  Inner-approximate reachability analysis involves calculating subsets of
reachable sets, known as inner-approximations. This analysis is crucial in the
fields of dynamic systems analysis and control theory as it provides a reliable
estimation of the set of states that a system can reach from given initial
states at a specific time instant. In this paper, we study the
inner-approximate reachability analysis problem based on the set-boundary
reachability method for systems modelled by ordinary differential equations, in
which the computed inner-approximations are represented with zonotopes. The
set-boundary reachability method computes an inner-approximation by excluding
states reached from the initial set's boundary. The effectiveness of this
method is highly dependent on the efficient extraction of the exact boundary of
the initial set. To address this, we propose methods leveraging boundary and
tiling matrices that can efficiently extract and refine the exact boundary of
the initial set represented by zonotopes. Additionally, we enhance the
exclusion strategy by contracting the outer-approximations in a flexible way,
which allows for the computation of less conservative inner-approximations. To
evaluate the proposed method, we compare it with state-of-the-art methods
against a series of benchmarks. The numerical results demonstrate that our
method is not only efficient but also accurate in computing
inner-approximations.
