# System Identification and Control Using Lyapunov-Based Deep Neural Networks without Persistent Excitation: A Concurrent Learning Approach

arXiv: https://arxiv.org/abs/2505.10678 · HTML: https://mlsanity.com/paper/2505.10678/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 15 May 2025.

## Builds on (most cited first, 16 of 16)

- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local Minima](https://mlsanity.com/paper/1712.00779/) (2017)
- [The power of deeper networks for expressing natural functions](https://mlsanity.com/paper/1705.05502/) (2017)
- [Depth Creates No Bad Local Minima](https://mlsanity.com/paper/1702.08580/) (2017)
- [Depth with Nonlinearity Creates No Bad Local Minima in ResNets](https://mlsanity.com/paper/1810.09038/) (2018)
- [Learning Quadrotor Dynamics Using Neural Network for Flight Control](https://mlsanity.com/paper/1610.05863/) (2016)
- [Deep Neural Networks for Improved, Impromptu Trajectory Tracking of Quadrotors](https://mlsanity.com/paper/1610.06283/) (2016)
- [Concurrent learning for parameter estimation using dynamic state-derivative estimators](https://mlsanity.com/paper/1507.08903/) (2015)
- [New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-time Cases](https://mlsanity.com/paper/1908.05125/) (2019)
- [Adaptive Deep Neural Network-Based Control Barrier Functions](https://mlsanity.com/paper/2406.14430/) (2024)
- [Simultaneous Online System Identification and Control using Composite Adaptive Lyapunov-Based Deep Neural Networks](https://mlsanity.com/paper/2311.13056/) (2023)
- [Uncertainty-Aware Guidance for Target Tracking subject to Intermittent Measurements using Motion Model Learning](https://mlsanity.com/paper/2402.00671/) (2024)
- [Bounds on Deep Neural Network Partial Derivatives with Respect to Parameters](https://mlsanity.com/paper/2503.21007/) (2025)

## Built on by (most cited first, 2 of 2)

- [Predictive reinforcement learning based adaptive PID controller](https://mlsanity.com/paper/2506.08509/) (2025)
- [Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees](https://mlsanity.com/paper/2609.32289/) (2026)

## Abstract (arXiv)

Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the challenge of identifying the system dynamics using the DNN. This paper presents the first result on simultaneous trajectory tracking and online system identification using a DNN-based controller, without requiring persistent excitation. Two new concurrent learning adaptation laws are constructed for the weights of all the layers of the DNN, achieving convergence of the DNN's parameter estimates to a neighborhood of their ideal values, provided the DNN's Jacobian satisfies a finite-time excitation condition. A Lyapunov-based stability analysis is conducted to ensure convergence of the tracking error, weight estimation errors, and observer errors to a neighborhood of the origin. Simulations performed on a range of systems and trajectories, with the same initial and operating conditions, demonstrated 40.5% to 73.6% improvement in function approximation performance compared to the baseline, while maintaining a similar tracking error and control effort. Simulations evaluating function approximation capabilities on data points outside of the trajectory resulted in 58.88% and 74.75% improvement in function approximation compared to the baseline.