Generalized State-Feedback Controller Synthesis for Underactuated Systems through Bayesian Optimization

Underactuated systems pose the challenge of being able to control a plant whose degrees of freedom are not necessarily directly linked to an actuator or where such a relationship is not straightforward. Rotary inverted pendulum is an example of such systems, which on its simplest representation consists of a pendulum whose vertical angle should be taken up to the upward unstable position based on the impulse given from another bar and an appropriate control strategy, bar that is controlled by an electrical motor. This problem is often tackled by linear control theory with state-feedback controllers that is frequently obtained by means of designing a feedback gain meeting some constraints. This article reports a Bayesian Optimization approach for designing a generalized state-feedback controller, that involves more parameters than a simple state-feedback control law, but with the benefit of achieving lower control effort in terms of the signal amplitude. The source code is made publicly available to facilitate further research.