2015/07/22 by Yinan Li, Jun Liu, Li, Yinan +3
Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Electrical engineering #FOS: Mathematics #Formal Methods in Verification #Optimization and Control (math.OC) #Petri Nets in System Modeling #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1507.06248
openalex publication_date 2015/07/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical function to provide bounds on the reachable sets of nonlinear systems, which can be conservative and lead to spurious transitions in the abstract systems. This problem is even more pronounced in the presence of imperfect measurements and modelling uncertainties, where control synthesis can easily become infeasible due to added spurious transitions. To mitigate this problem, we propose to compute finite abstractions with robustness margins by over-approximating the local reachable sets of nonlinear systems. We do so by linearizing the nonlinear dynamics into linear affine systems and keeping track of the linearization error. It is shown that this approach provides tighter approximations and several numerical examples are used to illustrate of effectiveness of the proposed methods.