Gradient-Based Adaptive Prediction and Control for Nonlinear Dynamical Systems

TL;DR

This paper develops a gradient-based adaptive prediction and control method for nonlinear stochastic systems, ensuring global convergence without persistent excitation, and demonstrates its effectiveness on real-world data and simulations.

Contribution

It introduces a novel adaptive prediction and control framework applicable to a wide range of nonlinear models under weak convexity conditions, with proven convergence and performance guarantees.

Findings

Global convergence of the adaptive predictor is established.

Explicit asymptotic performance rates are derived.

The method is validated on real-world and simulated data.

Abstract

This paper investigates gradient-based adaptive prediction and control for nonlinear stochastic dynamical systems under a weak convexity condition on the prediction-based loss. This condition accommodates a broad range of nonlinear models in control and machine learning such as saturation functions, sigmoid, ReLU and tanh activation functions, and standard classification models. Without requiring any persistent excitation of the data, we establish global convergence of the proposed adaptive predictor and derive explicit rates for its asymptotic performance. Furthermore, under a classical nonlinear minimum-phase condition and with a linear growth bound on the nonlinearities, we establish the convergence rate of the resulting closed-loop control error. Finally, we demonstrate the effectiveness of the proposed adaptive prediction algorithm on a real-world judicial sentencing dataset. The adaptive control performance will also be evaluated via a numerical simulation.