Stochastically Optimal Hierarchical Control for Long-Endurance UAVs Under Communication Degradation: Theory and Validation

This paper establishes a theoretical framework for treating communication quality as a navigable resource in long-endurance unmanned aerial vehicle (UAV) control under stochastic degradation. We prove that a hierarchical architecture integrating communication-aware model predictive control (MPC) achieves ε-optimality with respect to the intractable stochastic dynamic programming formulation while maintaining exponential stability guarantees under switched system dynamics governed by continuous-time Markov chains. Three primary theoretical contributions were made: (1) A stochastic optimality theorem is given showing that sigmoid penalty function approximation yields bounded suboptimality of η≤0.12 under mild ergodicity conditions; (2) a formal stability result for mode switching based on hysteresis was established using multiple Lyapunov functions, and it showed exponentially fast convergence with a decay rate of λ≥0.23; and (3) bifurcation analysis showed that there is a critical time threshold of 72 h at which thermal-induced gyro-drift in the GPS sensor causes a transition in navigation error dynamics from linear to catastrophic nonlinear growth. The validation through 2430 Monte Carlo missions over 54,686 flight hours resulted in an average increase in endurance by 243% (18.2 days versus 5.3 days), while keeping CEP at approximately 8.7 m and achieving 82% mission success under extreme communication degradation (qcomm<0.3). The statistical results confirm a very strong positive relationship between the Resilience Quotient (RQ) and the length of successful missions (R2=0.89, p<0.001), supporting the theoretical model with empirical evidence.