arXiv subjects

Shengping Gong

Publications and source records attributed to Shengping Gong.

At least 37 records · Page 2Linked to original sources

arXiv2025

Discontinuous Behavior of Time-of-Flight Distribution for Bi-impulsive Earth-Moon Transfers in the Three-Body Model

As interest in the Earth-Moon transfers renewed around the world, understanding the solution space of transfer trajectories facilitates the construction of transfers. This paper is devoted to reporting a novel or less-reported phenomenon about the solution space of bi-impulsive Earth-Moon transfers in the Earth-Moon planar circular restricted three-body problem. Differing from the previous works focusing on the transfer characteristics of the solution space, we focus on the distribution of the construction parameters, i.e., departure phase angle at the Earth parking orbit, initial-to-circular velocity ratio, and time of flight. Firstly, the construction method of bi-impulsive transfers is described, and the solutions satisfying the given constraints are obtained from the grid search method and trajectory correction. Then, the distribution of the obtained solutions is analyzed, and an interesting phenomenon about the discontinuous behavior of the time-of-flight distribution for each departure phase angle is observed and briefly reported. This phenomenon can further provide useful insight into the construction of bi-impulsive transfers, deepening the understanding of the corresponding solution space.

math.OC↗

arXiv2025

Recursive Gaussian Process State Space Model

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models (GPSSMs) have recently gained significant attention due to their combination of flexibility and interpretability. However, for online learning, the field lacks an efficient method suitable for scenarios where prior information regarding data distribution and model function is limited. To address this issue, this paper proposes a recursive GPSSM method with adaptive capabilities for both operating domains and Gaussian process (GP) hyperparameters. Specifically, we first utilize first-order linearization to derive a Bayesian update equation for the joint distribution between the system state and the GP model, enabling closed-form and domain-independent learning. Second, an online selection algorithm for inducing points is developed based on informative criteria to achieve lightweight learning. Third, to support online hyperparameter optimization, we recover historical measurement information from the current filtering distribution. Comprehensive evaluations on both synthetic and real-world datasets demonstrate the superior accuracy, computational efficiency, and adaptability of our method compared to state-of-the-art online GPSSM techniques.

cs.LG↗

arXiv2025

Recursive Inference for Heterogeneous Multi-Output GP State-Space Models with Arbitrary Moment Matching

Accurate learning of system dynamics is becoming increasingly crucial for advanced control and decision-making in engineering. However, real-world systems often exhibit multiple channels and highly nonlinear transition dynamics, challenging traditional modeling methods. To enable online learning for these systems, this paper formulates the system as Gaussian process state-space models (GPSSMs) and develops a recursive learning method. The main contributions are threefold. First, a heterogeneous multi-output kernel is designed, allowing each output dimension to adopt distinct kernel types, hyperparameters, and input variables, improving expressiveness in multi-dimensional dynamics learning. Second, an inducing-point management algorithm enhances computational efficiency through independent selection and pruning for each output dimension. Third, a unified recursive inference framework for GPSSMs is derived, supporting general moment matching approaches, including the extended Kalman filter (EKF), unscented Kalman filter (UKF), and assumed density filtering (ADF), enabling accurate learning under strong nonlinearity and significant noise. Experiments on synthetic and real-world datasets show that the proposed method matches the accuracy of SOTA offline GPSSMs with only 1/100 of the runtime, and surpasses SOTA online GPSSMs by around 70% in accuracy under heavy noise while using only 1/20 of the runtime.

stat.ML↗

arXiv2025

Energy Transition Domain and Its Application in Constructing Gravity-Assist Escape Trajectories

This Note proposes the concept and theory of energy transition domain (ETD) defined by the mechanical energy of spacecraft in the Earth-Moon planar circular restricted three-body problem (PCR3BP) inspired by the pioneering work from Ano{è} et al. (2024) on the ETD defined by the two-body energy with respect to the secordary body in the PCR3BP. An effective construction method of gravity-assist escape trajectories is then proposed. Firstly, the concept of the ETD defined by the mechanical energy is presented, and its dependency on the Jacobi energy is analyzed. This dependency may provide prior knowledge about selecting the range of the Jacobi energy in the construction of escape trajectories. Then, gravity-assist escape trajectories departing from the 167 km low Earth orbit and 36000 km geosynchronous Earth orbit are constructed based on the ETD. The initial states are selected in the sphere of influence of the Moon, and the trajectories are searched from the forward and backward integration. Finally, the obtained solutions are presented and analyzed.

astro-ph.EP↗

arXiv2025

Families of Transfers from circular low Earth orbit to Distant Prograde Orbit around the Moon

Distant prograde orbits around the Moon exhibit remarkable potential for practical applications such as cislunar surveillance activities and low-energy transfers due to their instability. Previous works on transfers from circular low Earth orbit to distant prograde orbits mainly focused on construction methods based on dynamical structures, lacking a comprehensive analysis of the solution space of this transfer scenario. This paper investigates the solution space and identifies families of transfers from a 167 km circular low Earth orbit to a 1:1 distant prograde orbit. In particular, grid search and trajectory continuation are performed to construct these transfer trajectories. Initial guesses of the transfers are selected in the 1:1 distant prograde orbit through a backward propagation strategy and are then corrected to satisfy specified constraints. Based on the obtained solutions, a linear predictor is derived to predict more feasible solutions and a predictor-corrector continuation method is used to extend the solution space. Twelve transfer families are identified, most of which are new or previously underexplored. The distributions of construction parameters and transfer characteristics of these twelve families are analyzed and discussed, showing which families are applicable to which types of specific practical missions. Comparison between the obtained solution and solution developed by previous works is further performed to imply the effects of the selection of dynamical model on transfer construction.

astro-ph.EP↗

arXiv2025

Learning-Based Stable Optimal Control for Infinite-Time Nonlinear Regulation Problems

Infinite-time nonlinear optimal regulation control is widely utilized in aerospace engineering as a systematic method for synthesizing stable controllers. However, conventional methods often rely on linearization hypothesis, while recent learning-based approaches rarely consider stability guarantees. This paper proposes a learning-based framework to learn a stable optimal controller for nonlinear optimal regulation problems. First, leveraging the equivalence between Pontryagin Maximum Principle (PMP) and Hamilton-Jacobi-Bellman (HJB) equation, we improve the backward generation of optimal examples (BGOE) method for infinite-time optimal regulation problems. A state-transition-matrix-guided data generation method is then proposed to efficiently generate a complete dataset that covers the desired state space. Finally, we incorporate the Lyapunov stability condition into the learning framework, ensuring the stability of the learned optimal policy by jointly learning the optimal value function and control policy. Simulations on three nonlinear optimal regulation problems show that the learned optimal policy achieves near-optimal regulation control and the code is provided at https://github.com/wong-han/PaperNORC

eess.SY↗

arXiv2025

Design and Continuation of Nonlinear Teardrop Hovering Formation along the Near Rectilinear Halo Orbit

This short communication is devoted to the design and continuation of a teardrop hovering formation along the Near Rectilinear Halo orbit and provides further insights into future on-orbit services in the cislunar space. First, we extend the concept of the teardrop hovering formation to scenarios along the Near Rectilinear Halo orbit in the Earth-Moon circular restricted three-body problem. Then, we develop two methods for designing these formations based on the nonlinear model for relative motion. The first method addresses the design of the teardrop hovering formations with relatively short revisit distances, while the second method continues hovering trajectories from short to longer revisit distances. In particular, new continuation method is developed to meet the design requirements of this new scenario. Simulation results verify the effectiveness of the proposed methods, and a near-natural teardrop hovering formation is achieved by considering the dynamical properties near the NRHO. Comparisons between design results obtained using linear and nonlinear models further strengthen the necessity of using the nonlinear model.

math.OC↗

arXiv2025

Confidence-Aware Learning Optimal Terminal Guidance via Gaussian Process Regression

Modern aerospace guidance systems demand rigorous constraint satisfaction, optimal performance, and computational efficiency. Traditional analytical methods struggle to simultaneously satisfy these requirements. While data driven methods have shown promise in learning optimal guidance strategy, challenges still persist in generating well-distributed optimal dataset and ensuring the reliability and trustworthiness of learned strategies. This paper presents a confidence-aware learning framework that addresses these limitations. First, a region-controllable optimal data generation method is proposed leveraging Hamiltonian state transition matrices, enabling efficient generation of optimal trajectories of specified data distribution. Then, to obtain a lightweight and effective dataset for efficient strategy learning, an error-distribution-smoothing method is incorporated to employ data filtering, which reduces dataset size by almost 90% while preserving prediction accuracy. To assess the operational domain of the learned strategy, a confidence-aware learning guidance strategy is proposed based on gaussian process regression, achieving constraint satisfaction even beyond training distributions. Numerical simulations validate the effectiveness and reliability of the proposed learning framework in terms of data generation, data filtering and strategy learning.

eess.SY↗

arXiv2025

Analytical Strategies and Winning Conditions for Elliptic-Orbit Target-Attacker-Defender Game

This paper proposes an analytical framework for the orbital Target-Attacker-Defender game with a non-maneuvering target along elliptic orbits. Focusing on the linear quadratic game, we derive an analytical solution to the matrix Riccati equation, which yields analytical Nash-equilibrium strategies for the game. Based on the analytical strategies, we derive the analytical form of the necessary and sufficient winning conditions for the attacker. The simulation results show good consistency between the analytical and numerical methods, exhibiting 0.004$\%$ relative error in the cost function. The analytical method achieves over 99.9$\%$ reduction in CPU time compared to the conventional numerical method, strengthening the advantage of developing the analytical strategies. Furthermore, we verify the proposed winning conditions and investigate the effects of eccentricity on the game outcomes. Our analysis reveals that for games with hovering initial states, the initial position of the defender should be constrained inside a mathematically definable set to ensure that the attacker wins the game. This constrained set further permits geometric interpretation through our proposed method. This work establishes the analytical framework for orbital Target-Attacker-Defender games, providing fundamental insights into the solution analysis of the game.

math.OC↗

arXiv2025

Stability Enhancement in Reinforcement Learning via Adaptive Control Lyapunov Function

Reinforcement Learning (RL) has shown promise in control tasks but faces significant challenges in real-world applications, primarily due to the absence of safety guarantees during the learning process. Existing methods often struggle with ensuring safe exploration, leading to potential system failures and restricting applications primarily to simulated environments. Traditional approaches such as reward shaping and constrained policy optimization can fail to guarantee safety during initial learning stages, while model-based methods using Control Lyapunov Functions (CLFs) or Control Barrier Functions (CBFs) may hinder efficient exploration and performance. To address these limitations, this paper introduces Soft Actor-Critic with Control Lyapunov Function (SAC-CLF), a framework that enhances stability and safety through three key innovations: (1) a task-specific CLF design method for safe and optimal performance; (2) dynamic adjustment of constraints to maintain robustness under unmodeled dynamics; and (3) improved control input smoothness while ensuring safety. Experimental results on a classical nonlinear system and satellite attitude control demonstrate the effectiveness of SAC-CLF in overcoming the shortcomings of existing methods.

cs.LG↗

arXiv2024

Analytical Pursuit-Evasion Game Strategy in Arbitrary Keplerian Reference Orbits

This paper develops an analytical strategy for solving the linear quadratic pursuit-evasion game in arbitrary Keplerian reference orbits. The motion of the pursuer and evader is described using the controlled Tschauner-Hempel equations, and the optimal game strategies of the pursuer and evader are presented by the solution of the differential Riccati equation.The analytical solution of the differential Riccati equation is presented for elliptic, parabolic, and hyperbolic reference orbits, thereby enabling an analytical pursuit-evasion game strategy. Then, the procedure to solve the pursuit-evasion game using this analytical strategy is proposed. Simulations of pursuit-evasion game in elliptic, parabolic, and hyperbolic reference orbits validate the effectiveness of the developed analytical strategy. Results indicates that the analytical strategy saves the CPU time by more than 99.8$\%$ compared to the numerical one, highlighting the efficiency of the developed strategy. The developed analytical strategy is also applicable to pursuit-evasion game scenarios considering orbital disturbances. Compared to the conventional strategy, which succeed in only two out of six test scenarios, the developed strategy achieves success in all six cases, particularly demonstrating its effectiveness in high-eccentricity cases.

math.OC↗

arXiv2024

Interior transit orbits in the planar bicircular restricted four-body problem: classification and application

Low-energy transfers are advantageous for lunar exploration missions due to low fuel consumption and extended launch periods. This paper is devoted to the classification of interior transit orbits and their application on low-energy transfer in the Sun-Earth/Moon planar bicircular restricted four-body problem (PBCR4BP). First, the Lagrangian coherent structures (LCSs) are introduced to generate the interior transit orbits. The number of periapses about the Moon is selected as the classification parameter and mapped into the LCSs, achieving clear classification boundaries. Then, the evolution laws of the classifications with respect to energy and solar gravity perturbation are discussed and summarized. Construction strategies for low-energy transfer are proposed based on the classifications and their evolution laws. Numerical simulation of the transfer trajectories verifies the effectiveness of the proposed strategies. The dynamical behaviors and transfer characteristics of transit orbits and their families are revealed, and a direct link between transit orbit families and low-energy transfers is finally established.

astro-ph.EP↗

arXiv2019

On the Instability of Saturn's Hypothetical Retrograde Co-orbitals

We find an interesting fact that fictitious retrograde co-orbitals of Saturn, or small bodies inside the retrograde 1:1 resonance with Saturn, are highly unstable in our numerical simulations. It is shown that in the presence of Jupiter, the retrograde co-orbitals will get ejected from Saturn's co-orbital space within a timescale of 10 Myr. This scenario reminds us of the instability of Saturn Trojans caused by both the Great Inequality and the secular resonances. Therefore, we carry out in-depth inspections on both mechanisms and prove that the retrograde resonance overlap, raised by Great Inequality, cannot serve as an explanation for the instability of retrograde co-orbitals, due to the weakness of the retrograde 2:5 resonance with Jupiter at a low eccentricity. However, we discover that both $ν_5$ and $ν_6$ secular resonances contribute to the slow growth of the eccentricity, therefore, are possibly the primary causes of the instability inside Saturn's retrograde co-orbital space.

astro-ph.EP↗

arXiv2019

Solar-Sail Deep Space Trajectory Optimization Using Successive Convex Programming

This paper presents a novel methodology for solving the time-optimal trajectory optimization problem for interplanetary solar-sail missions using successive convex programming. Based on the non-convex problem, different convexification technologies, such as change of variables, successive linearization, trust regions and virtual control, are discussed to convert the original problem into the formulation of successive convex programming. Because of the free final-time, successive linearization is performed iteratively for the nonconvex terminal state constraints. After the convexification process, each of problems becomes a convex problem, which can be solved effectively. An augmented objective function is introduced to ensure the convergence performance and effectiveness of our algorithm. After that, algorithms are designed to solve the discrete sub-problems in a successive solution procedure. Finally, numerical results demonstrate the effectiveness and accuracy of our algorithms.

cs.CE↗

arXiv2019

Gradient-index Solar Sail and its Optimal Orbital Control

Solar sails with the capability of generating a tangential radiation pressure at the sun-pointing attitude, such as refractive sails can provide more efficient methods for attitude and orbital control of sailcraft. This paper presents the concept of gradient-index sail as an advanced class of refractive sail, which operates by guiding the solar radiation through a structure made of graded refractive index material. The design of the sail's refractive index distribution is performed by transformation optics, and the resultant index realized by the effective refractive index of non-resonant bulk metamaterials made of silica. The performance of the sail was evaluated by using ray tracing for a broad spectrum of solar radiation under the normal incidence angle, which showed an efficiency of 90.5% for generation of a tangential radiation pressure. We also studied the orbital control of the tangential-radiation-pressure-generating sails, and showed that the full orbital control, including the modification of orbital axes, eccentricity, and inclination can be applied by changing the attitude of the sail merely around the sun-sail axis, while the sail keeps the sun-pointing attitude at every point of the orbit.

physics.space-ph↗

arXiv2019

Solar-Sail Trajectory Design for Multiple Near Earth Asteroid Exploration Based on Deep Neural Networks

In the preliminary trajectory design of the multi-target rendezvous problem, a model that can quickly estimate the cost of the orbital transfer is essential. The estimation of the transfer time using solar sail between two arbitrary orbits is difficult and usually requires to solve an optimal control problem. Inspired by the successful applications of the deep neural network in nonlinear regression, this work explores the possibility and effectiveness of mapping the transfer time for solar sail from the orbital characteristics using the deep neural network. Furthermore, the Monte Carlo Tree Search method is investigated and used to search the optimal sequence considering a multi-asteroid exploration problem. The obtained sequences from preliminary design will be solved and verified by sequentially solving the optimal control problem. Two examples of different application backgrounds validate the effectiveness of the proposed approach.

cs.CE↗

arXiv2019

All-dielectric Tailored-index Index-matched Arbitrary Waveguides based on Transformation Optics

Transformation optics based on conformal mapping (CM) technique provides a practical approach to designing arbitrary-shaped all-dielectric devices. However, CM may result in large impractical refractive indices unachievable by current fabrication techniques. Furthermore, due to the low design flexibility of CM, the index-matching conditions at the ports of the device can not be realized as well. In this paper we introduce a method for tailoring the CM generated graded refractive index, in order to decrease its maximum value and apply index-matching, while maintaining the propagation path within the device unchanged. This technique is applied to two arbitrary index-matched waveguides. The full-wave simulation is performed to show the efficiency of the tailored-index index-matched waveguides for different relative wavelengths.

physics.app-ph↗

arXiv2019

Long-range optical pulling force device based on vortex beams and transformation optics

In this work a method for generating a long-range optical pulling force is presented which is realized by utilizing a vortex beam and a device designed based on transformation optics through conformal mapping. The device works by transforming an input perfect vortex beam into an almost non-paraxial plane wave, and generates a pulling force by maximizing the forward momentum of the beam. A three-dimensional full-wave analysis of the device is performed and the optical force is computed by the Maxwell stress tensor method. The simulation results show a very good agreement with the theoretical calculations.

physics.optics↗