INTRODUCTION TO CYBERNETICAL PHYSICS

INTRODUCTION TO CYBERNETICAL PHYSICS www.phwiki.com

INTRODUCTION TO CYBERNETICAL PHYSICS

Yang, Leo, Field Producer has reference to this Academic Journal, PHwiki organized this Journal INTRODUCTION TO CYBERNETICAL PHYSICS Alex in addition to er FRADKOV, Institute as long as Problems of Mechanical Engineering St.Petersburg, RUSSIA Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” ——— Prague, UTIA, November 1, 2006 Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” OUTLINE 1. Introduction 2. Features of the control problems in physical systems 3. Results from the “Control of Complex Systems” Lab 3.1. Energy control of conservative systems 3.2. Excitability analysis of dissipative systems 3.3. Examples: Kapitsa pendulum, escape from potential well; 3.4. Control of molecular systems: classical or quantum 3.4.1. Dissociation of diatomic molecules 3.4.2. Dissociation of triatomic molecules 3.5.Controlled synchronization of two pendulums 3.6 Excitation of oscillations in addition to waves in a chain of oscillators. 4. Conclusions Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Publications on “Control of chaos” in addition to “Quantum control” in 1990-2004 based on data from Science Citation Index (Web of Science)

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Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Publications of 1990-2004 in Physical Review A-E, Physical Review Letters with the term “control” in the title Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Publications of 2003: “Control AND Chaos” – – – – – – – 462 “Control AND Quantum” – – – – 658 Total – 1120 ======================================================== IEEE Trans. Autom. Control – – – – – – – – 321 IFAC Automatica – – – – – – – – – – – – – – – – 220 Systems & Control Letters – – – – – – – – – – 107 Intern. Journal of Control – – – – – – – – – – 172 Total – 820 (In Russian – 3 journals, ~350 papers) “Control AND Lasers” – 180 “Control AND Thermodynamics” – – – 79 “Control AND Beams” – 260 “Control AND Plasma AND Tokamaks”- 102 Institute as long as Problems of Mechanical Engineering of RAS Laboratory «Control of Complex Systems» – There are two fields of application of controlling friction. Obviously there will be technological applications as long as reducing vibration in addition to wear. But controlling friction experiments can also be used to increase our underst in addition to ing of the physics of dry friction. For example, using these methods one can measure the effective friction as long as ce as a function of the sliding. ( Elmer F.J. Phys. Rev. E, V.57, 1998, R490-R4906.) – We have summarized some recently proposed appications of control methods to problems of mixing in addition to coherence in chaotic dynamical systems. This is an important problem both as long as its own intrinsic interest in addition to also from the point of view of applications. Those methods provide insights also into the origin of mixing in addition to unmixing behavior in natural systems. (Sharma A., Gupte, N. Pramana – J. of Physics, V.48, 1997, 231-248. ) – We develop novel diagnostics tools as long as plasma turbulence based on feedback. This allows qualitative in addition to quantitative inference about the dynamical model of the plasma turbulence. (Sen A.K., Physics of Plasmas, V.7, 2000, 1759-1766.) – The aim of the researches is twofold: – to create a particular product that is unattainable by conventional chemical means; – to achieve a better underst in addition to ing of atoms in addition to molecules in addition to their interactions. (Rabitz H. et al., Science, 2000, 288, 824-828.)

Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Cybernetical physics – studying physical systems by cybernetical means Fields of research: Control of oscillations Control of synchronization Control of chaos, bifurcations, Control of phase transitions, stochastic resonance Control of mechanical in addition to micromechanical systems Optimal control in thermodynamics Control of plasma, particle beams Control of molecular in addition to quantum systems John Doyle Control in addition to Dynamical Systems, Caltech http://www.cds.caltech.edu/~doyle/ A new physics CDC 2001 PLENARY LECTURE: Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Connecting physical processes at multiple time in addition to space scales in quantum, statistical, fluid, in addition to solid mechanics, remains not only a central scientific challenge but also one with increasing technological implications. CDC 2004 PLENARY PANEL DISCUSSION: Challenges in addition to Opportunities as long as the Future of Control Moderator: John Doyle Panelists: Jean Carlson, Christos Cass in addition to ras, P. R. Kumar, Naomi Leonard, in addition to Hideo Mabuchi http://control.bu.edu/ieee/cdc04/

2. TYPES AND FEATURES OF CONTROL PROBLEMS IN PHYSICAL SYSTEMS Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Type 0: u=const (parameter optimization, bifurcation analysis) Type 1: u=u(t) (program control; u=Asin(t) – vibrational control) Type 2: u=u(t,y) – feedback control Features: 1. Control is small: x – state, u – input (control), y – output (observation). 2. Goal is “soft” is small. Control goals: Excitation Chaotization/ dechaotization Extension: partial stabilization Results: trans as long as mation laws ( instead of conservation laws) Synchronization Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” 3. RESULTS OBTAINED IN CCS Lab: 3.1. Energy control of conservative systems u=u(t) – control ( as long as ces, fields, parameters). Control goal : Problem: Find control algorithm u=U(q,p), ensuring the control goal as long as Difficulties: 1. Control is weak: 2. Nonlocal solutions are needed

Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Speed-Gradient (SG) algorithms System: Goal: goal function where (e.g. Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Existing results (Fradkov, 1979, 1985): Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Speed-gradient energy control Theorem. 1. Let Then 2. Let in a countable set. Then either Control algorithm:

Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Extension: Stabilization of invariants ( h(x)=0 – invariant surface of free system) Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Theorem (Fradkov, Shiriaev et al, 1997) Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” 3.2. Excitability analysis of dissipative systems Example. Swinging the damped pendulum

Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Upper in addition to lower excitability indices: Passivity: V(x) – storage (energy-like) function, w=w(x) – “passive output” Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Theorem. (Fradkov, 2001) Remark: To prove the left inequality is substituted. Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Special case: Euler-Lagrange systems with dissipation R – vector of dissipative as long as ces Total energy: Upper in addition to lower excitability indices: – Theorem. Corollary. Remark. Locally optimal control is:

Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Excitability of pendular systems: Simple pendulum: Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Coupled pendulums [A.Fradkov, B. Andrievsky, K. Boykov. Mechatronics, V.15 (10), 2005 ] Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Laboratory set-up Mechanical unit; Electrical unit (interface init); Pentium III personal computer

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Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” 3.3. Example 1: Stephenson-Kapitsa pendulum b) Feedback control: a) Classical Stephenson-Kapitsa pendulum: Speed-gradient algorithm: Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems”

Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Example 2: Control of escape from a potential well Nonlinear oscillator: Duffing potential: Problem: find conditions as long as escape from a potential well by means of excitation of minimum intensity A) Harmonic excitation: (H.B. Stewart, J.M.T. Tompson, U. Ueda, A.N. Lansburg, Physica D, v. 85, 1995, pp. 259-295.) B) Speed-gradient excitation: Theory: Experiment: Simulation results Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems”

Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Publications: Fradkov A.L. Exploring nonlinearity by feedback. Physica D, 128(1999), pp. 159-168. Fradkov A.L. Investigation of physical systems by means of feedback. Automation & Remote Control, 1999, N 3. .. . :, 2003. Fradkov A.L. Application of cybernetical methods in physics. Physics-Uspekhi, Vol. 48 (2), 2005, 103-127. Fradkov A.L. Cybernetical Physics: From Control of Chaos to Quantum Control, Springer-Verlag, 2006. Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Institute as long as Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” More info at: http://physcon.ru/ 1st International Conference PHYSICS in addition to CONTROL (PhysCon 2003) 20–22 Aug. 2003, Saint Petersburg, RUSSIA 2nd International Conference PHYSICS in addition to CONTROL (PhysCon 2005) 24–26 Aug. 2005, Saint Petersburg, RUSSIA (200-250 participants, 30-33 countries)

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