Model Updating for Nonlinear Systems with Stability Guarantees

TL;DR

This paper introduces a novel framework for updating nonlinear system models by learning uncertainties while ensuring stability, using semi-definite programming and robust filtering techniques, demonstrated through vehicle roll plane simulations.

Contribution

It develops a stability-guaranteed model updating method for nonlinear systems using semi-definite programs and a robust uncertainty estimation filter, advancing model accuracy and reliability.

Findings

Enhanced model accuracy demonstrated in vehicle simulations

Stability guarantees maintained through set invariance and input-to-state stability

Effective uncertainty estimation with robustness to disturbances and noise

Abstract

To improve the predictive capacity of system models in the input-output sense, this paper presents a framework for model updating via learning of modeling uncertainties in locally (and thus also in globally) Lipschitz nonlinear systems. First, we introduce a method to extend an existing known model with an uncertainty model so that stability of the extended model is guaranteed in the sense of set invariance and input-to-state stability. To achieve this, we provide two tractable semi-definite programs. These programs allow obtaining optimal uncertainty model parameters for both locally and globally Lipschitz nonlinear models, given uncertainty and state trajectories. Subsequently, in order to extract this data from the available input-output trajectories, we introduce a filter that incorporates an approximated internal model of the uncertainty and asymptotically estimates uncertainty and state realizations. This filter is also synthesized using semi-definite programs with guaranteed robustness with respect to uncertainty model mismatches, disturbances, and noise. Numerical simulations for a large data-set of a roll plane model of a vehicle illustrate the effectiveness and practicality of the proposed methodology in improving model accuracy, while guaranteeing stability.