A Necessary Condition on Chain Reachable Robustness of Dynamical Systems. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Fitzsimmons, Maxwell; Liu, Jun
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 1850
• Page End: 1855
• Publication Date: 2020
• Subjects: Reachability analysis -- Robustness -- Computability -- Discrete-time dynamics -- Stability analysis -- Minimal sets; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.2353
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: It is "folklore" that the solution to a set reachability problem for a dynamical system is only noncomputable because of non-robustness reasons. A robustness condition that can be imposed on a dynamical system is the requirement of the chain reachable set to equal the closure of the reachable set. We claim that this condition necessarily imposes strong conditions on the dynamical system. For instance, if the space is connected and compact and we are computing a chain reachable robust single valued function f then f cannot have an unstable fixed point or unstable periodic cycle.