Knowledge‐driven approximate model predictive controller with probabilistic performance validation

Abstract The aim of approximate model predictive control (MPC) is to alleviate the computational cost by learning an explicit control policy using data generated from offline solutions to MPC problems. However, directly constructing a neural network using these input‐output data cannot guarantee learning efficiency or constraint satisfaction. This study integrates prior knowledge from solving MPC optimization problems into the construction and training of a neural network‐based approximate controller, proposing a knowledge‐driven approximate MPC scheme. First, by designing a differentiable optimization layer, the constraints of the optimization problem are embedded into the neural network structure, ensuring that the generated approximate control inputs satisfy the constraints. Subsequently, derivative information is explicitly incorporated into the neural network, and a new loss function is designed, effectively reflecting the characteristics of the optimization problem during training. Finally, to ensure that the neural network meets performance requirements when approximating the MPC controller, statistical validation techniques are used for a posteriori evaluation of the accuracy of the resulting approximate controller. Through simulation examples, we demonstrate the significant potential of this method as an approximation for predictive control laws. Compared to existing methods, this new approach proves to achieve efficient learning while ensuring constraint satisfaction.