# Combining Learning and Model Based Control via Discrete-Time Chen-Fliess Series

## TL;DR

This paper introduces a control method that combines learning and model-based approaches for nonlinear systems using discrete-time Chen-Fliess series, effectively integrating physical models with data-driven control.

## Contribution

It develops a novel control framework leveraging Chen-Fliess series for nonlinear plants, incorporating algebraic structures for multivariable systems, demonstrated on a Lotka-Volterra example.

## Key findings

- Successful control of a two-input, two-output Lotka-Volterra system
- Integration of physical model knowledge with learning control
- Extension of Chen-Fliess series to multivariable discrete-time systems

## Abstract

A learning control system is presented suitable for control affine nonlinear plants based on discrete-time Chen-Fliess series and capable of incorporating knowledge of a given physical model. The underlying noncommutative algebraic and combinatorial structures needed to realize the multivariable case are also described. The method is demonstrated using a two-input, two-output Lotka-Volterra system.