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

Miguel A. Solis, Sinnu S. Thomas, Christian A. Choque-Surco (), Edgar A. Taya-Acosta and Francisca Coiro
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Miguel A. Solis: Faculty of Engineering, Universidad Andres Bello, Santiago 7500971, Chile
Sinnu S. Thomas: School of Computer Science and Engineering, Digital University Kerala (Formerly IIITMK), Kerala 695317, India
Christian A. Choque-Surco: School of Computer and Systems Engineering, Jorge Basadre Grohmann National University, Tacna 23001, Peru
Edgar A. Taya-Acosta: Academic Department of Computer and Systems Engineering, Jorge Basadre Grohmann National University, Tacna 23001, Peru
Francisca Coiro: Faculty of Education, Pontificia Universidad Catolica de Valparaiso, Valparaiso 2530388, Chile

Mathematics, 2025, vol. 13, issue 19, 1-25

Abstract: 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.

Keywords: Bayesian Optimization; double inverted pendulum; rotary inverted pendulum; state-feedback controller; underactuated plants (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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