TY - JOUR
T1 - Reachability analysis of nonlinear differential-algebraic systems
AU - Althoff, Matthias
AU - Krogh, Bruce H.
PY - 2014/2
Y1 - 2014/2
N2 - This paper presents a numerical procedure for the reachability analysis of systems with nonlinear, semi-explicit, index-1 differential-algebraic equations. The procedure computes reachable sets for uncertain initial states and inputs in an overapproximative way, i.e. it is guaranteed that all possible trajectories of the system are enclosed. Thus, the result can be used for formal verification of system properties that can be specified in the state space as unsafe or goal regions. Due to the representation of reachable sets by zonotopes and the use of highly scalable operations on them, the presented approach scales favorably with the number of state variables. This makes it possible to solve problems of industry-relevant size, as demonstrated by a transient stability analysis of the IEEE 14-bus benchmark problem for power systems.
AB - This paper presents a numerical procedure for the reachability analysis of systems with nonlinear, semi-explicit, index-1 differential-algebraic equations. The procedure computes reachable sets for uncertain initial states and inputs in an overapproximative way, i.e. it is guaranteed that all possible trajectories of the system are enclosed. Thus, the result can be used for formal verification of system properties that can be specified in the state space as unsafe or goal regions. Due to the representation of reachable sets by zonotopes and the use of highly scalable operations on them, the presented approach scales favorably with the number of state variables. This makes it possible to solve problems of industry-relevant size, as demonstrated by a transient stability analysis of the IEEE 14-bus benchmark problem for power systems.
KW - Formal safety verification
KW - nonlinear differential-algebraic equations (DAEs)
KW - power systems
KW - reachability analysis
KW - zonotopes
UR - http://www.scopus.com/inward/record.url?scp=84893620195&partnerID=8YFLogxK
U2 - 10.1109/TAC.2013.2285751
DO - 10.1109/TAC.2013.2285751
M3 - Article
AN - SCOPUS:84893620195
SN - 0018-9286
VL - 59
SP - 371
EP - 383
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 2
M1 - 6632887
ER -