Computing Controlled Invariant Sets of Nonlinear Control-Affine Systems

In this paper, we consider the computation of controlled invariant sets (CIS) of discrete-time nonlinear control-affine systems. We propose an iterative refinement procedure based on polytopic inclusion functions, which is able to inner-approximate the maximal controlled invariant set to within a guaranteed robustness margin. In particular, this procedure allows us to guarantee the invariance of the resulting near-maximal CIS while also computing sets of control inputs which enforce the invariance. Further, we propose an alternative version of this procedure which refines the CIS by computing backward reachable sets of individual components of set unions, rather than all at once. This reduces the total number of inclusion checking operations required for convergence, especially when compared with existing methods. Finally, we compare our methods to a sampling based approach and demonstrate the improved accuracy and faster convergence.