Constrained sliding mode control: Invariant cylinder methodology

This paper focuses on the problem of designing a sliding mode controller in the presence of state and control constraints. Recent theoretical results developed by the author and co-workers introduce invariant sets formed by the intersection of a robust positively-invariant cylinder and the constraint set. Conditions were given for the intersection to become robust positively-invariant itself, leading to the specification of a safe operating set. This paper proposes a methodology to guide the search for a combination of invariant cylinder and switching gain to meet state and control constraints with few iterations and low conservatism. A detailed example is offered using a third-order unstable plant with box constraints.