# Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guarantees

arXiv: https://arxiv.org/abs/2404.07373 · HTML: https://mlsanity.com/paper/2404.07373/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 10 Apr 2024.

## Builds on (most cited first, 20 of 20)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming](https://mlsanity.com/paper/1903.01287/) (2019)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllers](https://mlsanity.com/paper/2006.07579/) (2020)
- [Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees](https://mlsanity.com/paper/2206.01913/) (2022)
- [Stability-certified reinforcement learning: A control-theoretic perspective](https://mlsanity.com/paper/1810.11505/) (2018)
- [Certifying Incremental Quadratic Constraints for Neural Networks via Convex Optimization](https://mlsanity.com/paper/2012.05981/) (2020)
- [Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems](https://mlsanity.com/paper/2109.03861/) (2021)
- [Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System](https://mlsanity.com/paper/2112.04219/) (2021)
- [Neural network training under semidefinite constraints](https://mlsanity.com/paper/2201.00632/) (2022)
- [Synthesis of Stabilizing Recurrent Equilibrium Network Controllers](https://mlsanity.com/paper/2204.00122/) (2022)
- [Linear systems with neural network nonlinearities: Improved stability analysis via acausal Zames-Falb multipliers](https://mlsanity.com/paper/2103.17106/) (2021)
- [Learning Over Contracting and Lipschitz Closed-Loops for Partially-Observed Nonlinear Systems (Extended Version)](https://mlsanity.com/paper/2304.06193/) (2023)
- [Dissipativity and Integral Quadratic Constraints, Tailored computational robustness tests for complex interconnections](https://mlsanity.com/paper/2105.07401/) (2021)
- [Stabilizing reinforcement learning control: A modular framework for optimizing over all stable behavior](https://mlsanity.com/paper/2310.14098/) (2023)

## Built on by (most cited first, 4 of 4)

- [Assumed Density Filtering and Smoothing with Neural Network Surrogate Models](https://mlsanity.com/paper/2511.09016/) (2025)
- [Demystifying Lipschitz verification: positive matrices, negative results](https://mlsanity.com/paper/2603.28113/) (2026)
- [Implicit Neural Networks as Static Controllers: Certificates and Performance Separation](https://mlsanity.com/paper/2607.11122/) (2026)
- [Scalable Incremental Robustness Analysis of Neural Network Feedback Systems](https://mlsanity.com/paper/2609.22576/) (2026)

## Abstract (arXiv)

This paper presents a method to synthesize neural network controllers to maximize reward subject to the hard constraint that the feedback system of plant and controller be dissipative, certifying requirements such as stability and L2 gain bounds. It considers nonlinear and uncertain plants, modeled as the interconnection of a linear time-invariant (LTI) system and an uncertainty block, which incorporates nonlinearities. The uncertainty of the plant and the activation functions of the neural network are both described using integral quadratic constraints (IQCs). First, a dissipativity condition is derived for uncertain LTI systems. Second, this condition is used to construct a linear matrix inequality (LMI) which can be used to synthesize neural network controllers. Finally, this convex condition is used in a projection-based training method to synthesize neural network controllers with dissipativity guarantees. Numerical examples on an inverted pendulum and a flexible rod on a cart are provided to demonstrate the effectiveness of this approach.