Paper Info
Title
On Reachability Under Uncertainty
Abstract
The paper studies the problem of reachability for linear systems in the presence of uncertain (unknown but bounded) input disturbances that may also be interpreted as the action of an adversary in a game-theoretic setting. It defines possible notions of reachability under uncertainty emphasizing the differences between reachability under open-loop and closed-loop control. Solution schemes for calculating reachability sets are then indicated. The situation when observations arrive at given isolated instances of time leads to problems of anticipative (maxmin) or nonanticipative (minmax) piecewise open-loop control with corrections and to the respective notions of reachability. As the number of corrections tends to infinity, one comes in both cases to reachability under nonanticipative feedback control. It is shown that the closed-loop reach sets under uncertainty may be found through a solution of the forward Hamilton--Jacobi--Bellman--Isaacs (HJBI) equation. The basic relations are derived through the investigation of superpositions of value functions for appropriate sequential maxmin or minmax problems of control.
Year
DOI
Venue
2002
10.1137/S0363012999361093
SIAM J. Control and Optimization
Keywords
Field
DocType
closed-loop reach set,closed-loop control,solution scheme,minmax problem,nonanticipative feedback control,forward hamilton,appropriate sequential maxmin,reachability set,piecewise open-loop control,basic relation,open loop control,uncertainty,closed loop control,reachability,linear system,value function,dynamic programming,differential inclusions,feedback control
Differential inclusion,Dynamic programming,Mathematical optimization,Minimax,Linear system,Infinity,Reachability,Piecewise,Mathematics,Bounded function
Journal
Volume
Issue
ISSN
41
1
0363-0129
Citations 
PageRank 
References 
13
1.85
3
Authors
2
Name
Order
Citations
PageRank
Alexander B. Kurzhanski120425.02
Pravin Varaiya22543298.93