Enclosing Reachable Sets for Nonlinear Control Systems using Complementarity-Based Intervals

Enclosing the reachable sets of nonlinear control systems is useful in state estimation and safety verification for chemical process models. We present a new approach for computing time-varying interval bounds for ordinary differential equation models based on differential inequalities. Instead of using interval arithmetic like established approaches, we instead generate bounding information for the right-hand side (RHS) function by optimizing its convex relaxations. Complementarity formulations are explored, and are found to be particularly beneficial if the RHS function is quadratic and we employ the αBB relaxations.