Neural Control: Concurrent Learning of Optimal Control and System Dynamics for Unknown Dynamical Systems

Belangrijkste concepten

Neural Control (NC) is a novel framework that combines the learning of optimal control functions and system dynamics within a coupled neural ODE structure, enabling concurrent identification of unknown dynamics and optimization of control policies.

Samenvatting

The paper introduces Neural Control (NC), a novel framework that integrates the processes of learning optimal control functions and identifying system dynamics within a coupled neural ODE structure.
Key highlights:

NC eliminates the need for separate system identification prior to control optimization in the classical optimal control framework.
The coupled neural ODE structure in NC allows for concurrent learning of the optimal control function and the underlying system dynamics.
Through an intriguing interplay between the controller and dynamics learner neural networks, NC harnesses the full potential of the neural ODE model for controlling continuous-time systems with unknown dynamics.
Experiments on linear and nonlinear dynamical systems, such as the CartPole problem, demonstrate the effectiveness of NC in learning optimal control with high data efficiency compared to traditional reinforcement learning methods.
The alternative training scheme proposed for NC enables the controller and dynamics learner to mutually supervise and shape each other's learning, leading to refined coordination between the two components.

Statistieken

The system dynamics for the linear control task are given by:
˙x = Ax + Bu
The CartPole system dynamics are described by the following system of differential equations:
˙x = ˙x
¨x = (F + mp l (˙θ^2 sin θ - ¨θ cos θ)) / (mc + mp)
˙θ = ˙θ
¨θ = (g sin θ + cos θ * (-F - mp l ˙θ^2 sin θ) / (mc + mp)) / (4/3 - mp cos^2 θ / (mc + mp))

Citaten

"Through an intriguing interplay between the controller and dynamics learner neural networks, NC harnesses the full potential of the neural ODE model for controlling continuous-time systems with unknown dynamics."
"The alternative training scheme proposed for NC enables the controller and dynamics learner to mutually supervise and shape each other's learning, leading to refined coordination between the two components."

Belangrijkste Inzichten Gedestilleerd Uit

Neural Control: Concurrent System Identification and Control Learning with Neural ODE

by Cheng Chi om arxiv.org 04-23-2024

https://arxiv.org/pdf/2401.01836.pdf

Diepere vragen

How can the NC framework be extended to handle partially observable or stochastic dynamical systems?

The NC framework can be extended to handle partially observable dynamical systems by incorporating techniques from Partially Observable Markov Decision Processes (POMDPs). In POMDPs, the agent does not have full observability of the system state, which aligns with the scenario of partially observable dynamical systems. To adapt NC for such systems, one can introduce an observation function that maps the hidden state to the observable state. This observation function can be learned using neural networks in a similar fashion to the dynamics learner and controller in NC. By incorporating the observation function, the NC model can effectively handle partial observability by inferring the hidden state from the observable state.
For stochastic dynamical systems, the NC framework can be extended by incorporating probabilistic models such as Gaussian Processes or Variational Autoencoders. These models can capture the uncertainty in the system dynamics and provide probabilistic predictions. By integrating probabilistic models into the dynamics learner component of NC, the model can learn to account for stochasticity in the system dynamics. Additionally, techniques from Reinforcement Learning under Uncertainty can be employed to optimize control policies that are robust to stochasticity in the system.

What are the potential limitations of the coupled neural ODE structure in NC, and how can they be addressed?

One potential limitation of the coupled neural ODE structure in NC is the computational complexity and training instability that may arise when dealing with high-dimensional or complex dynamical systems. The integration of two neural networks in a coupled ODE framework can lead to increased computational overhead and difficulty in training the model effectively. To address this limitation, techniques such as regularization methods, parameter sharing, and architecture simplification can be employed. Regularization techniques like weight decay or dropout can help prevent overfitting and improve the generalization of the model. Parameter sharing between the dynamics learner and controller can reduce the number of parameters and enhance training stability. Additionally, simplifying the architecture of the neural networks by reducing the number of layers or neurons can make the model more tractable and efficient.
Another limitation is the potential for the model to get stuck in suboptimal solutions or local minima during training. To mitigate this, techniques such as curriculum learning, ensemble methods, and meta-learning can be utilized. Curriculum learning involves gradually increasing the complexity of the training tasks, allowing the model to learn progressively. Ensemble methods can combine multiple NC models to improve robustness and generalization. Meta-learning approaches can help the model adapt to new tasks and environments by leveraging past experiences.

How can the insights from the NC framework be applied to other areas of control theory and reinforcement learning beyond optimal control of dynamical systems?

The insights from the NC framework can be applied to various areas of control theory and reinforcement learning beyond optimal control of dynamical systems. One application is in robotics, where NC can be used for robot control and motion planning tasks. By integrating NC with robotic systems, it can learn to control robot movements in complex environments and adapt to changing conditions.
In the field of autonomous vehicles, NC can be utilized for trajectory planning and decision-making processes. By training the NC model on real-world driving data, it can learn to navigate traffic scenarios, optimize fuel efficiency, and ensure passenger safety.
Furthermore, in the domain of finance, NC can be applied to portfolio optimization, risk management, and algorithmic trading. By modeling financial systems as dynamical systems, NC can learn optimal control strategies for investment decisions and asset allocation.
Overall, the insights from the NC framework can be leveraged to enhance control systems in various domains, enabling adaptive and intelligent decision-making in dynamic environments.