2014/05/06 by Getachew K. Befekadu, Panos J. Antsaklis, Befekadu, Getachew K. +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #34K10 #37H10 #47A75 #58J37 #93E15 #93E20 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.DS #msc:34K10 #msc:37H10 #msc:47A75 #msc:58J37 #msc:93E15 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1405.1333
12 Pages
openalex publication_date 2014/05/06 · arxiv created 2014/08/20 · arxiv updated 2014/08/21 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We consider the problem of minimizing the asymptotic exit rate with which the controlled-diffusion process of a stochastically perturbed multi-channel dynamical system exits from a given bounded open domain. In particular, for a class of admissible bounded linear feedback operators, we establish a connection between the asymptotic exit rate with which such a controlled-diffusion process exits from the given domain and the asymptotic behavior (i.e., a probabilistic characterization) of the principal eigenvalue of the infinitesimal generator, which corresponds to the stochastically perturbed dynamical system, with zero boundary conditions on the given domain. Finally, we briefly remark on the implication of our result for evaluating the performance of the associated deterministic multi-channel dynamical system, when such a dynamical system is composed with a set of (sub)-optimal admissible linear feedback operators.