  This paper deals with the computation of the largest robust control invariant
sets (RCISs) of constrained nonlinear systems. The proposed approach is based
on casting the search for the invariant set as a graph theoretical problem.
Specifically, a general class of discrete-time time-invariant nonlinear systems
is considered. First, the dynamics of a nonlinear system is approximated with a
directed graph. Subsequently, the condition for robust control invariance is
derived and an algorithm for computing the robust control invariant set is
presented. The algorithm combines the iterative subdivision technique with the
robust control invariance condition to produce outer approximations of the
largest robust control invariant set at each iteration. Following this, we
prove convergence of the algorithm to the largest RCIS as the iterations
proceed to infinity. Based on the developed algorithms, an algorithm to compute
inner approximations of the RCIS is also presented. A special case of input
affine and disturbance affine systems is also considered. Finally, two
numerical examples are presented to demonstrate the efficacy of the proposed
method.
