Fixed-complexity piecewise ellipsoidal representation of the continual reachability set based on ellipsoidal techniques

In a previous paper we showed how the continual reachability set can be numerically computed using efficient maximal reachability tools. The resulting set is in general arbitrarily shaped and in practice possibly non-convex. Here, we present a fixed-complexity piecewise ellipsoidal under-approximation of the continual reachability set computed using ellipsoidal techniques. This provides a simple approximation of an otherwise relatively complicated set that can be used when a closed-form representation is needed. We demonstrate the results on a problem of control of anesthesia.