Exit problem and control theory
The paper considers the Freidlin-Wentzell exit problem for systems of the form \(dx=f(x)dt+\epsilon \sigma dw_ t.\) The ''usual'' conditions (i) nondegeneracy of the noise, (ii) invariance of the basic domain D, (iii) the quasipotential attains its relative minimum at one point, are generalized to (a) controllability conditions on \(\dot y=f(y)+\sigma u\) (note: there is a misprint in equation (12)), (b) stability conditions on \(\dot z=f(z)\), (c) continuity requirements on the quasipotential. Then results on the exit rate and exit set hold similar to the Freidlin- Wentzell estimates. Linear systems \(dX=AXdt+\epsilon \sigma dw_ t\) are considered in more detail for stable matrices A, and applications to feedback stability of these systems are given.
continuity requirements on the quasipotential
scientific article; zbMATH DE number 3949415