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Presented at the 21st Ieee Conference on Hierarchical Aggregation of Diffusion Processes with Multiple Equilibrium Points ~h(e)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Castañón, David A. |
| Abstract | SUMMARY leaves the domain of attraction of equilibrium point i for the domain of attraction of equilibrium point j. When a dynamical system with multiple equilibrium Define the finite state Markov process z(T) on the state points is perturbed by continous wide-band noise, it is space {xl,..xn by its infinitesimal transition rate known that transitions between different equilibrium points occur with probability one. An important problem associated with the analysis of these systems is ij ij) () (2) the statistical characterization of the jump process which represents the transitions between different do-hi(E) mains of attraction. A physical example of a dynamical system with multiple equilibrium point are common is an The main result can be stated as follows: interconnected power system, where the swing equations Let A(xt) = xi if xt is in the domain of attraction [1] represent a system with many possible equilibrium i of the equilibrium point x angles, defined by a power balance between electrical supply and demand. When the demand fluctuations and Define the initial distribution of z(o) as: unmodeled effects are represented as additive random noise, the resulting system undergoes transitions be-rz(o)-p A() = tween the equilibrium points. In this paper, we study the long-term behavior of a class of models with multiple equilibrium points and Theorem: Consider any scale function g < h additive white noise distrubances. These models are The finite dimensional distributions of the process characterized by the presence of a small parameter in A(xt/g(c)) converge as co to the distributions of the the description of the process. The objective of the process z (T h(e)\ for all t in (6,) for 6>o. Further-paper is to obtain a simplified aggregate model of the g(-)/ original process. more, the finite dimensional distributions of the pro-Specifically, we study the long-term behavior of the cess Xt/g(c) will converge to those of zJT h(C) also. trajectories of the diffusion process-! The theorem implies that the approximation z(T) cap-dx = f(x) dt + dw (1) tures all of the slow time behavior of the evolution of dxt t t the xt process. Under additional restrictions, this evolution can be decomposed further into a hierarchy of where the function f is a gradient vector field, as time scales, along the lines of [2]. Based on the above approximations, analytical expressions for the ergodic f(xt) V V g (xt) distributions can be derived. It is conjectured that the … |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://dspace.mit.edu/bitstream/handle/1721.1/2842/P-1273-15680701.pdf;jsessionid=790BC45699D9BC56D76DEFD73648DF6C?sequence=1 |
| Alternate Webpage(s) | http://dspace.mit.edu/bitstream/handle/1721.1/2842/P-1273-15680701.pdf?sequence=1 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
