Bassam Bamieh
University of California at Santa Barbara
Professor, Mechanical Engineering
Affiliate, Electrical & Computer Engineering
Affiliate, Center for Control, Dynamical Systems and Computation
College of Engineering
University of California at Santa Barbara
Welcome to my website. I am a Professor of Mechanical Engineering at the University of California at Santa Barbara (UCSB). I also have a courtesy appointment in the department of Electrical and Computer Engineering, and I am a member of the Center for Control, Dynamical Systems and Computation (CCDC). This interdisciplinary center brings together faculty and graduate students from across the College of Engineering departments and Mathematics.
My core research area is Controls and Dynamical Systems (CDS), and I do quite a bit of cross-disciplinary work at the interface between CDS and other fields such as Network Science, Fluid Mechanics, Statistical Physics, Machine Learning and Mathematics. The “Research” link to the left contains more information about the research work of my group.
News
| I was recently interviewed on the In-Control Podcast | Poorva’s paper on localization phenomena in large-scale networks in Control Systems Letters, with expanded version on arXiv | Karthik’s paper on Parametric Resonance in Networked Oscillators appeared in IEEE TCNS. arXiv version is here |
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| Pascal’s paper on “spurious modes” appeared in JCP , and arXiv | Max’s paper on optimal control of continuum swarms | A new perspective on classical Linear/Quadratic optimal control |
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Book Drafts
| Lecture Notes on Linear Algebra and Functional Analysis: A partial draft of a textbook I am writing on functional analysis and linear algebra for systems and controls research | Lecture Notes on Vibrations and Waves: A draft of a textbook on vibrations which I teach to 3rd year Mechanical Engineering students at UCSB | Coming soon: The first draft of Signals, Systems, Dynamics and Control: Volume 1 - Foundations, which I use for teaching graduate level systems and controls material |
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Tutorial Papers
I write tutorial papers based on a “discovery” pedagogical principle. For example, most treatments of the Fourier transform first define the transform, and then explore its many useful properties. I come at it with a different approach, how would you have discovered the Fourier transform if no one ever showed it to you? This amounts to taking the “scenic route” while developing the subject, rather than the fastest or most expedient route to a result. This way, one can take in the lay of the land and explore related concepts, which can then form connections with other subjects that will be useful to a researcher later on when unfamiliar questions arise.
- Discovering Transforms: A Tutorial on Circulant Matrices, Circular Convolution, and the Discrete Fourier Transform: This is a way to think about a large class of transform methods as a linear algebra (or functional analysis) problem of simultaneous diagonalization of a class of matrices or operators, and then discover them using this “universal” procedure.
- A Tutorial on Solution Properties of State Space Models of Dynamical Systems: The matrix exponential, the Peano-Baker Series, the Variations of Constants (Cauchy) formula, and the Picard iteration are various manifestations of one concept, namely a fixed-point iteration, which is the Neumann series in the linear case. All these various formulas can be “discovered” (including the definition of the matrix exponential) through various applications of the Neumann series when interpreted with a slight bit of abstraction. See also the abridged version which appeared in the magazine IEEE Control Systems.
- A Tutorial on Matrix Perturbation Theory (using compact matrix notation): Analytic matrix perturbation theory is an immensely useful tool in many areas. It is very ironic (to me) that standard treatments of this theory do not use matrix notation! Here I present this theory using compact matrix notation which I believe simplifies the usually messy formulas and gives some additional insight. In particular, the matrix Sylvester Equation plays a prominent role in finding the eigenvectors perturbations.
- A Short Introduction to the Koopman Representation of Dynamical Systems: The title describes what this is. I try to develop the basic concept with the minimum of unnecessary distractions. In particular, special attention is paid to the duality between initial conditions and output maps in both the original system and its Koopman representation (i.e. initial conditions of the original system become output operators in the Koopman representation and vice versa).