The field of model predictive control is moving towards leveraging machine learning and linearization techniques to improve performance and stability in nonlinear systems. Researchers are exploring the use of neural networks and Koopman theory to transform complex nonlinear dynamics into linear frameworks, enabling more efficient control strategies. This shift is enabling the development of more robust and applicable control methods, particularly in systems with complex interactions between state and control variables. Notable papers in this area include:

• One that proposes a convex data-based economic predictive control method using a neural network to transform the system output into a new state space.
• Another that presents an innovative approach to model predictive control by combining Koopman theory and deep reinforcement learning to enhance controller performance.
• A paper that integrates Koopman theory and Lyapunov stability to develop a robust model predictive control approach for nonlinear systems.
• And a study that uses a Koopman eigenfunction model to identify and optimize nonlinear control of a turbojet engine.