Large Deviations for Two-Time-Scale Diffusions, With Delays

Decentralized Model Reference Adaptive Control of Large Scale Interconnected Systems with Time-Delays in States and Inputs

This paper investigates the problem of decentralized model reference adaptive control (MRAC) for a class of large scale systems with time varying delays in interconnected terms and state and input delays. The upper bounds of the interconnection terms are considered to be unknown. Time varying delays in the nonlinear interconnection terms are bounded and nonnegative continuous functions and thei...

Quenching Time for a Nonlocal Diffusion Problem with Large Initial Data

A new virtual leader-following consensus protocol to internal and string stability analysis of longitudinal platoon of vehicles with generic network topology under communication and parasitic delays

In this paper, a new virtual leader following consensus protocol is introduced to perform the internal and string stability analysis of longitudinal platoon of vehicles under generic network topology. In all previous studies on multi-agent systems with generic network topology, the control parameters are strictly dependent on eigenvalues of network matrices (adjacency or Laplacian). Since some ...

Large deviations for diffusions with time periodic drift and stochastic resonance

We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period T and a small Gaussian random perturbation of intensity ε, and therefore mathematically described as weakly time inhomogeneous diffusion processes. A system is in stochastic resonance provided the small no...

Large Deviations for Two Scaled Diffusions

Mathematical Subject Classification (1991) 60F10 Summary. We formulate large deviations principle (LDP) for diffusion pair (X, ξ) = (X t , ξ ε t ), where first component has a small diffusion parameter while the second is ergodic Markovian process with fast time. More exactly, the LDP is established for (X, ν) with ν(dt, dz) being an occupation type measure corresponding to ξ t . In some sense ...