Information for Spring 2024 MAE 288A

Do not attempt to take this course unless you are either a PhD student, or a student that is highly trained in mathematics and in possession of an unhealthy desire for further exploration.

General information:

The course syllabus may be found here in pdf format.

Time and Location: T/Th 5-6:20pm, 105 EBU2.

Contact:

TA: Yifei Zheng
- Office: 1601 EBU1.
- Email: yiz152@ucsd.edu
- Problem session/office hour: W, 2-2:50, 105 EBU2.
- Problem session/office hour: M, 1-1:50, Zoom: https://ucsd.zoom.us/j/97128199593 (or contact Yifei to set up a time).

Instructor: Prof. William McEneaney
- Office hour: T 2-3, 1809 EBU1 (or contact me to set up a time).
- Office: 1809 EBU1.
- Email: wmceneaney@ucsd.edu

Piazza: https://piazza.com/ucsd/spring2024/mae288a

Gradescope entry code: 7DYZPG

The course grade will be obtained from the grades on the homework assignments, any class-participation contributions and the take-home final.

Homework Assignments:

Homework Assignment #1 may be found here in pdf format.

Topics:

Probability Review
- Probability spaces, sigma-algebras, distribution and density functions.
- Normal random variables.
- Gauss-Markov sequences.

Discrete-time, continuous-space, stochastic control.
- Finite-time horizon problem definition.
- Dynamic programming principle.
- Dynamic programming equation (discrete-time).
- Linear-quadratic gaussian regulator case.
- Infinite-time horizon problem definitions.
- Convexity.
- Value iteration.
- Policy iteration.
- Nonlinear example.

Discrete-time, discrete-space, stochastic control.
- Markov chains.
- Finite and infinite time-horizon problem definitions.
- Value iteration and example.
- Policy iteration and example.

Continuous-time, continuous-space, determinstic control.
- Finite-time horizon problem definition.
- Dynamic programming equation (a.k.a. Hamilton-Jacobi-Bellman PDE).
- Viscosity solution definition and examples.
- Computational example.

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Email me at wmceneaney@ucsd.edu