The average NonLinear Programming: some theoretical and practical aspects

This research is centered around average NonLinear Programming (aNLP); a conceptual technique that provides some theoretical insights into the area of trajectory optimization. In short, NLP transcribes a continuous (infinite dimensional) trajectory optimization into a finite-dimensional problem (i.e., involving an n −dimensional minimizer). In this respect, aNLP relates an n − dimensional minimizer to an m − dimensional minimizer ( m). We also exhibit how the n−dimensional optimal solution is reachable by solving the m−dimensional problem through an iterative fixed point method. Moreover, we show that aNLP is useful to find the geometry of the optimal solution quickly and accurately. We first solve trajectory optimization problems by aNLP. Then, the upshots are fed to either an indirect solver (exploiting the Pontryagin Maximum Principle) or a direct solver (employing an optimization module) to solve the following new examples: 1) Mach-constrained time-optimal aircraft in the climbing phase in the presence of wind and 2) time-fuel-optimal free routing aircraft flight.