Syllabus

Basic Linear Algebra:(8 hours)
Vector Spaces & Linear Maps, Eigenvalue Decompositions, Matrix Norms & Perturbation Theory, Singular Value Decomposition (SVD), Lyapunov Equations, Kronecker Products & Matrix Equations, Non-Negative Matrices, Generalized Inverses. (Linked to CO1)

Advanced Linear Algebra: (8 hours)
QR/Schur Decompositions, Structured Matrices, Convex Sets & Functions, Semidefinite Programming, Tensor Decompositions, Randomized Linear Algebra, Koopman Operator Theory, Learning-Based Control. (Linked to CO2, CO3)

Algebra1(4 hours):
Set, Topllogical properties of Set, Algebraic Group: Groups & Symmetry, Rings & Modules, Field Extensions, (linked to CO4)

MID SEMESTER EXAMINATION

Algebra2 (4 hours):
Algebraic Geometry, Matrix Rings & Factorization, Algebraic Invariants, (linked to CO4)

Differential Geometry(8 hours)
Manifolds & Smooth Maps, Tangent Bundles & Vector Fields, Cotangent Bundles & 1-Forms, Lie Derivatives, Distributions & Frobenius Theorem, Lie Groups & Algebras, Lie Brackets & Controllability, Differential Forms. (linked to CO 5)

Advanced Differential Geometry (8 hours)
Affine Connections, Riemannian Metrics, Hamiltonian Mechanics, Feedback Linearization, Disturbance Decoupling, Differential Flatness, Geometric Control Synthesis

To provide a foundational understanding of linear algebra principles, including vector spaces, decompositions, and matrix equations, essential for analyzing linear systems in control engineering.

To develop proficiency in advanced linear algebra techniques, encompassing optimization methods, tensor decompositions, and randomized algorithms, for practical engineering applications.

To introduce abstract algebraic structures, such as groups, rings, and field extensions, with an aim to enhance modeling and robustness aspects in dynamic systems,

To explore differential geometry concepts, including manifolds, tangent structures, and Lie derivatives, for the analysis of nonlinear flows and controllability.

To equip students with skills in geometric control synthesis, incorporating feedback mechanisms and Hamiltonian mechanics, for modern applications in robotics and dynamics.

Demonstrate proficiency in matrix theory and decompositions to solve linear systems and assess system stability.

Implement advanced decompositions and optimization methods for practical engineering problems.

Apply abstract algebraic concepts to model and ensure robustness in control systems.

Utilize differential geometry principles to analyze manifolds, flows, and nonlinear control synthesis techniques.

Synthesize geometric control strategies for nonlinear and modern applications in robotics and dynamics.

Gilbert Strang , Linear Algebra and Its Applications, Wellesley-Cambridge Press. ISBN: 978-0980232776. , https://math.mit.edu/~gs/linearalgebra/ila5/ILA5_Complete_150.pdf (MIT OpenCourseWare resource).

Griffiths, P., & Harris, J., Principles of Algebraic Geometry (Reprint of 1978 ed.), Wiley-Interscience. ISBN: 978-0471050599 , https://agorism.dev/book/math/ag/griffiths_phillip_harris_joseph-principles-of-algebraic-geometry-wiley.pdf.

Bullo, F., & Lewis, A. D., Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems, Springer. ISBN: 978-0-387-22195-3 , https://fbullo.github.io/gcms/#downloads

Agrachev, A. A., & Sachkov, Y. L., ontrol Theory from the Geometric Viewpoint, Springer. ISBN: 978-3-540-21037-4. , https://www.researchgate.net/profile/Yuri-Sachkov/publication/243787858_Control_Theory_from_the_Geometric_Viewpoint/links/5a1682b0aca272dfc1ed0720/Control-Theory-from-the-Geometric-Viewpoint.pdf. 9 web pages

Sontag, E.D. , Mathematical Control Theory: Deterministic Finite Dimensional Systems, Springer. ISBN: 978-1-4612-0577-7 , http://www.sontaglab.org/FTPDIR/sontag_mathematical_control_theory_springer98.pdf.

Axler, S., Linear Algebra Done Right, Springer. ISBN: 978-3031410253. , https://linear.axler.net/LADR4e.pdf

Roman, S., Advanced Linear Algebra, Springer. ISBN: 978-0387728285. , https://s2pnd-matematika.fkip.unpatti.ac.id/wp-content/uploads/2019/03/Graduate-Texts-in-Mathematics-135-Steven-Roman-Advanced-Linear-Algebra-Third-Edition-Graduate-Texts-in-Mathematics-Springer-2008.pdf.

https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9

https://www.sciencedirect.com/journal/automatica

https://epubs.siam.org/journal/sjcodc

https://epubs.siam.org/journal/sjaday