An auxiliary goal is designing the controlling actions required to achieve a prespecified property change.
In 1990 a paper [1] was published in Physical Review Letters by Edward Ott, Celso Grebogi and James Yorke from the University of Maryland reporting that even small feedback action can dramatically change the behavior of a nonlinear system, e.g., turn chaotic motions into periodic ones and vice versa.
The idea almost immediately became popular in the physics community, and since 1990 hundreds of papers have been published demonstrating the ability of small control, with or without feedback, to significantly change the dynamics of real or model systems.
[3][4][5][6] It is important that the results obtained were interpreted as discovering new properties of physical systems.
Thousands of papers were published that examine and predict properties of systems based on the use of control, identification and other cybernetic methods.
This produces a temperature difference between the two parts of the vessel, which seems to contradict the second law of thermodynamics.
Recent papers discussed issues relating to the experimental implementation of Maxwell's demon, particularly at the quantum-mechanical level.
[9] At the end of the 1970s the first mathematical results for the control of quantum mechanical models appeared based on control theory[10] At the end of the 1980s and beginning of the 1990s rapid developments in the laser industry led to the appearance of ultrafast, so-called femtosecond lasers.
A consequence of such an application is the possibility of realizing the alchemists' dream of changing the natural course of chemical reactions.
Ahmed Zewail from Caltech was awarded the 1999 Nobel Prize in Chemistry for his work on femtochemistry.
Using modern control theory, new horizons may open for studying the interaction of atoms and molecules, and new ways and possible limits may be discovered for intervening in the intimate processes of the microworld.
Besides, control is an important part of many recent nanoscale applications, including nanomotors, nanowires, nanochips, nanorobots, etc.
Carnot saw that, in order to operate continuously, the engine requires also a cold reservoir with the temperature
By simple logic he established the famous ‘’’Carnot Principle’’’: ‘’No heat engine can be more efficient than a reversible one operating between the same temperatures’’.
However, most work was devoted to studying stationary systems over infinite time intervals, while for practical purposes it is important to know the possibilities and limitations of the system's evolution for finite times as well as under other types of constraints caused by a finite amount of available resources.
The pioneer work devoted to evaluating finite time limitations for heat engines was published by I. Novikov in 1957,[11] and independently by F.L.
Later, the results[12][11] were extended and generalized for other criteria and for more complex situations based on modern optimal control theory.
[13] By the end of the 1990s it had become clear that a new area in physics dealing with control methods had emerged.
Even if the plant model is not given (the case in many real world applications) it should be determined in some way.
For example, a typical problem of chaos control can be formulated as tracking an unstable periodic solution (orbit).
The problem is to find out if it is possible to drive it into an oscillatory mode with the desired characteristics (energy, frequency, etc.)
Such problems are well known in electrical, radio engineering, acoustics, laser, and vibrational technologies, and indeed wherever it is necessary to create an oscillatory mode for a system.
Such a class of control goals can be related to problems of dissociation, ionization of molecular systems, escape from a potential well, chaotization, and other problems related to the growth of the system energy and its possible phase transition.
The last class of control goals is related to the modification of some quantitative characteristics that limit the behavior of the system.
Ott, Grebogi and Yorke[1] and their followers introduced a new class of control goals not requiring any quantitative characteristic of the desired motion.
Additionally, the desired degree of chaoticity may be specified by specifying the Lyapunov exponent, fractal dimension, entropy, etc.
Such a restriction is needed to avoid "violence" and preserve the inherent properties of the system under control.
Implementation of a feedback control requires additional measurement devices working in real time, which are often hard to install.
The possibilities of changing system behavior by means of feedback control can then be studied.
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