Control of dynamical systems with neural networks

2025-10-06

AI Summary

This work addresses the optimal control problem for high-dimensional, nonlinear, and analytically intractable dynamical systems—including discrete/continuous-time and deterministic/stochastic settings. We propose an end-to-end learning framework based on neural ordinary differential equations (Neural ODEs) and differentiable parameterization. The method jointly models system dynamics via Neural ODEs, represents control policies using deep neural networks, and leverages automatic differentiation and gradient-based optimization to enable implicit, differentiable parameterization of control inputs and efficient backpropagation through time. Compared to conventional numerical or analytical approaches, our framework significantly reduces computational overhead, avoids biases introduced by model simplification, and supports data-driven control under black-box dynamics. We validate its high accuracy, strong generalization, and cross-domain applicability across diverse real-world applications—including biological regulation, engineering systems, physical simulation, and medical intervention—establishing a scalable deep learning paradigm for computationally intensive dynamic system control.

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Abstract

Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation have made applying these methods to control problems increasingly practical. In this paper, we examine the use of neural networks and modern machine-learning libraries to parameterize control inputs across discrete-time and continuous-time systems, as well as deterministic and stochastic dynamics. We highlight applications in multiple domains, including biology, engineering, physics, and medicine. For continuous-time dynamical systems, neural ordinary differential equations (neural ODEs) offer a useful approach to parameterizing control inputs. For discrete-time systems, we show how custom control-input parameterizations can be implemented and optimized using automatic-differentiation methods. Overall, the methods presented provide practical solutions for control tasks that are computationally demanding or analytically intractable, making them valuable for complex real-world applications.

Problem

• Parameterizing control inputs for dynamical systems using neural networks
• Solving control problems across discrete and continuous time domains
• Addressing computationally demanding control tasks with machine learning

Innovation

• Neural networks parameterize control inputs for systems
• Neural ODEs handle continuous-time dynamical systems control
• Automatic differentiation optimizes discrete-time control parameterizations