Aspproximating Model Predictive Controller With Biased ReLU Neural Network

It is a popular research area to use neural network to approximate the designed MPC controller to control the system with reduced computational burden while maintaining stability and constraint satisfaction. A new strategy called constraints tightening is used on the MPC controller to ensure robustness to input disturbance within given bound in order that the constraints satisfaction and recursive feasibility can be achieved. Training a neural network is usually time-consuming especially when the activation function is nonlinear, which leads the implementation unpratical. To reduce the time for training we use a biased ReLU neural network to approximate the controller. The performance of the biased ReLU neural network and fully connected neural network in approximating the MPC controller is compared. The training time for the biased ReLU neural network is much shorter while achieving the similar level of accuracy.