1 / 66

INTRODUCTION TO CYBERNETICAL PHYSICS

Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems ”. INTRODUCTION TO CYBERNETICAL PHYSICS . Alexander FRADKOV, Institute for Problems of Mechanical Engineering St.Petersburg, RUSSIA.

bell
Télécharger la présentation

INTRODUCTION TO CYBERNETICAL PHYSICS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” INTRODUCTION TO CYBERNETICAL PHYSICS Alexander FRADKOV, Institute for Problems of Mechanical Engineering St.Petersburg, RUSSIA ------------------------------------------------------------------------ Prague, UTIA, November 1, 2006

  2. Institute for 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 and waves in a chain of oscillators. 4. Conclusions

  3. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Publications on “Control of chaos” and “Quantum control”in 1990-2004 based on data from Science Citation Index (Web of Science)

  4. Institute for 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

  5. Institute for 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

  6. Institute for 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 for reducing vibration and wear. But controlling friction experiments can also be used to increase our understanding of the physics of dry friction. For example, using these methods one can measure the effective friction force 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 and coherence in chaotic dynamical systems. This is an important problem both for its own intrinsic interest and also from the point of view of applications. Those methods provide insights also into the origin of mixing and unmixing behavior in natural systems. (Sharma A., Gupte, N. Pramana - J. of Physics, V.48, 1997, 231-248. ) - We develop novel diagnostics tools for plasma turbulence based on feedback. This ... allows qualitative and 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 understanding of atoms and molecules and their interactions. (Rabitz H. et al., Science, 2000, 288, 824-828.)

  7. Institute for 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 and micromechanical systems • Optimal control in thermodynamics • Control of plasma, particle beams • Control of molecular and quantum systems

  8. CDC 2001 PLENARY LECTURE: Anew physics? John Doyle Control and Dynamical Systems, Caltech http://www.cds.caltech.edu/~doyle/

  9. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” CDC 2004 PLENARY PANEL DISCUSSION: Challenges and Opportunities for the Future of Control Moderator: John Doyle Panelists: Jean Carlson, Christos Cassandras, P. R. Kumar, Naomi Leonard, and Hideo Mabuchi http://control.bu.edu/ieee/cdc04/ Connecting physical processes at multiple time and space scales in quantum, statistical, fluid, and solid mechanics, remains not only a central scientific challenge but also one with increasing technological implications.

  10. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” 2. TYPES AND FEATURES OF CONTROL PROBLEMS IN PHYSICAL SYSTEMS x– state, u – input (control),y – output (observation). Type 0: u=const (parameter optimization, bifurcation analysis) Type 1: u=u(t) (program control; u=Asin(ωt) - vibrational control) Type 2: u=u(t,y) - feedback control Features:1. Control is small: is small. 2. Goal is “soft”

  11. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Control goals: • Excitation • Synchronization • Chaotization/ • dechaotization Extension: partial stabilization Results: transformation laws ( instead of conservation laws)

  12. Institute for 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 (forces, fields, parameters). Control goal : Problem: Find control algorithm u=U(q,p), ensuring the control goal for Difficulties:1. Control is weak: 2. Nonlocal solutions are needed

  13. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Speed-Gradient (SG) algorithms System: Goal: goal function where (e.g.

  14. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Existing results (Fradkov, 1979, 1985):

  15. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Speed-gradient energy control Control algorithm: Theorem. 1. Let Then 2. Let in a countable set. Then either

  16. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Extension: Stabilization of invariants ( h(x)=0 - invariant surface of free system)

  17. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Theorem (Fradkov, Shiriaevet al, 1997)

  18. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” 3.2. Excitability analysis of dissipative systems Example. Swinging the damped pendulum

  19. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Upper and lower excitability indices: Passivity: V(x) - storage (energy-like) function, w=w(x) - “passive output”

  20. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Theorem. (Fradkov, 2001) Remark: To prove the left inequality is substituted.

  21. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Special case: Euler-Lagrange systems with dissipation R - vector of dissipative forces Total energy: Upper and lower excitability indices: __ Theorem. Corollary. Remark. Locally optimal control is:

  22. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Excitability of pendular systems: Simple pendulum:

  23. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Coupled pendulums [A.Fradkov, B. Andrievsky, K. Boykov.Mechatronics, V.15 (10), 2005 ]

  24. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” • Laboratory set-up • Mechanical unit; • Electrical unit (interface init); • Pentium III personal computer

  25. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems”

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

  27. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems”

  28. Institute for 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 for 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:

  29. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Simulation results

  30. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems”

  31. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Efficiency of feedback

  32. Institute for Problems of Mechanical Engineering of RAS Laboratory «Control of Complex Systems» 3.4. Control of molecular systems - femtotechnologies

  33. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” 3.4.1. Controlled dissociation of 2-atomic molecules Classical Morse oscillator: Quantum Morse oscillator: dissociation energy Example: hydrogen fluoride (HF) a.u. of length

  34. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” M.Goggin, P.Milonni (LANL). Phys.Rev.A 38 (10), 5174 (1988). a,c) - classical model; b,d) - quantum model

  35. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Control of HF molecules dissociation - classical dynamics Linear chirping: Speed-gradient:

  36. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Control of HF molecules dissociation - quantum dynamics Linear chirping: Speed-gradient:

  37. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” (Ananjevskij M., Fradkov A.,Efimov A., Krivtsov A., PhysCon’03)

  38. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems”

  39. Institute for Problems of Mechanical Engineering of RAS Laboratory «Control of Complex Systems» • 3.4.2.Controlled dissociation of 3-atomic moleculeAux.problem:Controlled Energy Exchange • cooling of molecules; - selective dissociation; • localization of modes; - passage through resonance

  40. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Controlled dissociation of 3-atomic molecule Full Hamiltonian of moleculein external field: Molecular Hamiltonian (Rabitz, 1995; Fujimura, 2000) : R1, R2- displacements of bond length; P1, P2 - conjugate momenta; E(t) - controlling field. Control goal: Speed-gradient control algorithm:

  41. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems”

  42. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems”

  43. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” 3.5. Control of chaos by linearization of Poincare map ‘

  44. Institute for Problems of Mechanical Engineering of RAS Laboratory “Control of Complex Systems” Method of Ott-Grebogi-Yorke (OGY): The problem is reduced to a standard linear control problem. Challenge: How much time and energy is needed for control?

  45. 3.5. CONTROLLED SYNCHRONIZATION • 3.5.1. Model of coupled pendulums Andrievsky B.R.,Fradkov A.L. Feedback resonance in single and coupled 1-DOF oscillators // Intern. J of Bifurcation and Chaos, 1999, N 10, pp.2047-2058.

  46. 3.5.2 Design of synchronization algorithm

  47. Total system energy:

  48. 3.5.3 Synchronization algorithms:

  49. 3.5.4 Simulation results

More Related