Safe Optimal Control of Quadrotor Formations Using Multilayer Neural Networks and Continual Learning

ABSTRACT This article presents an integral reinforcement learning‐based optimal formation tracking scheme for multiple quadrotor unmanned aerial vehicles (QUAVs) experiencing nonlinear coupled dynamics and subject to constraints. We use multilayer neural networks (MNN) within an actor‐critic framework where the MNN weights are tuned using singular value decomposition (SVD) of the activation function gradient to approximate optimal control policy via backstepping. Additionally, barrier Lyapunov functions (BLF) are introduced to ensure set invariance, thereby maintaining the quadrotors within a defined safety space due to constraints. A novel weight update law for each layer is derived using the HJB approximation error and control input error. Stabilizing terms for the output layer, obtained through Lyapunov analysis, are included to enhance stability and ensure the boundedness of the system. To improve performance on multitasking missions and address the issue of catastrophic forgetting, online continual learning is incorporated in each layer of actor‐critic MNNs. Moreover, this method is applied for leader–follower formation using spherical coordinates. The control objectives for the followers involve tracking the leader with the desired separation, angle of incidence, and bearing through auxiliary velocity control. The simulation results indicate potential improvements over traditional methods.