This article proposes a recursive Gaussian process regression with a joint optimization-based iterative learning control algorithm to estimate and predict disturbances and model uncertainties affecting a flight. The algorithm proactively compensates for the predicted disturbances, improving precision in aircraft trajectory tracking. Higher precision in trajectory tracking implies an improvement of the aircraft trajectory predictability and, therefore, of the air traffic management system efficiency. Airlines can also benefit from this higher predictability by reducing the number of alterations when following their designed trajectories, which entails a reduction of costs and emissions. The iterative learning control algorithm is divided into two steps: first, a recursive Gaussian process regression estimates and predicts perturbations and model errors with no need for prior knowledge about their dynamics and with low computational cost, and second, this information is used to update the control inputs so that the subsequent aircraft intending to fly the same planned trajectory will follow it with greater precision than the previous ones. This method is tested on a simulated commercial aircraft performing a continuous climb operation and compared to an iterative learning algorithm using a Kalman filter estimator in a similar scenario. The results show that the proposed approach provides 62 and 42% precision improvement in tracking the desired trajectory, as compared to the Kalman filter approach, in two experiments, where no prior knowledge of the unmodeled dynamics was available, also achieving it in less iterations.

This paper presents an iterative learning control method for precise aircraft trajectory tracking. Given a trajectory to be followed by an aircraft with a dynamical model which is assumed to be known, the proposed algorithm improves the system performance in following the trajectory using the spatial and temporal deviations suffered by previous flights to anticipate recurring disturbances and compensate for them proactively by generating a new reference trajectory to be followed, which is the input for the aircraft’s own trajectory tracking controller. The proposed method is tested in a simulated busy terminal maneuvering area in which the time-based separation between aircraft is short enough for similar weather conditions to be expected. The numerical experiments are conducted considering aircraft of the same type, which are assumed to follow the same trajectory in two operations in which precise trajectory tracking is essential: continuous climb and descent operations. The obtained results show a significant reduction of the trajectory tracking error in few iterations, proving the effectiveness of the iterative learning control method applied to commercial aircraft trajectory tracking. Higher precision in trajectory tracking implies higher predictability of aircraft trajectories, which results in an improvement of the efficiency and capacity of the air traffic management system and in reductions of costs and emissions.

In this paper, a spectral approach is used to formulate and solve robust optimal control problems for compartmental epidemic models, allowing the uncertainty propagation through the optimal control model to be represented by a polynomial expansion of its stochastic state variables. More specifically, a statistical moment-based polynomial chaos expansion is employed. The spectral expansion of the stochastic state variables allows the computation of their main statistics to be carried out, resulting in a compact and efficient representation of the variability of the optimal control model with respect to its random parameters. The proposed robust formulation provides the designers of the optimal control strategy of the epidemic model the capability to increase the predictability of the results by simply adding upper bounds on the variability of the state variables. Moreover, this approach yields a way to efficiently estimate the probability distributions of the stochastic state variables and conduct a global sensitivity analysis. To show the practical implementation of the proposed approach, a mathematical model of COVID-19 transmission is considered. The numerical results show that the spectral approach proposed to formulate and solve robust optimal control problems for compartmental epidemic models provides healthcare systems with a valuable tool to mitigate and control the impact of infectious diseases.(C) 2022 The Author(s). Published by Elsevier B.V.