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کنترل چگالی آرایش ماهواره ها با ترکیب انتقال بهینه و رویکرد LQR
حضرتی آزاد، مهدی Hazrati Azad, Mehdi
Density Control of Satellite Formations Using Optimal Transport and LQR Approach
Hazrati Azad, Mehdi | 2025
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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 58398 (45)
- University: Sharif University of Technology
- Department: Aerospace Engineering
- Advisor(s): Asadian, Nima; Pourtakdoust, Hossein
- Abstract:
- The formation control of satellites, and in particular the control of large-scale satellite swarms, constitutes one of the critical technical and practical challenges in contemporary space missions. The proliferation of emerging space applications — including the simultaneous deployment of a large number of satellites — alongside recent advances in sensor, actuator, and communication technologies, has increasingly drawn research attention toward satellite systems operating in swarm configurations. Simultaneously, the likelihood of anomalies during deployment processes may lead to the intermingling of multiple swarms, increasing the risk of collisions and reducing mission efficiency. This clearly highlights the need for a control theory capable of ensuring the separation of these swarms. In this dissertation, optimal transport theory is first developed for linear-quadratic control systems with free terminal conditions, and fundamental theorems, including the existence and uniqueness of the problem solution, are explicitly stated and proven. This framework is then compared with the corresponding problem under fixed terminal conditions in the literature, from which new theoretical results not reported previously are derived and proven. Subsequently, conditions under which the problem admits a closed-form solution are identified, demonstrating that, with appropriate selection of the upper bound on the terminal density, the upper bound of the induced optimal density over time can be partially controlled. Based on these theoretical findings, a practical method is proposed for the rapid and sub-optimal passage of large-scale swarms through narrow corridors. For verification, the satellite swarm transfer problem is compared with a traditional approach based on attractive potentials. Finally, by combining a macroscopic perspective (optimal transport on linear-quadratic control systems with free terminal conditions) and a microscopic perspective (repulsive forces generated by Gaussian artificial potentials to avoid collisions), the mixed-swarm separation problem is addressed. Numerical simulations demonstrate that the proposed approach can achieve collision-free, optimal transfers of satellites. The results of this dissertation provide both theoretical and practical foundations for the scalable and safe control of satellite swarms in simultaneous deployment scenarios
- Keywords:
- Density Control ; Optimal Transport ; Linear Quadratic Control ; Collision Avoidance ; Artificial Potential Field ; Formation Control ; Mixed Swarms ; Optimal Transport on Linear-Quadratic Control Systems ; Linear Quadratic Requlator (LQR)
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