Extended State Observer‐Based Constraint‐Following Control for Underactuated Systems With Uncertainty and Input Saturation

Underactuated systems have been widely studied and applied due to their unique performance advantages. This paper investigates constraint‐following control based on an extended state observer to address the control problems in underactuated systems caused by uncertainty and input saturation. Firstly, a modified extended state observer is used to estimate the equivalent acceleration variation caused by uncertainty. Secondly, relying on the equivalent acceleration estimation, a constraint‐following uncertainty compensation control is proposed, enabling the system to autonomously counteract uncertainty. Finally, stability is guaranteed by a gain saturation strategy while avoiding the control inputs from exceeding the preset boundaries. In addition, a projection operator is selected to decompose uncertainty into matched and mismatched portions. A necessary and sufficient condition to ensure that mismatched uncertainty does not affect stability is also given, which reduces the number of required effective constraints. The Lyapunov method is used to prove the uniform ultimate boundedness of the estimation error and the first‐order tracking error. Simulation examples illustrate the effectiveness of the proposed control scheme.