Design and Simulation of a Model Reference Adaptive Control System Employing Reproducing Kernel Hilbert Space for Enhanced Flight Control of a Quadcopter

This thesis presents the integration of reproducing kernel Hilbert spaces (RKHSs) into the model reference adaptive control (MRAC) framework to enhance the control systems of quadcopters. Traditional MRAC systems, while robust under predictable conditions, can struggle with the dynamic uncertainties typical in unmanned aerial vehicle (UAV) operations such as wind gusts and payload variations. By incorporating RKHS, we introduce a non-parametric, data-driven approach that significantly enhances system adaptability to in-flight dynamics changes.

The research focuses on the design, simulation, and analysis of an RKHS-enhanced MRAC system applied to quadcopters. Through theoretical developments and simulation results, the thesis demonstrates how RKHS can be used to improve the precision, adaptability, and error handling of MRAC systems, especially in managing the complexities of UAV flight dynamics under various disturbances. The simulations validate the improved performance of the RKHS-MRAC system compared to traditional MRAC, showing finer control over trajectory tracking and adaptive gains.

Further contributions of this work include the exploration of the computational impact and the relationship between the configuration of basis centers and system performance. Detailed analysis reveals that the number and distribution of basis centers critically influence the system's computational efficiency and adaptive capability, demonstrating a significant trade-off between efficiency and performance.

The thesis concludes with potential future research directions, emphasizing the need for further tests and implementations in real-world scenarios to explore the full potential of RKHS in adaptive UAV control, especially in critical applications requiring high precision and reliability. This work lays the groundwork for future explorations into scalable RKHS applications in MRAC systems, aiming to optimize computational resources while maximizing control system performance.