Integrated Observer-Based Kalman Filter and LQR Control with Lyapunov Stability Analysis for Tractor-Trailer Systems

<b><sc>Abstract</sc></b> An integrated approach is presented for combining Kalman filtering, Linear Quadratic Regulator (LQR) control, and Lyapunov stability analysis for the state estimation, control, and stability verification of tractor-trailer systems. The mathematical model of the system, derived from its geometric and dynamic properties, is used as the basis for implementing these techniques. The Kalman filter ensures robust state estimation despite noisy measurements, while the LQR optimizes control inputs to minimize trajectory tracking errors and control effort. To ensure theoretical rigor, Lyapunov analysis is utilized to validate global asymptotic stability, providing a robust framework for system stability assessment. Simulation results, including covariance matrix behavior, control commands, estimation errors, and Lyapunov function trajectories, demonstrate the efficacy of the proposed methodology. This research highlights the synergy between filtering, control, and stability analysis for advanced autonomous systems.