Characterization, Verification and Computation of Robust Controlled Invariants for Monotone Dynamical Systems

In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and disturbances respect a given partial order. Then, we present set-based and trajectory-based characterizations of robust controlled invariants for the considered class of systems. Based on these characterizations, we propose algorithmic approaches for the verification and computation of robust controlled invariants. Finally, illustrative examples are provided showing the merits of the proposed approach.