Examinando por Autor "Olivares, Alberto"

Mostrando 1 - 8 de 8

A statistical moment-based spectral approach to the chance-constrained stochastic optimal control of epidemic models
(Elsevier, 2023) Olivares, Alberto; Staffetti, Ernesto
This paper presents a spectral approach to the uncertainty management in epidemic models through the formulation of chance-constrained stochastic optimal control problems. Specifically, a statistical moment-based polynomial expansion is used to calculate surrogate models of the stochastic state variables of the problem that allow for the efficient computation of their main statistics as well as their marginal and joint probability density functions at each time instant, which enable the uncertainty management in the epidemic model. Moreover, the surrogate models are employed to perform the corresponding sensitivity and risk analyses. The proposed methodology provides the designers of the optimal control policies with the capability to increase the predictability of the outcomes by adding suitable chance constraints to the epidemic model and formulating a proper cost functional. The chance-constrained optimal control of a COVID-19 epidemic model is considered in order to illustrate the practical application of the proposed methodology.
A Stochastic Switched Optimal Control Approach to Formation Mission Design for Commercial Aircraft
(IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, 2022-03-23) Cerezo-Magaña, María; Staffetti, Ernesto; Olivares, Alberto
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.
Chance-constrained stochastic optimal control of epidemic models: A fourth moment method-based reformulation
(Elsevier, 2024-12) Buelta, Almudena; Olivares, Alberto; Staffetti, Ernesto
This work proposes a methodology for the reformulation of chance-constrained stochastic optimal control problems that ensures reliable uncertainty management of epidemic outbreaks. Specifically, the chance constraints are reformulated in terms of the first four moments of the stochastic state variables through the so-called fourth moment method for reliability. Moreover, a spectral technique is employed to obtain surrogate models of the stochastic state variables, which enables the efficient computation of the required statistics. The practical implementation of the proposed approach is demonstrated via the optimal control of two different stochastic mathematical models of the COVID-19 transmission. The numerical experiments confirm that, unlike those reformulations based on the Chebyshev–Cantelli’s inequality, the proposed method does not exhibit the undesired outcomes that are typically observed when a higher precision is required for the risk level associated to the given chance constraints
Data-Driven Probabilistic Methodology for Aircraft Conflict Detection Under Wind Uncertainty
(IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, 2023-03-01) Cerezo-Magaña, María; Staffetti, Ernesto; Olivares, Alberto; de la Mota, Jaime
Assuming the availability of a reliable aircraft trajectory planner, this article presents a probabilistic methodology to detect conflicts between aircraft in the cruise phase of flight in the presence of wind velocity forecasting uncertainty. This uncertainty is quantified by ensemble weather forecasts, the members of which are regarded as realizations of correlated random processes and used to derive the eastward and northward components of the wind velocity. First, the Karhunen¿Loève (KL) expansion is used to obtain a series expansion of the components of the wind velocity in terms of a set of uncorrelated random variables and deterministic coefficients. Then, the uncertainty generated by these uncorrelated random variables in the outputs of the aircraft trajectory planner is quantified using the arbitrary polynomial chaos technique. Finally, the probability density function of the great circle distance between each pair of aircraft is derived from the polynomial expansions using a Gaussian kernel density estimator and used to estimate the probability of conflict. The arbitrary polynomial chaos technique allows the effects of uncertainty in complex nonlinear dynamical systems, such as those underlying aircraft trajectory planners, to be quantified with high computational efficiency, only requiring the existence of a finite number of statistical moments of the random variables of the KL expansion while avoiding any assumptions on their probability distributions. To demonstrate the effectiveness of the proposed conflict detection method, numerical experiments are conducted via an optimal control-based aircraft trajectory planner for a given wind velocity forecast represented by an ensemble prediction system.
Formation Mission Design for Commercial Aircraft Using Switched Optimal Control Techniques
(IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, 2021-02-24) Cerezo-Magaña, María; Staffetti, Ernesto; Olivares, Alberto
In this article, the formation mission design problem for commercial aircraft is studied. Given the departure times and the departure and arrival locations of several commercial flights, the relevant weather forecast, and the expected fuel savings during formation flight, the problem consists in establishing how to organize them in formation or solo flights and in finding the trajectories that minimize the overall direct operating cost of the flights. Each aircraft can fly solo or in different positions inside a formation. Therefore, the mission is modeled as a switched dynamical system, in which the discrete state describes the combination of flight modes of the individual aircraft and logical constraints in disjunctive form establish the switching logic among the discrete states of the system. The formation mission design problem has been formulated as an optimal control problem of a switched dynamical system and solved using an embedding approach, which allows switching decision among discrete states to be modeled without relying on binary variables. The resulting problem is a classical optimal control problem which has been solved using a knotting pseudospectral method. Several numerical experiments have been conducted to demonstrate the effectiveness of this approach. The obtained results show that formation flight has great potential to reduce fuel consumption and emissions.
Multi-Aircraft Transfer Learning for Aircraft Trajectory Tracking in Continuous Climb and Descent Operations
(Institute of Electrical and Electronics Engineers, 2024-06-03) Buelta, Almudena; Olivares, Alberto; Staffetti, Ernesto
This paper presents a control technique for aircraft trajectory tracking that combines Iterative Learning Control (ILC) with Model Reference Adaptive Control (MRAC). ILC enhances the accuracy of aircraft in following a predefined trajectory based on the deviations in space and time observed in previous flights to anticipate repetitive disturbances proactively. However, ILC requires the system to be repetition-invariant, which is not applicable in real operations where different aircraft consecutively perform flights along the same trajectory. To address this drawback, a multi-aircraft transfer learning strategy is considered. At each iteration of the ILC, this strategy allows learned trajectory knowledge to be transferred among different aircraft. The proposed approach involves augmenting the baseline aircraft trajectory tracking controller with an MRAC, which ensures that the aircraft behaves similarly to a given reference model, while the ILC acts as a high-level adaptation scheme, compensating for repetitive disturbances affecting the flight. Numerical experiments are conducted using various simulated aircraft following the same trajectory in continuous climb and descent operations. Results show that the MRAC-ILC method outperforms the combination of ILC with the baseline feedback controller without MRAC augmentation, achieving a substantial reduction in the trajectory tracking error after a few iterations. This improvement remains consistent even in the presence of model uncertainties, disturbances, and changing aircraft dynamics. In summary, the MRAC-ILC method makes ILC suitable for real operations, enhances the predictability of aircraft trajectories, and consequently improves the efficiency of the air traffic management system.
Planning and Control of Aircraft Ground Movement Operations with Towbarless Robotic Tractors
(Institute of Electrical and Electronics Engineers, 2024-07-18) Buelta, Almudena; Olivares, Alberto; Staffetti, Ernesto
This article studies the automation of aircraft ground movement operations using towbarless robotic tractors. The tractor-aircraft system is modeled as a car-like mobile robot with an off-hooked trailer, in which an accurate dynamic model of the tractor-aircraft system is employed. The primary objective of this study is to determine the control inputs and the resulting collision-free trajectories to steer the aircraft from the initial to the final position, under the assumption that the model of the system and the positions of the obstacles are known. This trajectory planning problem is formulated as an energy-time optimal control problem, which is solved using a pseudospectral knotting numerical method. The effects of the uncertainty in the weight of the aircraft on the solution of the planning problem are also quantified. Since, in general, the tractor-aircraft system moves backwards during ground movement operations, the issue of jackknifing is also addressed. Therefore, the secondary objective of this article is to deal with the problem of tracking the planned trajectory while preventing jackknifing. The trajectory tracking problem is solved using a Jacobian linearization of the offset dynamics about the planned trajectory, in which the optimal control inputs are used as feedforward terms to improve tracking precision
Robust Optimal Control of Compartmental Models in Epidemiology: Application to the COVID-19 Pandemic
(Elsevier, 2022) Olivares, Alberto; Staffetti, Ernesto
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.