Koopman-Based MPC With Learned Dynamics: Hierarchical Neural Network Approach.

Area of Science:

• Control Theory
• Dynamical Systems
• Machine Learning

Background:

• Nonlinear dynamical systems pose significant challenges for traditional control methods.
• Linearization techniques are often limited in scope and applicability.
• Data-driven approaches offer a promising avenue for controlling complex systems.

Purpose of the Study:

• To develop a generalized Koopman framework for nonlinear control systems.
• To introduce a deep learning-based method for approximating Koopman representations.
• To design a computationally efficient Koopman-based Model Predictive Control (MPC) strategy for nonlinear systems with constraints.

Main Methods:

• Generalizing the Koopman framework to nonlinear control systems.
• Employing a hierarchical neural network (HNN) with a scale-invariant constrained network for Koopman approximation.
• Designing a Koopman-based MPC scheme utilizing a modified MPC with a saturation-like function on the lifted linear system.

Main Results:

• Accurate approximation of finite Koopman eigenfunctions and the Koopman operator using the HNN.
• Successful stabilization of nonlinear dynamical systems using the proposed Koopman-based MPC.
• Demonstrated higher computational efficiency compared to classical linear and nonlinear MPC.

Conclusions:

• The proposed data-driven Koopman-based control strategy effectively linearizes and stabilizes nonlinear dynamical systems.
• The hierarchical neural network approach provides accurate Koopman representation approximation.
• The Koopman-based MPC offers a computationally efficient and effective control solution for constrained nonlinear systems, validated by experimental results.