Nonlinear Model Predictive Control Based on Deep Learning for Hindmarsh–Rose Neuron Model

The online solution of the optimization problems associated to the model predictive control (MPC) of constrained systems requires significant computational efforts. The Hindmarsh-Rose (HR) neuron model, which can simulate the functioning of biological neurons, is an example of a complex nonlinear system exhibiting chaotic behavior. Various control design methods have been applied to control the HR model, including nonlinear MPC based on online optimization. This paper proposes the design of an optimal controller for the HR model by using the NMPC approach based on deep neural networks (NMPC-DNN). The DNN of the controller is trained offline by using the optimal control trajectories obtained for a set of initial states of the HR model. Then online, the control input is computed simply by evaluating the function realized by the DNN. The advantages of the NMPC-DNN approach applied to the HR model are the significant reduction of the online computational complexity, as well as the simple software implementation of the controller. The performance of the NMPC-DNN controller designed for the HR model is studied by simulation experiments.