A robust optimal control approach in the weighted Sobolev space for underactuated mechanical systems. (March 2021) - Cardoso, Daniel N.; Esteban, Sergio; Raffo, Guilherme V.
Abstract: This paper proposes new robust nonlinear optimal control formulations in the weighted Sobolev space, here called nonlinear W 2 and W ∞ controllers, to handle with two classes of underactuated mechanical systems: the reduced ones with a reduced number of DOF; and the entire underactuated mechanical systems with input coupling. The optimal control problems are formulated via dynamic programming and particular solutions are presented for the resulting Hamilton–Jacobi equations with the corresponding stability analysis. Also, the concepts of W m, p, σ -stability and W m, p, σ -gain for a general class of systems are established, with the demonstration for the particular case of study. The novel W 2 and W ∞ controllers are synthesized for an unmanned aerial vehicle benchmark. The results demonstrate that these controllers provide better transient performance with faster response against external disturbances in comparison with a classic nonlinear H ∞ controller, in addition to have a simple design.