<p>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 it increasingly practical to apply these methods to control problems. This paper provides an accessible overview of how neural networks and modern machine learning frameworks can be used to parameterize control inputs for both discrete-time and continuous-time systems, encompassing deterministic and stochastic dynamics. Applications are highlighted across multiple domains, including biology, engineering, physics, and medicine. For continuous-time dynamical systems, neural ordinary differential equations (neural ODEs) provide a useful approach to parameterizing control inputs, while in discrete-time settings, custom control-input parameterizations can be implemented and optimized using automatic differentiation. Overall, the methods presented offer practical solutions for control tasks that are computationally demanding or analytically intractable, making them valuable for complex real-world applications.</p>

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Control of dynamical systems with neural networks

  • Lucas Böttcher

摘要

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 it increasingly practical to apply these methods to control problems. This paper provides an accessible overview of how neural networks and modern machine learning frameworks can be used to parameterize control inputs for both discrete-time and continuous-time systems, encompassing deterministic and stochastic dynamics. Applications are highlighted across multiple domains, including biology, engineering, physics, and medicine. For continuous-time dynamical systems, neural ordinary differential equations (neural ODEs) provide a useful approach to parameterizing control inputs, while in discrete-time settings, custom control-input parameterizations can be implemented and optimized using automatic differentiation. Overall, the methods presented offer practical solutions for control tasks that are computationally demanding or analytically intractable, making them valuable for complex real-world applications.