2023/04/23 by Scott Brown, Mohammad Khajenejad, Brown, Scott +5 · 3 citations
Engineering · Physics and Astronomy · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Electrical engineering #FOS: Mathematics #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2304.11757
openalex publication_date 2023/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 approximate the maximal controlled invariant set to within a guaranteed precision. In particular, this procedure allows us to guarantee the invariance of the resulting near-maximal CIS while also computing sets of control inputs that enforce the invariance. Further, we propose an accelerated 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 iterations 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.