First order inertial optimization algorithms with threshold effects associated with dry friction

Optimization with First-Order Surrogate Functions

In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we provide a unified viewpoint for several first-order optimization techniques such as accelerated proximal gradient, block coordinate descent, or FrankWolfe algori...

Identification of a system with dry friction

Torsion Spring Oscillator with Dry Friction

Free and forced oscillations of a torsion spring pendulum damped by viscous and dry (Coulomb) friction are investigated analytically and with the help of computer simulations. An idealized mathematical model of dry friction described by the so-called z-characteristic is assumed. This simple physical model can explain many peculiarities in behavior of various oscillatory systems with dry frictio...

Control of Mechanical Systems with Dry Friction

A technique to design a dynamic continuous controller to regulate a class of full-actuated mechanical systems with dry friction is proposed. It is shown that the control eliminates the steady-state error and is robust with respect to parameter uncertainties. A simple method to find the parameters of the controller is also proposed. Moreover, an application of this result to control a 2-DOF unde...

Random-Direction Optimization Algorithms with Applications to Threshold Controls

This work develops a class of stochastic optimization algorithms. It aims to provide numerical procedures for solving thresholdtype optimal control problems. The main motivation stems from applications involving optimal or suboptimal hedging policies, for example, production planning of manufacturing systems including random demand and stochastic machine capacity. The proposed algorithm is a co...