach where commonly used linearization methods fail.