Courses
UCSD ECE 250: Random Processes
This course is the core graduate level course on foundation of random processes. The course notes are available here.
Topics include:
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foundation of probability theory,
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sum of independent random processes, strong law of large numbers, and central limit theorem,
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conditional expectation, martingale theory,
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estimation theory,
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discrete time homogeneous Markov chains, and
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processing of stationary processes.
Joseph Doob and his students, Blackwell, Halmos, and Ambrose
UCSD ECE 272A: Advanced Linear Systems Theory
This course is a first graduate level (core) course on dynamics and control which focuses on theoretical foundation of linear systems theory.
Topics include:
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continuous time linear systems,
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existence and uniqueness of solutions to LTV systems,
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stability of linear systems: direct and indirect Lyapunov method,
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controllability and stabilizability of LTI systems, and
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observer design for LTI systems.
Roger Brockett, Eduardo Sontag, Mike Warren, and Alberto Isidori (source)
UCSD ECE 101: Linear Systems Theory (Signals and Systems)
This is the main undergrad core course on signals and systems that discusses topics including signals and linear time-invarying systems. The slides are available here.
UCSD ECE 285: Stochastic Approximation, theory and applications
This course is about a powerful tool in learning theory, random processes, stochastic optimization, adaptive control, etc.
The topics to be covered include:
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Motivating Examples:
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SGD, Qlearning, Simulated Annealing, Replicator Dynamics, Adaptive Control
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Mathematical Preliminaries:
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Convergence in metric spaces
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Background in Probability
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Martingale theory
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Ordinary Differential Equations: existence and uniqueness of solutions, stability
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Robbins-Monro Algorithm
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Kiefer-Wolfowitz Algorithm
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The ODE approach to Stochastic Approximation
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Stochastic Approximation: two time scale
