Related papers: Singularly Perturbed Averaging with Application to…
We analyze a class of high-amplitude, high-frequency oscillatory systems in which periodicity occurs on two distinct time scales and establish the convergence of its trajectories to a suitably averaged system by recursively applying the…
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…
We present a novel extremum seeking method for affine connection mechanical control systems. The proposed control law involves periodic perturbation signals with sufficiently large amplitudes and frequencies. A suitable averaging analysis…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
We study novel robust zero-order algorithms with acceleration for the solution of real-time optimization problems. In particular, we propose a family of extremum seeking dynamics that can be universally modeled as singularly perturbed…
All the existing source-seeking algorithms for unicycle models in GPS-denied settings guarantee at best an exponential rate of convergence over an infinite interval. Using the recently introduced time-varying feedback tools for…
We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or…
We study the problem of global extremum seeking in the presence of local extrema. We investigate two different perturbation-based methods: 1) a well-known classical extremum seeking scheme for steady-state output optimization, and 2) a…
In this paper, we study gradient-based classical extremum seeking (ES) for uncertain n-dimensional (nD) static quadratic maps in the presence of known large constant distinct input delays and large output constant delay with a small…
We propose a new design strategy for extremum seeking control for a multi-dimensional single-integrator system in the presence of local extrema. The proposed method employs suitably designed sinusoidal dither signals, which force the…
Power systems are globally experiencing an unprecedented growth in size and complexity due to the advent of nonconventional generation and consumption technologies. To navigate computational complexity, power system dynamic models are often…
In this paper a novel stochastic optimization and extremum seeking algorithm is presented, one which is based on time-delayed random perturbations and step size adaptation. For the case of a one-dimensional quadratic unconstrained…
This paper studies a constrained optimization problem over networked systems with an undirected and connected communication topology. The algorithm proposed in this work utilizes singular perturbation, dynamic average consensus, and saddle…
The main aim of this work is to present two different methodologies for configuration averaging in disordered systems. The Recursion method is suitable for the calculation of spatial or self-averaging, while the Augmented space formalism…
In this paper, we develop an extremum seeking control method integrated with iterative learning control to track a time-varying optimizer within finite time. The behavior of the extremum seeking system is analyzed via an approximating…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…
Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi time-scale systems. In this paper a contraction theory based framework is proposed for…