classical control methods such as pontryagin maximum principle and bang-bang principle and other methods are not usually useful for solving opti-mal control systems (ocs) specially optimal control of nonlinear systems (ocns). in this paper, we introduce a new approach for solving ocns by using some combination of atomic measures. we define a criterion for controllability of lumped nonlinear con...

The present status of the heavy-ion program to search for quark-gluon plasma is reviewed. The goal of this program is to recreate the Big Bang in the laboratory, by generating small chunks of exploding quark-gluon plasma (“The Little Bang”). I argue that the analogues of the three pillars of Big Bang Theory (Hubble flow, microwave background radiation, and primordial nucleosynthesis) have now b...

We study numerically the inhomogeneous pre-big-bang inflation in a spherically symmetric space-time. We find that a large initial inhomogeneity suppresses the onset of the pre-big-bang inflation. We also find that even if the pre-big-bang inflationary stage is realized, the initial inhomogeneities are not homogenized. Namely, during the pre-big-bang inflation “hairs”(irregularities) do not fall...

Discontinuous dynamical systems arise in a large number of applications. In optimal control problems, open-loop bang-bang controllers switch discontinuously between extremum values of the bounded inputs to generate minimum-time trajectories from one state to another. Thermostats implement closed-loop bang-bang controllers to regulate room temperature. In nonsmooth mechanics, the evolution of ri...

A discrete-time periodic model with bang-bang feedback control is investigated. It is shown that each solution tends to one of four different types of limit 2-cycles. Furthermore, the accompanying initial regions for each type of solutions can be determined. When a threshold parameter is introduced in the bang-bang function, our results form a complete bifurcation analysis of our control model....

This paper introduces a novel bang–bang sliding control of a class of single-input bilinear systems. The sliding function is chosen via the well-known pole-assignment method for linear time-invariant systems. Importantly, the bang–bang sliding control generates a reaching-and-sliding region and a stable-sliding region, each expressed by a set of linear inequalities. Both regions comprise the eq...