A Neural Network to A Neural Network: A Structured Neural Network Controller Design with Stability and Optimality Guarantees

As deep neural networks (DNNs) are black-box models, ensuring closed-loop stability and optimality when learning DNN controllers is a critical issue. Previous work has proposed DNN controllers for specific systems, where closed-loop stability is guaranteed by carefully designing the structure of the DNN controller. However, since the controller’s structure is fixed, the DNN controller needs to be retrained for changing initial states, making it unsuitable for receding horizon control. In this paper, we propose an improved structured DNN controller design to address this issue. The proposed controller comprises a primary and a secondary neural network. The primary neural network simulates the conventional structured controller, with weights determined by the output of the secondary neural network. The input of the secondary neural network is the initial state of the system. Using this approach, the primary neural network provides stability guarantees, and the secondary neural network can be optimized to allow for improved adaptability to changing initial states. The method is validated through several experiments, demonstrating its effectiveness in improving the performance of the conventional structured DNN controller.