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

Dominique Monnet, Juan Luis Rosendo, Hernán De Battista, Benoit Clement, Jordan Ninin, Fabricio Garelli

Research output: Contribution to journalArticlepeer-review


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 specifications, 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 sufficient conditions are fulfilled 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.

Original languageEnglish
Pages (from-to)128-133
Number of pages6
Issue number25
Publication statusPublished - 2018
Externally publishedYes


  • Global optimization
  • Interval analysis
  • Robust control design
  • Sliding Modes


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