Bayesian Optimization for the Synthesis of Generalized State-Feedback Controllers in Underactuated Systems

Underactuated systems, such as rotary and double inverted pendulums, challenge traditional control due to nonlinear dynamics and limited actuation. Classical methods like state-feedback and Linear Quadratic Regulators (LQRs) are commonly used but often require high gains, leading to excessive control effort, poor energy efficiency, and reduced robustness. This article proposes a generalized state-feedback controller with its own internal dynamics, offering greater design flexibility. To automate tuning and avoid manual calibration, we apply Bayesian Optimization (BO), a data-efficient strategy for optimizing closed-loop performance. The proposed method is evaluated on two benchmark underactuated systems, including one in simulation and one in a physical setup. Compared with standard LQR designs, the BO-tuned state-feedback controller achieves a reduction of approximately 20% in control signal amplitude while maintaining comparable settling times. These results highlight the advantages of combining model-based control with automatic hyperparameter optimization, achieving efficient regulation of underactuated systems without increasing design complexity.