Orbit control of asteroids in libration point orbits for resource exploitation

The fascinating idea of shepherding asteroids for science and resource utilisation is being considered as a very credible concept in a not too distant future. Past studies have identified asteroids which could be injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system, by means of a low-cost manoeuvre. However, the periodic orbits as well as the manifolds are highly unstable, and small errors in the capture manoeuvre would bring to complete mission failure, with potential danger of collision with the Earth itself. The main source of injection error in position and velocity is the epistemic uncertainty of the asteroid mass, which cannot be measured directly. For this reason, asteroid orbit control will be a strict requirement for such mission. This paper investigates the controllability of some asteroids during the transfer and along the period orbits, assuming the use of a solar-electric low-thrust engine. The control scheme is based on a linear quadratic regulator. A stochastic simulation with a Monte Carlo approach is used to simulate a range of different perturbed initial conditions. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets

Coordinate-free interpretations of the optimal costs for LQ-problems subject to implicit systems

Control Systems;operations research

Exponential Stabilisation of Continuous-time Periodic Stochastic Systems by Feedback Control Based on Periodic Discrete-time Observations

Since Mao in 2013 discretised the system observations for stabilisation problem of hybrid SDEs (stochastic differential equations with Markovian switching) by feedback control, the study of this topic using a constant observation frequency has been further developed. However, time-varying observation frequencies have not been considered. Particularly, an observational more efficient way is to consider the time-varying property of the system and observe a periodic SDE system at the periodic time-varying frequencies. This study investigates how to stabilise a periodic hybrid SDE by a periodic feedback control, based on periodic discrete-time observations. This study provides sufficient conditions under which the controlled system can achieve pth moment exponential stability for p > 1 and almost sure exponential stability. Lyapunov's method and inequalities are main tools for derivation and analysis. The existence of observation interval sequences is verified and one way of its calculation is provided. Finally, an example is given for illustration. Their new techniques not only reduce observational cost by reducing observation frequency dramatically but also offer flexibility on system observation settings. This study allows readers to set observation frequencies according to their needs to some extent

Stability of stochastic impulsive differential equations: integrating the cyber and the physical of stochastic systems

According to Newton's second law of motion, we humans describe a dynamical system with a differential equation, which is naturally discretized into a difference equation whenever a computer is used. The differential equation is the physical model in human brains and the difference equation the cyber model in computers for the dynamical system. The physical model refers to the dynamical system itself (particularly, a human-designed system) in the physical world and the cyber model symbolises it in the cyber counterpart. This paper formulates a hybrid model with impulsive differential equations for the dynamical system, which integrates its physical model in real world/human brains and its cyber counterpart in computers. The presented results establish a theoretic foundation for the scientific study of control and communication in the animal/human and the machine (Norbert Wiener) in the era of rise of the machines as well as a systems science for cyber-physical systems (CPS)

Control of asteroid retrieval trajectories to libration point orbits

The fascinating idea of shepherding asteroids for science and resource utilization is being considered as a credible concept in a not too distant future. Past studies identified asteroids which could be efficiently injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system. However, the trajectories are unstable, and errors in the capture maneuver would lead to complete mission failure, with potential danger of collision with the Earth, if uncontrolled. This paper investigates the controllability of some asteroids along the transfers and the periodic orbits, assuming the use of a solar-electric low-thrust system shepherding the asteroid. Firstly, an analytical approach is introduced to estimate the stability of the trajectories from a dynamical point of view; then, a numerical control scheme based on a linear quadratic regulator is proposed, where the gains are optimized for each trajectory through a genetic algorithm. A stochastic simulation with a Monte Carlo approach is used to account for different perturbed initial conditions and the epistemic uncertainty on the asteroid mass. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets

Dynamic Configuration of Large-Scale Cortical Networks: A Useful Framework for Clarifying the Heterogeneity Found in Attention-Deficit/Hyperactivity Disorder

The heterogeneity of attention-deficit/hyperactivity disorder(ADHD) traits (inattention vs. hyperactivity/impulsivity) complicates diagnosis and intervention. Identifying how the configuration of large-scale functional brain networks during cognitive processing correlate with this heterogeneity could help us understand the neural mechanisms altered across ADHD presentations. Here, we recorded high-density EEG while 62 non-clinical participants (ages 18-24; 32 male) underwent an inhibitory control task (Go/No-Go). Functional EEG networks were created using sensors as nodes and across-trial phase-lag index values as edges. Using cross-validated LASSO regression, we examined whether graph-theory metrics applied to both static networks (averaged across time-windows: -500–0ms, 0–500ms) and dynamic networks (temporally layered with 2ms intervals), were associated with hyperactive/impulsive and inattentive traits. Network configuration during response execution/inhibition was associated with hyperactive/impulsive (mean R2across test sets = .20, SE = .02), but not inattentive traits. Post-stimulus results at higher frequencies (Beta, 14-29Hz; Gamma, 30-90Hz) showed the strongest association with hyperactive/impulsive traits, and predominantly reflected less burst-like integration between modules in oscillatory beta networks during execution, and increased integration/small-worldness in oscillatory gamma networks during inhibition. We interpret the beta network results as reflecting weaker integration between specialized pre-frontal and motor systems during motor response preparation, and the gamma results as reflecting a compensatory mechanism used to integrate processing between less functionally specialized networks. This research demonstrates that the neural network mechanisms underlying response execution/inhibition might be associated with hyperactive/impulsive traits, and that dynamic, task-related changes in EEG functional networks may be useful in disentangling ADHD heterogeneity

Quantum control of molecular rotation

The angular momentum of molecules, or, equivalently, their rotation in three-dimensional space, is ideally suited for quantum control. Molecular angular momentum is naturally quantized, time evolution is governed by a well-known Hamiltonian with only a few accurately known parameters, and transitions between rotational levels can be driven by external fields from various parts of the electromagnetic spectrum. Control over the rotational motion can be exerted in one-, two- and many-body scenarios, thereby allowing to probe Anderson localization, target stereoselectivity of bimolecular reactions, or encode quantum information, to name just a few examples. The corresponding approaches to quantum control are pursued within separate, and typically disjoint, subfields of physics, including ultrafast science, cold collisions, ultracold gases, quantum information science, and condensed matter physics. It is the purpose of this review to present the various control phenomena, which all rely on the same underlying physics, within a unified framework. To this end, we recall the Hamiltonian for free rotations, assuming the rigid rotor approximation to be valid, and summarize the different ways for a rotor to interact with external electromagnetic fields. These interactions can be exploited for control --- from achieving alignment, orientation, or laser cooling in a one-body framework, steering bimolecular collisions, or realizing a quantum computer or quantum simulator in the many-body setting.Comment: 52 pages, 11 figures, 607 reference