Notes

Here are some of the notes I wrote while taking courses or reading books since 2017. They are more than likely to contain some errors and you are more than welcomed to reach me had you spotted any.

Convex Optimization Theory

These are my reading notes for the textbook Convex Optimization Theory, by Prof. Dimitri P. Bertsekas. This part is under continous updating.

[COT-B1] Reading Notes: Convex Optimization Theory

Abstract Dynamic Programming

These are my reading notes for the monograph Abstract Dynamic Programming, 2nd Edition, by Prof. Dimitri P. Bertsekas. This part is under continous updating.

[ADP-B1] Reading Notes: Abstract Dynamic Programming

[ADP-N5] Box Condition of Some Bouneded Set

[ADP-N4] Sequence on the Extended Real Line

[ADP-N3] State-Dependent Weighted Multistep Mappings

[ADP-N2] Norm Construction for Linear Mapping

[ADP-N1] Convergence of Double Sequences

Probability and Random Processes

These are my notes of Lecture Slides of Probability and Random Processes, Edition: 2018, by Prof. Mikael Skoglund. This part is under continous updating.

[PRP-N8] Topologies, Metrics and Standard Spaces

[PRP-N7] Condition and Decomposition of Measures

[PRP-N6] Differentiation and Radon–Nikodym Theorem

[PRP-N5] Probability and Random Variables and the Law of Large Numbers

[PRP-N4] General Integration Theory

[PRP-N3] General Measure Theory

[PRP-N2] The Lebesgue Integral on the Real Line

[PRP-N1] Basics and Lebesgue Measure on the Real Line

Probability Theory

These are my reading notes of Lecture Notes: Probability and Random Processes at KTH, Edition: 2017, by Prof. Timo Koski.

[PT-N12] Karhunen-Loéve Expansion and Mean Square Integral

[PT-N11] Monotonicity of Means of Random Variables

[PT-N10] A Class of Equivalence Relation for the Almost Sure Convergence

[PT-N9] On the Proof of the Law of the Unconscious Statistician

[PT-N8] Independence between Sigma-Fields

[PT-N7] Expectation and Independence

[PT-N6] Regarding Conditional Expectation

[PT-N5] Random Variables Generated by Indexing

[PT-N4] Monotonicity of Lebesgue Integration

[PT-N3] Discrete Part of a Measure

[PT-N2] Expectation of Random Variables With Respect to Distribution

[PT-N1] Monotonicity of Means of Simple Random Variables

Model Predictive Control

These are my notes for Lecture Notes of Model Predictive Control, Edition: 2017, by Prof. Mikael Johansson.

[MPC-N4] On Woodbury Matrix Identity

[MPC-N3] On Optimality Condition for Constrainted Convex Optimization Problem

[MPC-N2] On Stability Condition of Continuous Time Linear Systems

[MPC-N1] On Calculation of Multivariable ODE

Discrete-Time Stochastic Systems

These are my reading notes for the first four chapters of Discrete-Time Stochastic Systems: Estimation and Control, 2nd Edition, by Prof. Torsten Söderström.

[DSS-N9] On Calculation of Jordan Block Power

[DSS-N8] Spectrum of Output in State Space Model

[DSS-N7] On the Solution of Sylvester’s Equation

[DSS-N6] Proof of Parseval’s Theorem

[DSS-N5] On Linear Innovations Sequence

[DSS-N4] On Linear Estimator Formula

[DSS-N3] On Absolute and Square Summability

[DSS-N2] On Hermitian Matrix and Positive-Definite Feature

[DSS-N1] On the Autoregressive Feature of ARMA