# Online-Learning Deep Neuro-Adaptive Dynamic Inversion Controller for Model Free Control

arXiv: https://arxiv.org/abs/2107.10383 · HTML: https://mlsanity.com/paper/2107.10383/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 21 references that are in the map.
- First posted on arXiv 21 Jul 2021.

## Builds on (most cited first, 8 of 8)

- [On weight initialization in deep neural networks](https://mlsanity.com/paper/1704.08863/) (2017)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [On the distance between two neural networks and the stability of learning](https://mlsanity.com/paper/2002.03432/) (2020)
- [Learning Deep Control Policies for Autonomous Aerial Vehicles with MPC-Guided Policy Search](https://mlsanity.com/paper/1509.06791/) (2015)
- [Learning compositional functions via multiplicative weight updates](https://mlsanity.com/paper/2006.14560/) (2020)
- [Deep Reinforcement Learning: Framework, Applications, and Embedded Implementations](https://mlsanity.com/paper/1710.03792/) (2017)
- [Online Deep Learning for Improved Trajectory Tracking of Unmanned Aerial Vehicles Using Expert Knowledge](https://mlsanity.com/paper/1905.10796/) (2019)
- [Learning to Guide: Guidance Law Based on Deep Meta-learning and Model Predictive Path Integral Control](https://mlsanity.com/paper/1904.06892/) (2019)

## Abstract (arXiv)

Adaptive methods are popular within the control literature due to the flexibility and forgiveness they offer in the area of modelling. Neural network adaptive control is favorable specifically for the powerful nature of the machine learning algorithm to approximate unknown functions and for the ability to relax certain constraints within traditional adaptive control. Deep neural networks are large framework networks with vastly superior approximation characteristics than their shallow counterparts. However, implementing a deep neural network can be difficult due to size specific complications such as vanishing/exploding gradients in training. In this paper, a neuro-adaptive controller is implemented featuring a deep neural network trained on a new weight update law that escapes the vanishing/exploding gradient problem by only incorporating the sign of the gradient. The type of controller designed is an adaptive dynamic inversion controller utilizing a modified state observer in a secondary estimation loop to train the network. The deep neural network learns the entire plant model on-line, creating a controller that is completely model free. The controller design is tested in simulation on a 2 link planar robot arm. The controller is able to learn the nonlinear plant quickly and displays good performance in the tracking control problem.