Characterizations and Computation of 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 an algorithmic approach to the computation of controlled invariants. Finally, we illustrate the proposed approach on an adaptive cruise control problem.