Safe Sliding Domains via Control Barrier Functions

ABSTRACT Robust control design that guarantees the safety of closed‐loop systems trajectories has become a problem of main interest in the last decades. While sliding mode control provides a powerful framework for designing robust control algorithms, how to incorporate given constraints in the state space into this framework has remained underexplored in the literature. We propose the construction of sliding domains that guarantee that chain integrator systems trajectories slide on a given safe set in the state space. The sliding domain is constructed by minimally modifying a standard relative‐degree‐one sliding surface with an additional function, obtained from a control barrier function‐based quadratic program, which enables rendering the reduced dynamics safe. Both discontinuous and adaptive unit control law‐based strategies are proposed, and numerical examples are provided throughout the paper to illustrate the presented approach.