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Massachusetts Institute of Technology (MIT) Course/Program Name
Application closes on
National :15 Dec 
International :15 Dec 

ME / MEng Dynamic Systems and Control

Catalog id : 6.241J / 16.338J
 Course Level
Masters / PG
 Type
Online

 Duration
0 Months
 Start month
October

 Tuition fee

International
48140 USD
National
48140 USD

Application fee

International 75 USD
National 75 USD
Department
Electrical engineering and computer science
Scores accepted
IELTS (min)7.5
TOEFL-IBT (min)90
TOEFL-PBT (min)577
GRE (avg)329
GMAT (avg)710

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About this course

The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions.

We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.

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Eligibility Criteria

Graduate Record Examination

Most MIT departments require the Graduate Record Examination (GRE) General Test and an appropriate Subject Test The fee for the GRE ranges approximately from $160 to $190 US. The General Test is offered only on the computer in the US and in most locations around the world. The computer-based GRE General Test is available year round, and appointments are scheduled on a first-come, first-served basis. Register early to maximize your chances of scheduling your preferred test date and time

International English Language Testing System

IELTS exam measures ability to communicate in English across all four language skills – listening, reading, writing, and speaking – for people who intend to study or work where English is the language of communication.

Test of English as a Foreign Language

 Students whose native language is not English may take the Test of English as a Foreign Language (TOEFL). A minimum score of 577 (233 for computer-based; 90 for internet-based) is required for visa certification

 

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Course Modules

Lec # Lecture Topics Readings

  • 1 Introduction to dynamic systems and control, matrix algebra Chapter 1
  • 2 Least squares error solutions of overdetermined / underdetermined systems Chapters 2 and 3
  • 3 Matrix norms, SVD, matrix perturbations Chapter 4
  • 4 Matrix perturbations Chapter 5
  • 5 State-space models, linearity and time invariance Chapters 6–8
  • 6 Solutions of state-space models Chapters 10 and 11
  • 7 Similarity transformations, modes of LTI systems, Laplace transform, transfer functions Chapter 12
  • 8 Stability, Lyapunov methods Chapters 13 and 14
  • 9 External I/O stability, storage functions Chapter 15
  • 10 Interconnected systems, feedback, I/O stability Chapters 15 and 17
  • 11 System norms Chapter 16
  • 12 Performance measures in feedback control Chapter 18
  • 13 Small gain theorem, stability robustness Chapter 19
  • 14 Stability robustness (MIMO) Chapters 20 and 21
  • 15 Reachability Chapter 22
  • 16 Reachability: standard and canonical forms, modal tests Chapter 23
  • 17 Observability Chapter 24
  • 18 Minimality, realization, Kalman decomposition, model reduction Chapter 25
  • 19 State feedback, observers, output feedback, MIMO poles and zeros Chapters 26–29
  • 20 Minimality of interconnections, pole/zero cancellations Chapter 30
  • 21 Parameterization of all stabilizing controllers 
  • 22 Optimal control synthesis: problem setup 
  • 23 H2 optimization 
  • 24 H∞ optimization

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How to Apply

ttp://ocw.mit.edu/courses/

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