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Massachusetts Institute of Technology (MIT) Course/Program Name
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ME / MEng Dynamics of Nonlinear Systems

Catalog id : 6.243J / 2.156J / 16.337J
 Course Level
Masters / PG

0 Months
 Start month

 Tuition fee

48140 USD
48140 USD

Application fee

International 75 USD
National 75 USD
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

This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

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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

This course studies state-of-the-art methods for modeling, analysis, and design of nonlinear dynamical systems with applications in control. Topics include:

Nonlinear Behavior

Mathematical Language for Modeling Nonlinear BehaviorDiscrete Time State Space Equations

  • Differential Equations on Manifolds
  • Input/Output Models
  • Finite State Automata and Hybrid Systems

LinearizationLinearization Around a Trajectory

  • Singular Perturbations
  • Harmonic Balance
  • Model Reduction
  • Feedback Linearization

System Invariants

  • Storage Functions and Lyapunov Functions
  • Implicitly Defined Storage Functions
  • Search for Lyapunov Functions

Local Behavior of Differential Equations

  • Local Stability
  • Center Manifold Theorems
  • Bifurcations

Controllability of Nonlinear Differential Equations

  • Frobenius Theorem
  • Existence of Feedback Linearization
  • Local Controllability of Nonlinear Systems

Nonlinear Feedback Design Techniques

  • Control Lyapunov Functions
  • Feedback Linearization: Backstepping, Dynamic Inversion, etc.
  • Adaptive Control
  • Invariant Probability Density Functions
  • Optimal Control and Dynamic Programming
  • .

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How to Apply

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