TY - GEN
T1 - A dynamic algorithm for approximate flow computations
AU - Prabhakar, Pavithra
AU - Viswanathan, Mahesh
PY - 2011
Y1 - 2011
N2 - In this paper we consider the problem of approximating the set of states reachable within a time bound T in a linear dynamical system, to within a given error bound ε. Fixing a degree d, our algorithm divides the interval [0,T] into sub-intervals of not necessarily equal size, such that a polynomial of degree d approximates the actual flow to within an error bound of ε, and approximates the reach set within each sub-interval by the polynomial tube. Our experimental evaluation of the algorithm when the degree d is fixed to be either 1 or 2, shows that the approach is promising, as it scales to large dimensional dynamical systems, and performs better than previous approaches that divided the interval [0,T] evenly into sub-intervals.
AB - In this paper we consider the problem of approximating the set of states reachable within a time bound T in a linear dynamical system, to within a given error bound ε. Fixing a degree d, our algorithm divides the interval [0,T] into sub-intervals of not necessarily equal size, such that a polynomial of degree d approximates the actual flow to within an error bound of ε, and approximates the reach set within each sub-interval by the polynomial tube. Our experimental evaluation of the algorithm when the degree d is fixed to be either 1 or 2, shows that the approach is promising, as it scales to large dimensional dynamical systems, and performs better than previous approaches that divided the interval [0,T] evenly into sub-intervals.
KW - Approximation
KW - Linear dynamical systems
KW - Post computation
UR - http://www.scopus.com/inward/record.url?scp=79956009868&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79956009868&partnerID=8YFLogxK
U2 - 10.1145/1967701.1967722
DO - 10.1145/1967701.1967722
M3 - Conference contribution
AN - SCOPUS:79956009868
SN - 9781450306294
T3 - HSCC'11 - Proceedings of the 2011 ACM/SIGBED Hybrid Systems: Computation and Control
SP - 133
EP - 142
BT - HSCC'11 - Proceedings of the 2011 ACM/SIGBED Hybrid Systems
T2 - 14th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2011
Y2 - 12 April 2011 through 14 April 2011
ER -