Abstract: To address the deep-stall recovery problem of V-tail aircraft, this paper proposes a novel deep-stall recovery hierarchical strategy that combines Penalized Proximal Policy Optimization (P3O) reinforcement learning with a fast predefined-time incremental control approach. First, a six-degree-of-freedom nonlinear model of the V-tail aircraft is established, and the deep-stall recovery problem is formulated as a constrained Markov Decision Process. Second, the existing predefined-time control theory is improved to enhance the transient performance of state responses under given convergence time. Based on this improved theory and a nonlinear incremental dynamic inversion method, an angular rate controller is designed, which ensures that angular rate accurately tracks the decision commands within the user-defined time. The predefined-time stability of the controller is theoretically proven via Lyapunov stability theory. Subsequently, a decision-making network based on P3O is constructed to improve the safety during deep-stall recovery, where safety constraints are incorporated as penalty terms to guide the agent in generating safe recovery actions. Finally, a series of simulations and Monte Carlo experiments are conducted to validate the proposed strategy. The results demonstrate its superior performance in terms of rapidity, robustness, safety, and interpretability.

Key words: V-tail aircraft, Deep-stall recovery, Penalized Proximal Policy Optimization, Fast predefined-time control, State safety constraints