# Optimal Robust Control of Nonlinear Systems with Unknown Dynamics via NN Learning with Relaxed Excitation

## TL;DR

This paper introduces a new neural network-based control method for nonlinear systems with unknown dynamics and disturbances.

## Contribution

A novel adaptive tuning law using Kreisselmeier’s regressor extension is proposed to relax the excitation conditions in neural network control.

## Key findings

- A system identifier using neural networks approximates unknown system matrices and disturbances.
- The proposed adaptive tuning laws relax the persistence of excitation requirement for convergence.
- Simulation results demonstrate the effectiveness of the new learning approach.

## Abstract

This paper presents an adaptive learning structure based on neural networks (NNs) to solve the optimal robust control problem for nonlinear continuous-time systems with unknown dynamics and disturbances. First, a system identifier is introduced to approximate the unknown system matrices and disturbances with the help of NNs and parameter estimation techniques. To obtain the optimal solution of the optimal robust control problem, a critic learning control structure is proposed to compute the approximate controller. Unlike existing identifier-critic NNs learning control methods, novel adaptive tuning laws based on Kreisselmeier’s regressor extension and mixing technique are designed to estimate the unknown parameters of the two NNs under relaxed persistence of excitation conditions. Furthermore, theoretical analysis is also given to prove the significant relaxation of the proposed convergence conditions. Finally, effectiveness of the proposed learning approach is demonstrated via a simulation study.