Finite Abstraction of Mixed Monotone Systems with Discrete and Continuous Inputs

We present an efficient computational procedure for finite abstraction of discrete-time mixed monotone systems by considering a rectangular partition of the state space. Mixed monotone systems are decomposable into increasing and decreasing components, and significantly generalize the well known class of monotone systems. We tightly overapproximate the one-step reachable set from a box of initial conditions by computing a decomposition function at only two points, regardless of the dimension of the state space. We first consider systems with a finite set of operating modes and then extend the formulation to systems with continuous control inputs. We apply our results to verify the dynamical behavior of a model for insect population dynamics and to synthesize a signaling strategy for a traffic network.