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Controllability, Stabilization, and the Regulator Problem for Random Differential Systems
 
Russell Johnson University of Florence, Florence, Italy
Mahesh Nerurkar Rutgers University, Camden, NJ
Controllability, Stabilization, and the Regulator Problem for Random Differential Systems
eBook ISBN:  978-1-4704-0235-8
Product Code:  MEMO/136/646.E
List Price: $44.00
MAA Member Price: $39.60
AMS Member Price: $26.40
Controllability, Stabilization, and the Regulator Problem for Random Differential Systems
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Controllability, Stabilization, and the Regulator Problem for Random Differential Systems
Russell Johnson University of Florence, Florence, Italy
Mahesh Nerurkar Rutgers University, Camden, NJ
eBook ISBN:  978-1-4704-0235-8
Product Code:  MEMO/136/646.E
List Price: $44.00
MAA Member Price: $39.60
AMS Member Price: $26.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1361998; 48 pp
    MSC: Primary 34; 93;

    This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness properties and which also preserves all the smoothness and recurrence properties of the coefficients. Finally, a general version of the local nonlinear feedback stabilization problem is solved.

    Readership

    Graduate students and research mathematicians working in dynamical systems.

  • Table of Contents
     
     
    • Chapters
    • 0. Introduction
    • 1. Basic dynamical notions
    • 2. Random linear control processes
    • 3. Some facts about random linear systems
    • 4. Sufficiency conditions for uniform controllability
    • 5. Dependence of controllability on the dynamics of the flow
    • 6. Global null controllability
    • 7. The feedback stabilization problem for random linear systems
    • 8. The rotation number
    • 9. The solution of the linear regulator and the stabilization problem
    • 10. Linearization of the regulator and the stabilization problem
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1361998; 48 pp
MSC: Primary 34; 93;

This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness properties and which also preserves all the smoothness and recurrence properties of the coefficients. Finally, a general version of the local nonlinear feedback stabilization problem is solved.

Readership

Graduate students and research mathematicians working in dynamical systems.

  • Chapters
  • 0. Introduction
  • 1. Basic dynamical notions
  • 2. Random linear control processes
  • 3. Some facts about random linear systems
  • 4. Sufficiency conditions for uniform controllability
  • 5. Dependence of controllability on the dynamics of the flow
  • 6. Global null controllability
  • 7. The feedback stabilization problem for random linear systems
  • 8. The rotation number
  • 9. The solution of the linear regulator and the stabilization problem
  • 10. Linearization of the regulator and the stabilization problem
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.