A global optimization approach for non-linear sliding mode control analysis and design

JORDAN NININ; JUAN LUIS ROSENDO; BENOIT CLEMENT; DOMINIQUE MONNET; FABRICIO GARELLI; HERNAN DE BATTISTA

Florianopolis

Simposio; 9th IFAC Symposium on Robust Control Design; 2018

The design of sliding mode (SM) comprises the selection of a sliding manifold on the state space and a switching logic. The sliding manifold design is associated with the desired dynamics and closed loop specications, whereas the switching logic is designed to drive and keep the state on the prescribe manifold. The classical design can lead to over or underestimation of the sliding domain, the closed loop robustness and the necessary control power. Here the design of SM is addressed from the global optimization approach using interval arithmetic. A solution to the analysis and synthesis problems of SM design is provided, where the necessary and suficient conditions are fullled in a guaranteed way. For the analysis problem the proposed methodology allows checking sliding mode behaviour over given state domain and parameter sets. For the synthesis problem, the methodology allows designing the sliding manifold and switching logic with a given optimization criterion. The methodology is illustrated with a concluding example.