Optimal control Theory is an exciting research area where new theoretical approaches and application problems both come into play. In such a scenario, mathematicians and engineers often work on the same problems using parallel languages and methodologies. Highly influential academic researchers and experts from industries and agencies will gather at the New Trends and Challenges in Optimization Theory Applied to Space Engineering conference to establish a bridge among their respective groups. The topics of the conference panels have been selected to include the most advanced areas of interest for Space applications. In line with the Gran Sasso Tech Foundation’s mission, we will promote interdisciplinary dialogue among sciences and encourage different experts to collaborate towards identifying new problems and generating new solutions. Covering a wide range of Space-related topics and challenges, this conference aims to lay the foundation for a long-lasting collaboration among different groups of experts.
INFO and Registration email: firstname.lastname@example.org
December 13, 2023
|11:00 – 12:20|
Welcome from InstitutionsFernando Ferroni, President, Gran Sasso Tech
Mario Cosmo, Director of Science and Research, Italian Space Agency (ASI)
Dante Galli, Space Rider Programme Manager, European Space Agency (ESA)
Massimo Claudio Comparini, Chief Executive Office, Thales Alenia Space Italia
Paola Inverardi, Rector, Gran Sasso Science Institute
Elena Grifoni Winters, Capo Ufficio Politiche Spaziali e Aerospaziali, Presidenza del Consiglio dei Ministri
|12:20 – 12:30|
Conference opening remarksLeonardo Mazzini, Chief Technical Officer, Thales Alenia Space Italia
Topic 1: Manifold dynamics, trajectory design, and related control aspects
|14:00 – 14:30|
Panel coordinator introductionAlessandra Celletti – Chair of Mathematical Physics, Department of Mathematics, Università di Roma Tor Vergata
|14:30 – 15:00|
Invariant manifolds of invariant tori: effective computation and applicationsAngel Jorba – Professor of department of Mathematics and Informatics, University of Barcelona
In this talk we will discuss the numerical computation of high order Taylor-Fourier approximations to the stable/unstable invariant manifolds of invariant tori. As applications, we will discuss the capture of an asteroid near the L3 point of the Earth-Moon system and the transfer and control of a spacecraft near an unstable torus.
|15:00 – 15:30|
On the impact of mission constraints on station-keeping at L1 and L2. Libration Point Orbits using Floquet modesAriadna Farres – Research fellow at the Flight Dynamics and Mission Design group, NASA Goddard Space Flight Center
Main author: Ariadna Farrés, University of Maryland at College Park, Maryland, United States
Co-Authors: David C. Folta (1), Cassandra Webster(1), Jeremy Petersen (2)
Over this decade, there has been an increase on space missions taking advantage of the natural dynamics around the L1 and L2 points in the Circular Restricted Three-Body (CRTBP). Libration Point orbits (LPOs around these two equilibrium points are ideal for space weather missions like Solar and Heliospheric Observatory (SoHO) and the Space Weather Follow-On (SWFO); or deep space observations like the James Webb Space Telescope (JWST) and the Roman Space Telescope (RST). It is well known that LPOs are linearly unstable and require routine station-keeping maneuvers for a spacecraft to remain close to them.
In  we used the Floquet mode reference frame to compare two different station-keeping strategies and describe the geometry behind them. The first strategy was the x-axis velocity constraint at the plain crossing, which has been used by NASA in operations for missions like SoHO and JWST. This approach looks for the delta-v required to ensure that at the 4th plane crossing Vx = 0, ensuring the spacecraft will orbit around the LPO. The second strategy was the Floquet mode approach proposed by the Dynamical System group in Barcelona and takes advantage of the natural dynamics around LPOs to determine the maneuver. This approach looks for the delta-v that cancels the unstable mode, bringing the trajectory close to the stable manifold or a reference orbit. In  we compared both strategies using high-order techniques and saw that both approaches have many basic geometrical common features, and that when we force both strategies to find the delta-v maneuver along a fixed thrust direction, the results are the same up to first order. This allows us to use the Floquet mode approach to describe the classical station-keeping strategy used during operations.
Understanding the geometry of station-keeping strategies allows us to study the dependence between thrust direction and the delta-v magnitude and the impact of constraints in the thrust directions, which play an important role on JWST. Here we want to discuss how to use the Floquet mode interpretation to envision strategies that can help mitigate the impact of mission constraints and other perturbations on the mission orbit. We focus our study on three different missions (JWST, RST and SWFO), each one with its challenges and particularities. For instance, JWSTs trajectory is largely affected by solar radiation pressure and has restrictions on the thrust direction , and SWFO has large momentum unloads that impact the size of station-keeping maneuvers . We will use the Floquet Modes to describe the impact of different mission constraints on the cost of station-keeping and derive strategies that can help mitigate them.
This is a joint work with Dave Folta, Cassandra Webster, and Jeremy Pettersen
 A. Farrés, C. Gao, J. Masdemont, G. Gomez, D. Folta, C. Webster, “Geometrical Analysis of Station-Keeping Strategies About Libration Point Orbits”, Journal of Guidance, Control, and Dynamics Vol. 45, No. 6, June 2022
 J. Petersen, “L2 station keeping maneuver strategy for the James Webb Space Telescope”, Proceedings of the 2019 AAS/AIAA Astrodynamics Specialist Conference. (AAS 19-806)
 A. Farrés, D. Folta, A. Michaels, C. Webster, “Mitigating the impact of Momentum Unloads on Station Keeping around Libration Point orbits”, Proceedings of the 2022 AAS/AIAA Astrodynamics Specialist Conference. (AAS 22-688)
|15:30 – 16:00|
Bang-Bang: Don’t Shoot the PMP PlayerLorenzo Casalino – Professor of Department of Mechanical and Aerospace Engineering, Politecnico di Torino
Bang-bang control often characterizes optimal solutions in dynamical problems that are linear in one of the control variables. This is typically the case of space trajectory opti-mization, where the diﬀerential equations that describe the state of the spacecraft are linear with respect to the thrust magnitude, and thrust is bounded between a minimum (usually, zero) and a maximum value. The optimal solution is usually made up by a succession of maximum-thrust and minimum-thrust arcs, i.e., a bang-bang control law (singular arcs with intermediate thrust arcs are optimal only in very limited cases, typically involving atmo-spheric ﬂight).
Bang-bang problems are particularly challenging in the context of indirect optimization method. These methods enforce necessary optimality conditions to transform the optimiza-tion problem into a boundary value problem (BVP), typically solved by a shooting method starting from a tentative solution. Pontryagin’s Maximum Principle (PMP), which states that the control variables must maximize the problem Hamiltonian, can be used to deter-mine the optimal control law. For the thrust magnitude, this means that arcs with either maximum or zero thrust alternate, according to the sign of the switching function. The discontinuities in the control variable makes the BVP solution hard, and aﬀect the method robustness in the sense that the convergence radius is usually small and a quite accurate tentative solution is needed.
Diﬀerent techniques can be envisaged to deal with these issues. Two large groups can be identiﬁed: approaches that, during integration, determine the instantaneous thrust according to the local value of the switching function (e.g., with smoothing techniques to avoid the discontinuities), versus techniques that preliminarily assume the problem switching structure and use PMP to modify the structure when required. The latter approach is considered here.
In this talk, diﬀerent strategies that exploit PMP to improve convergence and the perfor-mance of optimization algorithms are presented, in the context of various space missions and in conjunction with diﬀerent optimization approaches. In particular, examples concerning collaborative satellite deployment, escape maneuvers from Lagrangian points, lunar land-ing (in the context of indirect methods) and orbit transfer and formation reconﬁguration (treated with pseudospectral methods) will be presented.
|16:00 – 16:30|
Challenges of Rendezvous and Optimal Orbital Phasing in Cislunar EnvironmentsStéphanie Lizy-Destrez – Associate Professor of Space System Engineering, ISAE-SUPAERO, Toulouse
The exploration of the Moon, both through human and robotic missions, has emerged as a paramount objective in space engineering. Rendezvous and Docking (RVD) operations, including the critical phase of orbital phasing, play a pivotal role in enabling the deployment of the Lunar Gateway, station assembly, crew rotations, cargo deliveries, and lunar sample return, especially in the vicinity of Earth-Moon Lagrange Points (EML). While RVD in traditional two-body scenarios, such as Low Earth Orbit (LEO), Geostationary Earth Orbit (GEO), and Low Lunar Orbit (LLO), has accumulated significant experience, challenges persist in addressing orbital phasing in non-Keplerian environments, particularly around Lagrange points where standard Keplerian dynamics no longer apply.
In light of the inherent dynamical complexity of Lagrange point regions, this presentation aims to investigate strategies for achieving optimal orbital phasing in the cislunar environment. The focus will be on comparing multiple strategies to successfully execute this critical phase of RVD between a target (e.g., the Lunar Gateway) and a chaser (cargo spacecraft, crew vehicles, ascent/descent vehicles, station modules, etc.), taking into account the specific orbits of these objects. Additionally, exploration will encompass the development of semi-analytical tools to compute and model a range of orbits relevant to the Circular Restricted Three-Body Problem (CR3BP), including Halo orbits (including Near Rectilinear Halo Orbits, NRHO, a subgroup of the Halo family), Butterfly orbits, Dragonfly orbits, Disturbed Rectilinear Orbits (DRO), and quasi-periodic orbits. This approach becomes indispensable as weakly stable trajectories and chaotic dynamics demand a meticulously crafted strategy for approaching the station, making the utilization of quasi-periodic structures an innovative and promising solution.
While working to ensure the success of orbital phasing for rendezvous operations in the cislunar environment, this research adds to the ongoing discourse on optimization theory. Key optimization parameters in these endeavors include Time of Flight (TOF) and total consumption (DeltaV). These optimization scheme typically begin with an initial guess, which can be derived from a Lambert problem in a Keplerian approximation or generated using a stack method. Subsequently, differential corrections are then applied to refine the trajectory. To further enhance results, advanced techniques based on multi-impulsivee transfers are also employed. This research paves the way for more efficient and reliable operations within the challenging realm of Lagrange points, thus advancing the capabilities of future lunar exploration missions.
|16:30 – 17:00|
Designing Fuel-efficient Low-thrust Trajectories in Multi-body Dynamical RegimesRichard Epenoy – Research engineer in orbital mechanics, CNES, Toulouse
In this talk, we will first consider the Sun-Earth-Moon Bicircular Restricted Four-Body Problem and will compute minimum-fuel low-thrust Earth-Moon trajectories by means of an indirect optimal control approach. Thanks to a massive exploration of the set of unknown variables appearing in the optimality conditions, different families of locally optimal trajectories will be identified and classified according to the dynamical structures they leverage. The latter are invariant manifolds of the two underlying Earth-Moon and Sun-Earth Circular Restricted Three-Body Problems .
|17:00 – 17:30|
|17:30 – 18:00|
OFF-PANEL INTRODUCTION TO TOPIC 2: AI TECHNIQUES IN GUIDANCE CONTROL PROBLEM AND SPACE MISSIONS – Control and Machine LearningEnrique Zuazua – Head of the Chair for Dynamics, Control, Machine Learning and Numerics, University of Erlangen-Nuremberg
In this lecture we shall present some recent results on the interplay between control and Machine Learning, and more precisely, Supervised Learning, Universal Approximation and Normaliying flows.
December 14, 2023
Topic 2: AI techniques in guidance control problem and space missions
|09:00 – 09:30|
Panel coordinator introductionEmmanuel Trélat – Director of the Jacques-Louis Lions Laboratory, Sorbonne University, France
|09:30 – 10:00|
TBDDavid Sadek – Vice President Research, Technology & Innovation Thales Alenia Space
|10:00 – 10:30|
Optimal Control and Reinforcement LearningMichele Palladino – Assistant Professor (Rtd-B) Department of Information Engineering, Computer Science and Mathematics, Università degli studi dell’Aquila
The talk discusses one possible model problem for certain tasks in reinforcement learning. The model provides a framework to deal with situations in which the system dynamics are not known and encodes the available information about the state dynamics that an agent has as a measure on the space of functions. In this framework, a natural question is if whether the optimal policies and the value functions converge, respectively, to an optimal policy and to the value function of the real, underlying optimal control problem as soon as more information on the environment is gathered by the agent. We provide a positive answer in the linear-quadratic case and discuss some open problems and questions.
|10:30 – 11:00|
AI-enabled Guidance and Control applications at the European Space AgencyValentin Preda – Guidance, Navigation and Control System Engineer, ESA
The rapid advancements in artificial intelligence (AI) have revolutionized various fields, and the space industry is no exception. This talk provides an overview of recent developments in AI-enabled guidance and control (G&C) applications at the European Space Agency (ESA) through various research and development (R&D) studies and internal projects. The talk will begin with the motivation behind incorporating AI to enhance the accuracy and efficiency of space G&C systems. Next, the talk explores how some machine learning techniques can complement more traditional G&C strategies to enable spacecraft to autonomously navigate through complex & uncertain environments, enhance mission efficiency, and improve overall mission success rates. The talk then highlights key advancements in AI algorithms and techniques explored by ESA and the challenges encountered in implementing these techniques. The challenges range from limited computational resources, reliability & robustness, along with possible strategies to overcome them in some scenarios. Finally, the achievements, lessons learned, and future prospects for AI in G&C are presented.
|11:00 – 11:30|
AI techniques in guidance control problem and space missionsJoël Amalric – Thales Alenia Space
The use of AI techniques in guidance control problems and space missions has gained increasing attention in recent years due to their potential to improve the performance and reliability of space systems. In this session, there will be discussed a) the different AI techniques that can be used in guidance control problems and space missions, such as reinforcement learning, deep learning, and fuzzy logic and also b) present case studies and examples of the successful application of these techniques in various space missions.
On emerging guidance control problems in the satellite industry
The development of full electric satellite platforms equipped with electric propulsion has introduced in past decade new optimal control problems for the guidance function during the low-thrust orbit transfer operations.
|11:30 – 12:00|
Artificial Intelligence Algorithm for Space MissionsArturo Intelisano – Director Research and Innovation and Advanced Projects, Thales Alenia Space Italia
Since almost a decade many papers and studies are being directed in demonstrating that Artificial Intelligence (AI) will play a significant role in guidance and control problems for space missions; a large literature has proposed its application in various Space domains, where AI-based algorithms can enable spacecraft to autonomously perform either navigation or attitude control by processing sensor data and making real-time decisions.
The identification of specific metrics could help in a more general evaluation of the various methods and of the different theoretical approaches, helping the design of these complex algorithmic architectures. In particular it is shown how functions and conceptual instruments, typically used in statistical physics and in information theory ,could be of help to enforce the “explanatory knowledge” behind these techniques, in order to assess their feasibility for application in space.
|12:00 – 12:30|
On no-regret proceduresSylvain Sorin – Professor of Mathematics, Sorbonne University, France
We will recall the main properties of no-regret algorithms in discrete and continuous time and their use in on-line framework, game learning/ variational inequalities and convex optimization.
|12:30 – 13:00|
Topic 3: Optimization techniques for constellations with applications in space operations
|14:00 – 14:30|
Panel coordinator introductionMauro Pontani – Associate Professor of Aerospace Engineering, Department of Astronautical, Electrical, and Energy Engineering, Università Sapienza Roma
|14:30 – 15:00|
The ERC-Funded EXTREMA Project: Achieving Self-Driving Interplanetary CubeSatsFrancesco Topputo – Professor of Department of Aerospace Science and Technology, Politecnico di Milano
Since the beginning of the space era, interplanetary probes have commonly been operated from ground. Operations are conducted by flight control and involve per- forming a number of routine tasks, mainly of scientific, systems engineering, and flight-related nature. Governing the space flight consists of determining the space- craft position, planning its trajectory, and controlling its motion. Accordingly, these activities are known as a whole as Guidance, Navigation and Control (GNC). The EXTREMA project (Engineering Extremely Rare Events in Astrodynamics for Deep-Space Missions in Autonomy) aims towards a paradigm shift on how deep-space GNC is performed, enabling CubeSats with autonomous capabilities. The project has received a consolidator grant from the European Research Council (ERC), a prestigious acknowledgment that funds cutting-edge research in Europe. This presentation is intended to give an overview of EXTREMA, highlighting the approaches, methodologies and objectives; moreover, the expected results, outcomes, and impact on future space exploration scenarios are also discussed.
|15:00 – 15:30|
Distributed Optimization for Integer Programming Problems with application to Scheduling for Earth Observation Missions using Satellite ConstellationsVincenzo Basco – CTO R&T&D Associate, Thales Alenia Space
In on-board computing frameworks, the optimization of resource allocation and decision-making poses significant challenges, particularly in dynamic and different environments. However, distributed (also named, decoupled) optimization techniques have emerged as a promising approach to address these challenges by facilitating collaboration among multiple agents, leveraging their local knowledge. This talk focuses on the application of distributed optimization methods within multi-agent systems operating under time-varying communication networks. Integer linear programming is utilized as a mathematical framework to concentrate our attention. Indeed, such a setting, which provides a structured representation of scheduling problems, aligns seamlessly with the objective of improving response time in earth observation missions carried out by satellite constellations. To verify the effectiveness of the proposed approach, numerical simulations are conducted. These simulations allow for a comprehensive evaluation of the mathematical model’s performance and provide valuable insights into its practical implementation.
|15:30 – 16:00|
In-orbit servicing and assisted orbit transfer mission planningGiorgio Fasano – Researcher and practitioner – CTO Associate, Thales Alenia Space
The increasing demand of performing in-space activities is opening a new era of interest both for industry and academy . In this study, we consider a generic chaser spacecraft that is able to reach any target belonging to a given set of objects positioned on different Low Earth orbits (SSO) within an assigned time period. Once the chaser spacecraft is launched from Earth, it reaches a number of targets where it performs the requested services and finally returns to Earth (or performs a destructive reentry). A certain value, such as the economic return or a relative priority, is associated with each target/service. As, in general, different sequences and target selections are possible, those maximizing the overall value are searched for. Alternative optimization criteria, such as the minimization of the total time spent or the propellant consumed, can be considered.
 NASA Goddard Space Flight Center “On-Orbit Satellite Servicing Study”. Project Report, October 2010
|16:00 – 16:30|
Topic 4: Multi-stage control problems for launcher and landing problems
|16:30 – 17:00|
Panel coordinator introductionGiorgio Fasano – Researcher and practitioner, Thales Alenia Space
|17:00 – 17:30|
B-plane targeting optimization method for Moon injection, descent and landing trajectories designAndrea D’Ottavio – Mission Analysis & Operation Engineer, Thales Alenia Space
Spacecraft (S/C) interplanetary trajectories are typically perturbed by some external disturbance sources, such as third-bodies attraction, possibly drag force contributions during close or aerobraking (AEB) passages, solar radiation pressure, but also by initial thrust and/or attitude errors, for instance. Similar mission scenarios related to critical entry-descent and landing (EDL) phases exist. Such external inputs are injected into the S/C nominal expected transfer or descent trajectories as errors, accumulated continuously. Consequently, the capability to both determine the number and the entities of the so-called trajectory correction manoeuvres (TCMs) to recover or compensate such errors trajectories is one of the most important engineering activity along the entire cycle of the mission design process. It may have sensible impacts on the consolidation of the overall S/C propellant mass budget, which in turn strongly affects the definition of a reliable S/C design fitting with the imposed overall mission requirements. To target specific optimum midcourse, arrival or descent trajectory conditions, the B-plane targeting method is widely used in the field of Mission Analysis. Being the B-plane targeting method based on the differential correction method introduced by Battin , the goal of this study is to present the results obtained integrating such procedure in the definition of a reference coordinates map(s) where each coordinate set on the B-plane represents the optimal arrival or insertion conditions that shall be targeted by the general S/C in order to further realize a direct or indirect descent and landing trajectory profiles allowing the maximization of the payload mass to be deployed over the surface of the Moon. Such type of activities are explored in the frame of the “Argonaut” space exploration programme of the European Space Agency (ESA), i.e., the European flagship Moon exploration program. Additionally, several B-plane approaches that offer analytical solutions are explored and suggested [2,3,4].
|17:30 – 18:00|
On-line ‘emergency’ trajectory re-targeting for the landing of a re-usable vehicleEric Bourgeois – Launcher Trajectory, Guidance & Navigation Expert at CNES
Current initiatives for launcher stage recover and reuse rely on the assertion that these stages have a significant weight regarding the launch cost. The main objective of the Guidance function is to reach the recovery site and to perform a landing maneuver satisfying all kinematic conditions that respect the launcher physical integrity, to contribute to its reuse.
|18:00 – 18:30|
The moon lander optimal control problem revisitedFilippo Gazzola – Professor of Mathematics, Politecnico Milano
We revisit the classical safe landing optimal control problem in aerospace, intro-duced by Miele in the Sixties, where the target is to land a spacecraft on the moon surface at rest with minimal fuel consumption. We show that a detailed analysis in the related 3D phase space uncovers the existence of inﬁnitely many safe landing curves, contrary to several former 2D descriptions that implicitly claim the existence of just one such curve. Our results lead to a deeper understanding of the dynamics and allow for a precise characterization of the optimal control. Such control is known to be bang-bang and our results give a full characterization of the switch position.
|18:30 – 19:00|
Constrained optimization in launch trajectories: analytical derivations for ascent dynamics and near-optimal terminal guidancePaolo Teofilatto – Dean of the School of Aerospace Engineering of Sapienza-University of Rome
The problem of finding the optimal trajectories of multistage launch vehicles from ground to orbit injection implies the inclusion of severe path constraints, in particular during the atmospheric part of the ascent path. These constraints make the dynamics depending on a few parameters and open the possibility of analytic derivations, which can be used either to represent the flight in a sufficiently accurate way or to provide a good guess for iterative optimization algorithms. In particular, in the approach presented here, the atmospheric arcs of the launch vehicle depend on two parameters only: the final flight-path angle at the end of the gravity-turn arc and the duration of the coasting arc following the gravity-turn phase. These two parameters can be quickly obtained by analytical derivations. The exo-atmospheric arc of the trajectory precedes orbit injection. A semi-analytic explicit near-optimal guidance algorithm is presented that is based on the local projection of the position and velocity variables. A minimum-time problem is defined, and consists of finding the optimal thrust direction that minimizes the time of flight for the upper stage to enter the operational orbit. The optimal control problem at hand is proven to be amenable to an analytical solution. This allows translating the minimum-time problem into five nonlinear equations in five unknowns. Their numerical solution can be performed as a real-time process, because a suitable guess, related to intuitive dynamical variables, is available. This research shows that the overall performance of a launch vehicle can be predicted through the previously mentioned approach, based on analytic derivations for the ascent dynamics and near-optimal guidance for the upper stage. Keywords: multistage launch vehicles, explicit guidance.
|19:00 – 19:30|
December 15, 2023
Topic 5: Optimal control problems in presence of uncertain parameters
Topic 6: Improved sufficient and necessary conditions in optimal control problems for aerospace problems
|14:00 – 14:30|
Panel coordinator introductionPiermarco Cannarsa – Professor of mathematical analysis, Università di Roma Tor Vergata
|14:30 – 15:00|
Feedback Control of Astrodynamics Systems Using Solutions of the Hamilton-Jacobi-Bellman EquationBruce Conway – Professor of Aeronautical & Astronautical Engineering, University of Illinois at Urbana Champaign, IL, U.S.A.
Systems of interest to astrodynamics, for example launch vehicle trajectories, interplanetary trajectories, or spacecraft attitude maneuvers, are nonlinear systems in which it is important that the control be applied optimally. But determining such trajectories a priori, using some form of the necessary conditions of the Pontryagin Minimum Principle (PMP), the “indirect” approach, or a transcription of the problem into a NLP problem, the “direct” approach, is a computationally difficult task; not presently feasible in real time. The resulting trajectory is of course open-loop and is only guaranteed to be locally optimal. All of these astrodynamics problems can be subject to disturbances or error or uncertainties in the modeling of their dynamics, which will cause the realized trajectories and the expected trajectories to differ.
|15:00 – 15:30|
Optimal control for the moon lander: a minimum time problemElsa Maria Marchini – Professor of Mathematics, Politecnico di Milano
We study a variant of the classical safe landing optimal control problem in aerospace, introduced by Miele in the Sixties. Assuming that the spacecraft has a failure and that the thrust (representing the control) can act in both vertical directions, the new target be-comes to land safely by minimizing time, no matter of what the consumption is. In dependence of the initial data (height, velocity, and fuel), we prove that the optimal control can be of four diﬀerent kinds, all being piecewise constant. Our analysis covers all possible situations, including the nonexistence of a safe landing strategy due to the lack of fuel or for heights/velocities for which also a total braking is insuﬃcient to stop the spacecraft.
|15:30 – 16:00|
Second-order sufficient conditions for weak local minima in an optimal control problem with a general control constraintHelene Frankowska – Emeritus Research Director C.N.R.S. Sorbonne University, France
I will discuss second-order sufficient optimality conditions for weak local minima of the Mayer type optimal control problems with a general control constraint U in R^m. These conditions are formulated in terms of critical directions and second order tangents to U at critical directions. The obtained results are illustrated through an example of classical control constraints defined by inequalities involving functions with linearly independent gradients of active constraints, and also in the case when U is the union of two sets possibly having singularities at points of their intersection. This second case is the one where the known approaches do not apply.
|16:00 – 16:30|
On geometric and computational methods in optimal control applied to space mechanics: the control-toolbox initiativeJean-Baptiste Caillau – Professor of applied mathematics, Université Côte d’Azur, CNRS, Inria, LJAD
We report on recent progress in the numerical solution of optimal control problems, notably in aerospace engineering. These advancements leverage the availability of fast and high-level modern languages that offer a unified access to reliable solvers (for ODEs, nonlinear equations, optimisation…) and to crucial mechanisms such as automatic differentiation. Several examples from aerospace engineering will be discussed, from the classic though not so simple Goddard problem , to new results in solar sailing . These use cases belong to a set of problems solved thanks to software from the control-toolbox project [2, 3].
|16:30 – 17:00|
Extended Necessary Conditions for Multi-arc Optimal Control Problems and Application to Spacecraft TrajectoriesMauro Pontani – Associate Professor of Aerospace Engineering, Department of Astronautical, Electrical, and Energy Engineering, Università Sapienza Roma
Multi-arc optimal control problems regard dynamical systems governed by differential equations, subject to either discontinuities or constraints at several intermediate times. These constraints can involve both the state variables, the control variables, and the time-independent unknown parameters. The general formulation of the first-order necessary conditions for optimality leads to identifying a set of corner conditions, to enforce at the junction points between two subsequent subarcs. In their general form, these additional conditions do not lead to a closed-form solution for the jump relations of the costate variables at the junction times, except for some remarkable special cases of practical interest.To obtain a closed-form, sequential solution of the jump equations, distinct (and
Closing speech Deep digital technologies and impacts on future of computingCarlo Cavazzoni – Senior Vice President Cloud Computing, Leonardo SpA; Chair of the Industrial Advisory Board, Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing
- Piermarco Cannarsa, Università di Roma Tor Vergata
- Alessandra Celletti, Università di Roma Tor Vergata
- Giorgio Fasano, Thales Alenia Space
- Nicola Guglielmi, Gran Sasso Science Institute
- Leonardo Mazzini, Thales Alenia Space
- Mauro Pontani, Università Sapienza Roma
- Emmanuel Trélat, Sorbonne University
- Leonardo Mazzini, Thales Alenia Space
- Cristian Mendico, Università di Roma Tor Vergata
- Alessandro Pajewski, Gran Sasso Tech
- Amalia Scaricamazza, Gran Sasso Tech