arXiv subjects

Ossama Abdelkhalik

Publications and source records attributed to Ossama Abdelkhalik.

8 recordsLinked to original sources

arXiv2026

Conserved Quantities of Optimal Continuous-Thrust Trajectories in A Central Gravitational Field

This paper presents a mathematical derivation for three new conserved quantities in the motion of spacecraft on optimal continuous-thrust trajectories in a central gravitational field. The process presented in this paper is rooted in Noether's theorem that connects the point symmetries of a dynamic system with the associated conservation laws of the system. In the approach presented in this paper, the system's Lagrangian is modified to account for the non-conservative control force. Using this generalized Lagrangian, the action functional to be minimized is written. Then, Killing equations are formulated to find the dynamic symmetries for this system. In this paper a process is laid out for how to solve the Killing equations; Noether's theorem is applied to this solution of the Killing equations to write the conserved quantities of the system. Conserved quantities are presented for both the two-dimensional and the three-dimensional trajectories in several different coordinate frames. Numerical simulations and mathematical proofs are used to demonstrate that the computed quantities are conserved.

physics.class-ph↗

arXiv2026

Minimum Effort Control Using Variational Methods of Analytical Mechanics A New Approach For Optimal Control

Modern optimal control theory involves adjoining the already known equations of motion of a dynamic system to the objective function using dynamic costates; this is done in order to constrain the optimal control solutions to satisfy the equations of motion. The use of costates increases the number of variables and hence increases the complexity of the problem. On the other hand, variational methods of analytical mechanics finds the equations of motion by minimizing an action functional of the dynamic system, realizing control forces as external input to the system. In this paper a new disruptive approach for computing the optimal control is presented. This approach adopts the variational methods of analytical mechanics to derive equations for the control, in addition to the equations of motion. This is achieved by recognizing the control actuator as part of the dynamic system. In addition to the kinetic energy and potential energy, the action functional in this new approach includes additional energy terms that represent the control energy of the system. Two different methods are presented to write the modified action functional. The proposed approach is a significant departure from the modern optimal control theory, and it eliminates the need for costates when solving for the control. In this paper, a case study is presented to demonstrate the new approach.

math.OC↗

arXiv2025

Hybrid Wave-wind System Power Optimisation Using Effective Ensemble Covariance Matrix Adaptation Evolutionary Algorithm

Floating hybrid wind-wave systems combine offshore wind platforms with wave energy converters (WECs) to create cost-effective and reliable energy solutions. Adequately designed and tuned WECs are essential to avoid unwanted loads disrupting turbine motion while efficiently harvesting wave energy. These systems diversify energy sources, enhancing energy security and reducing supply risks while providing a more consistent power output by smoothing energy production variability. However, optimising such systems is complex due to the physical and hydrodynamic interactions between components, resulting in a challenging optimisation space. This study uses a 5-MW OC4-DeepCwind semi-submersible platform with three spherical WECs to explore these synergies. To address these challenges, we propose an effective ensemble optimisation (EEA) technique that combines covariance matrix adaptation, novelty search, and discretisation techniques. To evaluate the EEA performance, we used four sea sites located along Australia's southern coast. In this framework, geometry and power take-off parameters are simultaneously optimised to maximise the average power output of the hybrid wind-wave system. Ensemble optimisation methods enhance performance, flexibility, and robustness by identifying the best algorithm or combination of algorithms for a given problem, addressing issues like premature convergence, stagnation, and poor search space exploration. The EEA was benchmarked against 14 advanced optimisation methods, demonstrating superior solution quality and convergence rates. EEA improved total power output by 111%, 95%, and 52% compared to WOA, EO, and AHA, respectively. Additionally, in comparisons with advanced methods, LSHADE, SaNSDE, and SLPSO, EEA achieved absorbed power enhancements of 498%, 638%, and 349% at the Sydney sea site, showcasing its effectiveness in optimising hybrid energy systems.

cs.NE↗

arXiv2024

Sub-Optimal Fast Fourier Series Approximation for Initial Trajectory Design

The Finite Fourier Series (FFS) Shape-Based (SB) trajectory approximation method has been used to rapidly generate initial trajectories that satisfy the dynamics, trajectory boundary conditions, and limitation on maximum thrust acceleration. The FFS SB approach solves a nonlinear programming problem (NLP) in searching for feasible trajectories. This paper extends the development of the FFS SB approach to generate sub optimal solutions. Specifically, the objective function of the NLP problem is modified to include also a measure for the time of flight. Numerical results presented in this paper show several solutions that differ from those of the original FFS SB ones. The sub-optimal trajectories generated using a time of flight minimization are shown to be physically feasible trajectories and potential candidates for direct solvers.

math.OC↗

arXiv2024

Low Thrust Trajectory Design Using A Semi-Analytic Approach

Space missions that use low-thrust propulsion technology are becoming increasingly popular since they utilize propellant more efficiently and thus reduce mission costs. However, optimizing continuous-thrust trajectories is complex, time-consuming, and extremely sensitive to initial guesses. Hence, generating approximate trajectories that can be used as reliable initial guesses in trajectory generators is essential. This paper presents a semi-analytic approach for designing planar and three-dimensional trajectories using Hills equations. The spacecraft is assumed to be acted upon by a constant thrust acceleration magnitude. The proposed equations are employed in a Nonlinear Programming Problem (NLP) solver to obtain the thrust directions. Their applicability is tested for various design scenarios like orbit raising, orbit insertion, and rendezvous. The trajectory solutions are then validated as initial guesses in high-fidelity optimal control tools. The usefulness of this method lies in the preliminary stages of low-thrust mission design, where speed and reliability are key.

math.OC↗

arXiv2024

Design of Initial Guess Low Thrust Trajectories Using Clohessy-Wiltshire Equations

The commercial interest in producing low-cost space missions by exploiting the superior propellant management of low-thrust propulsion technology has become increasingly popular. Typical to such missions is the design of transfer trajectories between desired targets. This is a complex and computationally expensive process. Additionally, the optimal solvers used to generate these trajectories are extremely sensitive to initial guesses. One way to overcome this challenge is to use a reasonably approximate trajectory as an initial guess on optimal solvers. This paper presents a flexible approach to generating very low thrust trajectories. The initial guess is obtained from a flexible semi-analytic approach that can provide both planar and three-dimensional initial guess trajectories for various design scenarios like orbit raising, orbit insertion, phasing, and rendezvous. NASA's Evolutionary Mission Trajectory Generator (EMTG) and General Mission Analysis Tool (GMAT) are used as optimal solvers in this analysis. Numerical case studies are presented in this paper.

math.OC↗

arXiv2022

Dynamic modeling of the motions of variable-shape wave energy converters

In the recently introduced Variable-Shape heaving wave energy converters, the buoy changes its shape actively in response to changing incident waves. In this study, a Lagrangian approach for the dynamic modeling of a spherical Variable-Shape Wave Energy Converter is described. The classical bending theory is used to write the stress-strain equations for the flexible body using Love's approximation. The elastic spherical shell is assumed to have an axisymmetric vibrational behavior. The Rayleigh-Ritz discretization method is adopted to find an approximate solution for the vibration model of the spherical shell. A novel equation of motion is presented that serves as a substitute for Cummins equation for flexible buoys. Also, novel hydrodynamic coefficients that account for the buoy mode shapes are proposed. The developed dynamic model is coupled with the open-source boundary element method software NEMOH. Two-way and one-way Fluid-Structure Interaction simulations are performed using MATLAB to study the effect of using a flexible shape buoy in the wave energy converter on its trajectory and power production. Finally, the variable shape buoy was able to harvest more energy for all the tested wave conditions.

math.DS↗

arXiv2022

Dynamic Modeling Of Spherical Variable-Shape Wave Energy Converters

In the recently introduced Variable-Shape heaving wave energy converters, the buoy changes its shape in response to changing incident waves actively. In this study, the dynamic model for a spherical Variable-Shape Wave Energy Converter is developed using the Lagrangian approach. The classical bending theory is used to write the stress-strain equations for the flexible body using Love's first approximation. The elastic spherical shell is assumed to have an axisymmetric vibration behavior. The Rayleigh-Ritz discretization method is adopted to find an approximate solution for the vibration model of the spherical shell. One-way Fluid-Structure Interaction simulations are performed using MATLAB to validate the developed dynamic model and to study the effect of using a flexible buoy in the wave energy converter on its trajectory and power production.

math.DS↗