Endurance Maximizing Periodic Control of Unmanned Aerial Vehicles

Optimal Periodic Control of Unmanned Aerial Vehicles Based on Fourier Integral Pseudospectral and Edge-Detection Methods

“…It should be noted that the approximate optimal fuel consumption obtained by the FIPS-ED method is larger than those recorded in [32] using the shooting method and the differential flatness based method, which were 0.07686 kg/s and 0.07710 kg/s with periods 9.96 s and 10.08 s, respectively. However, there are a number of observations which largely support our results; we describe them in the following items:…”

“…includes the usual parameters σ and m, the final time T f , the time-dependent Lagrange multiplier associated with the UAV speed λ V , and a user-defined constant smoothing factor s m of large value, which varies depending on how sharp the bang-bang thrust is needed in the sense that lim s m →∞ Φ s m (t) = T (t) ∀t ∈ Ω T f . However, Φ s m is very ill-conditioned for λ V (0) values near the recorded numerical value −0.01626 in [32] with increasing sensitivity as s m → ∞. Table 2 shows the values of Φ s m for λ V (0) = −0.01626 and its perturbed value λV (0) = −0.01627 for some increasing values of s m ; the values of σ and m are as quoted from Table 3.…”

“…( 27)], Φ s m must be periodic with respect to λ V when holding all other parameters fixed, thus, T (0) = T (T f ) by Eq. ( 7), which does not conform to the thrust profile in [32,Figure 4].…”

“…• The basis function used in the differential flatness based method does not allow bang-bang profiles due to continuity constraints as reported in [32], so the bang-bang structure of the thrust profile is generally not preserved, and the method may skip some switching times of the optimal thrust policy.…”

“…This is commonly achieved by optimally regulating the thrust produced by the UAV propellers, attack angle, and bank angle to realize autonomous flight based on energy maximization. Closely related works in this direction investigated the possibility of finding optimal "periodic" solutions to enhance endurance rather than steady-state optimal solutions; [27][28][29][30][31][32]. This interesting subject is part of the optimal periodic control theory, which was originally motivated by problems from chemical engineering, as some studies have found that cycling a chemical reactor can increase the average output compared to steady-state operation [33].…”