Efficient Outer Approximations for Less Conservative 0‐Reachable Sets With Rate‐Bounded Disturbances

ABSTRACT In this paper, we address the problem of computing outer approximations of the potentially less conservative 0‐reachable set for asymptotically stable discrete linear time‐invariant systems, where disturbances are bounded both in magnitude and rate of change, under the assumption that both bounds are polytopic. We provide results that enable the computation of finite‐step invariant outer approximations of the 0‐reachable set, with conditions that allow for the a priori specification of the approximation accuracy. Furthermore, to handle the computational complexity introduced by system augmentation, we propose a tailored low‐complexity approximation algorithm based on linear programming and sample normals that computes the outer approximations within the desired accuracy. At the end of this paper, the effectiveness of the proposed approach is demonstrated through its application to the case studies of fin stabilization in ship roll dynamics and lateral dynamics control in an automated vehicle.