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This article studies the formation mission design problem for commercial aircraft in the presence of uncertainties. Specifically, it considers uncertainties in the departure times of the aircraft and in the fuel burn savings for the trailing aircraft. Given several commercial flights, the problem consists in arranging them in formation or solo flights and finding the trajectories that minimize the expected value of the DOC of the flights. The formation mission design problem is formulated as an optimal control problem of a stochastic switched dynamical system and solved using nonintrusive gPC-based stochastic collocation. The stochastic collocation method converts the SSOCP into an augmented deterministic switched optimal control problem. With this approach, a small number of sample points of the random parameters are used to jointly solve particular instances of the switched optimal control problem. The obtained solutions are then expressed as orthogonal polynomial expansions in terms of the random parameters using these sample points. This technique allows statistical and global sensitivity analysis of the stochastic solutions to be conducted at a low computational cost. The aim of this article is to establish if, in the presence of uncertainties, a formation mission is beneficial with respect to solo flight in terms of the expected value of the direct operating costs. Several numerical experiments have been conducted in which uncertainties on the departure times and on the fuel saving during formation flight have been considered. The obtained results demonstrate that benefits can be achieved even in the presence of these uncertainties. [ABSTRACT FROM AUTHOR]

In the Paris subway system, stations represent about one-third of the overall energy consumption. Within stations, ventilation is among the top consuming devices; it is operated at maximum airflow all day long, for air quality reasons. In this paper, we present a concept of energy system that displays comparable air quality while consuming much less energy. The system comprises a battery that makes it possible to recover the trains braking energy, arriving under the form of erratic and strong peaks. We propose an energy management system that, at short time scale, controls energy flows and ventilation airflow. By using proper optimization algorithms, we manage to match supply with demand, while minimizing energy daily costs. For this purpose, we have designed algorithms that take into account the braking variability. They are based on the so-called stochastic dynamic programming (SDP) mathematical framework. We fairly compare SDP-based algorithms with the widespread model predictive control (MPC) ones. First, both SDP and MPC yield energy/money operating savings of the order of one-third, compared to the current management without battery. Second, depending on the specific design, we observe that SDP outperforms MPC by a few percent, with an easier online numerical implementation. [ABSTRACT FROM AUTHOR]

Abstract: The motivation of this paper is to prove verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term, in the case where the value function is assumed to be continuous in time and once differentiable in the space variable () instead of once differentiable in time and twice in space (), like in the classical results. For this purpose, the replacement tool of the Itô formula will be the Fukushima–Dirichlet decomposition for weak Dirichlet processes. Given a fixed filtration, a weak Dirichlet process is the sum of a local martingale plus an adapted process which is orthogonal, in the sense of covariation, to any continuous local martingale. The decomposition mentioned states that a function of a weak Dirichlet process with finite quadratic variation is again a weak Dirichlet process. That result is established in this paper and it is applied to the strong solution of a Cauchy problem with final condition. Applications to the proof of verification theorems will be addressed in a companion paper. [Copyright &y& Elsevier]

Abstract: This paper is devoted to presenting a method of proving verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term. The value function is assumed to be continuous in time and once differentiable in the space variable () instead of once differentiable in time and twice in space (), like in the classical results. The results are obtained using a time dependent Fukushima–Dirichlet decomposition proved in a companion paper by the same authors using stochastic calculus via regularization. Applications, examples and a comparison with other similar results are also given. [Copyright &y& Elsevier]