Planar tilting maneuver of a spacecraft: singular arcs in the minimum time problem and chattering

In this paper, we study the minimum time planar tilting maneuver of a spacecraft, from the theoretical as well as from the numerical point of view, with a particular focus on the chattering phenomenon. We prove that there exist optimal chattering arcs when a singular junction occurs. Our study is based on the Pontryagin Maximum Principle and on results by M.I. Zelikin and V.F. Borisov. We give sufficient conditions on the initial values under which the optimal solutions do not contain any singular arc, and are bang-bang with a finite number of switchings. Moreover, we implement sub-optimal strategies by replacing the chattering control with a fixed number of piecewise constant controls. Numerical simulations illustrate our results.Comment: 43 pages, 18 figure

Minimum time control of the rocket attitude reorientation associated with orbit dynamics

In this paper, we investigate the minimal time problem for the guidance of a rocket, whose motion is described by its attitude kinematics and dynamics but also by its orbit dynamics. Our approach is based on a refined geometric study of the extremals coming from the application of the Pontryagin maximum principle. Our analysis reveals the existence of singular arcs of higher-order in the optimal synthesis, causing the occurrence of a chattering phenomenon, i.e., of an infinite number of switchings when trying to connect bang arcs with a singular arc. We establish a general result for bi-input control-affine systems, providing sufficient conditions under which the chattering phenomenon occurs. We show how this result can be applied to the problem of the guidance of the rocket. Based on this preliminary theoretical analysis, we implement efficient direct and indirect numerical methods, combined with numerical continuation, in order to compute numerically the optimal solutions of the problem.Comment: 33 pages, 14 figure

Spectral Efficiency and Scalability Analysis for Multi-Level Cooperative Cell-Free Massive MIMO Systems

This paper proposes a multi-level cooperative architecture to balance the spectral efficiency and scalability of cell-free massive multiple-input multiple-output (MIMO) systems. In the proposed architecture, spatial expansion units (SEUs) are introduced to avoid a large amount of computation at the access points (APs) and increase the degree of cooperation among APs. We first derive the closed-form expressions of the uplink user achievable rates under multi-level cooperative architecture with maximal ratio combination (MRC) and zero-forcing (ZF) receivers. The accuracy of the closed-form expressions is verified. Moreover, numerical results have demonstrated that the proposed multi-level cooperative architecture achieves a better trade-off between spectral efficiency and scalability than other forms of cell-free massive MIMO architectures.Comment: 5 pages, 3 figure

Allee optimal control of a system in ecology

International audienceThe Allee threshold of an ecological system distinguishes the sign of population growth either towards extinction or to carrying capacity. In practice human interventions can tune the Allee threshold for instance thanks to the sterile male technique and the mating disruption. In this paper we address various control objectives for a system described by a diffusion-reaction equation regulating the Allee threshold, viewed as a real parameter determining the unstable equilibrium of the bistable nonlinear reaction term. We prove that this system is the mean field limit of an interacting system of particles in which individual behaviours are driven by stochastic laws. Numerical simulations of the stochastic process show that population propagations are governed by wave-like solutions corresponding to traveling solutions of the macroscopic reaction-diffusion system. An optimal control problem for the macroscopic model is then introduced with the objective of steering the system to a target traveling wave. The relevance of this problem is motivated by the fact that traveling wave solutions model the fact that bounded space domains reach asymptotically an equilibrium configuration. Using well known analytical results and stability properties of traveling waves, we show that well-chosen piecewise constant controls allow to reach the target approximately in sufficiently long time. We then develop a direct computational method and show its efficiency for computing such controls in various numerical simulations. Finally we show the efficiency of the obtained macroscopic optimal controls in the microscopic system of interacting particles and we discuss their advantage when addressing situations that are out of reach for the analytical methods. We conclude the article with some open problems and directions for future research

Unifying Generic Group Models

To prove computational complexity lower bounds in cryp- tography, one often resorts to so-called generic models of computation. For example, a generic algorithm for the discrete logarithm is one which works independently from the group representation—and thus works generically for all group representations. There are a multitude of different models in the literature making comparing different results—and even matching lower and upper bounds proven in different models— rather difficult. In this work we view a model as a set of games with the same type of interactions. Using a standard notion of reduction between two games, we establish a hierarchy between models. Different models may now be classified as weaker and stronger if a reduction between them exists. We propose different extensions of the generic group model with different queries, explicitly capturing different information that an algorithm may need to exploit. Finally, we use the hierarchy between these models to systematically compare and improve the results in the literature. First we strengthen the model in which the baby-step giant-step algorithm is proven and weaken the model in which the matching lower bound is proven. We then analyse the discrete logarithm with preprocessing. Upper and lower bounds have been proven in the literature in mismatching models. We weaken the model of the lower bound and strengthen the model of the upper bound to close the gap between the two

Minimum Time-Energy Pull-up Maneuvers for Airborne Launch Vehicles

In this paper, the minimum time-energy pull-up maneuver problem for airborne launch vehicles (ALV) is studied with a focus on developing a numerical approach for solving the problem. Firstly, the six-degree-of-freedom (6DOF) dynamics for the motion of the ALV subject to the aerodynamic forces, the gravitational force, the propulsive force and the path constraints are established. Then, first-order necessary conditions are derived by applying the Pontryagin Maximum Principle, and the optimal control problem is transformed into a two-boundary value problem, which is generally solved numerically thanks to a shooting method. However, the convergence domain of the shooting method is very small due to high dimension and to nonlinear coupling of attitude and trajectory motions.To overcome this difficulty, we design an algorithm combining the multiple shooting method and the Predictor-Corrector continuation (PC continuation) method, where the choice of homotopy parameters relies on a careful analysis of the nature of the dynamics.Numerical results presented for pull-up maneuvers of an ALV show that the algorithm is efficient and robust with respect to terminal conditions. Our method is also applied to the problem of rapid maneuver of the upper stage of a launch vehicle (LV)

Passive Integrated Sensing and Communication Scheme based on RF Fingerprint Information Extraction for Cell-Free RAN

This paper investigates how to achieve integrated sensing and communication (ISAC) based on a cell-free radio access network (CF-RAN) architecture with a minimum footprint of communication resources. We propose a new passive sensing scheme. The scheme is based on the radio frequency (RF) fingerprint learning of the RF radio unit (RRU) to build an RF fingerprint library of RRUs. The source RRU is identified by comparing the RF fingerprints carried by the signal at the receiver side. The receiver extracts the channel parameters from the signal and estimates the channel environment, thus locating the reflectors in the environment. The proposed scheme can effectively solve the problem of interference between signals in the same time-frequency domain but in different spatial domains when multiple RRUs jointly serve users in CF-RAN architecture. Simulation results show that the proposed passive ISAC scheme can effectively detect reflector location information in the environment without degrading the communication performance.Comment: 11 pages, 6 figures, submitted on 28-Feb-2023, China Communication, Accepted on 14-Sep-202