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Midterm grades Final grades ASSIGNMENTS: ____________________________________________________________________________________ COURSE SYLLABUS: Differentiable manifolds, Differentiable functions and mappings, Ranks, immersions and submanifolds, Lie groups and subgroups, O(n), SO(n), SE(n) Tangent and cotangent spaces, Tensors and tensor fields, K-forms and wedge product, Integration on manifolds and Stokes theorem, Vector fields on Rn Lie algebra of vector fields on manifolds: exponential mapping, Lie derivatives and integral manifolds, Distributions and Frobenius theorem, Applications: Decomposition of nonlinear systems, Local reachability and observability, Disturbance rejection, Normal forms and feedback linearization, State estimation for nonlinear systems, Fault detection and isolation, Examples on robotics, Holonomic and nonholonomic constrains, Mobile robots, ___________________________________________________________________ GRADING: 1. Assignments: 20% 2. Mid-term exam: 30% 3. Final exam: 50% ___________________________________________________________________ REFERENCES: 1. William M. Boothby, An introduction to differentiable manifolds and Riemannian geometry, Academic Press, 1975, (SEE) 2. M. P. de Carmo, Differential forms and applications, Springer Verlag, 1994, (SEE) 3. Ivancevic, I., Applied differential geometry, a modern introduction, World Scientific, 2007, (SEE) 4. Selig, J., Geometric fundamentals in robotics, Springer, 2005, (SEE) 5. Isidori, A, Nonlinear control systems, Springer, 1995, (SEE) |
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Geometric approach to Dynamical Systems Credits: 3, Level: graduate, Prerequisite: Differential equations Hours: Sunday, Tuesday, 15:00-16:30 Location:
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Control systems are ubiquitous |
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Sharif university of technology Department of electrical engineering Digital systems group/Robotics
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