Model predictive control requires the real-time solution of an optimal control problem, which can be challenging on computationally limited systems. Approximating the solution such as by neural networks or series expansions, or deriving an explicit solution, can overcome this challenge. Using neural networks for approximation, a question arises as to how to guarantee closed-loop safety and stability. We use robust control theoretic tools to provide stability guarantees using a neural network trained to approximate a model predictive controller. Notably, the model predictive controller, which might offer desirable closed-loop performance, is not required to provide provable stability properties. To provide stability guarantees for the neural network approximated controller, the closed-loop system is reformulated as a diagonal nonlinear differential form, exploiting that the neural network activation functions are sector bounded and that their slopes are globally bounded. Based on this representation, we establish sufficient closed-loop stability conditions in form of linear matrix inequalities for the nominal and the disturbed system using the neural network approximated model predictive controller.

Robust Control Theory Based Stability Certificates for Neural Network Approximated Nonlinear Model Predictive Control

Automotive Applications

technical paper

The IFAC Conference on Nonlinear Model Predictive Control (NMPC 2021) aims to bring together researchers interested in and work in the MPC field from both academia and industry. This allows us to reflect and establish the current state-of-the-art and focus on the future development of the MPC field towards relevant directions.

Model predictive control (MPC) is indisputably one of the advanced control techniques that have significantly affected control engineering practice with thousands of controllers implemented in various fields, spanning from the process industry to automotive and robotics. This is due to its unique ability to handle constraints, take preview information about disturbances and setpoint changes into account, and optimize performance. Furthermore, MPC allows the consideration of various types of dynamics, from linear to nonlinear, discrete to continuous, as well as an online adaptation of models and parameters. The research community on MPC is very active, with hundreds of papers published every year. Over the past decades, many theoretical, as well as implementation results, have been achieved.

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Nonlinear Model Predictive Control Conference 2021

The IFAC Conference on Nonlinear Model Predictive Control (NMPC 2021) aims to bring together researchers interested in and work in the MPC field from both academia and industry. This allows us to reflect and establish the current state-of-the-art and focus on the future development of the MPC field towards relevant directions.

Hoang Hai Nguyen

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Robust Control Theory Based Stability Certificates for Neural Network Approximated Nonlinear Model Predictive Control

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