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2 changes: 1 addition & 1 deletion _pages/publications.md
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---

{% if site.author.googlescholar %}
<div class="wordwrap">All my publications are available on <a href="{{site.author.googlescholar}}">my Google Scholar profile</a>.</div>
<div class="wordwrap">All my publications are available on my <i class="fa-brands fa-google-scholar"></i> <a href="{{site.author.googlescholar}}">Google Scholar profile</a>.</div>
{% endif %}

{% include base_path %}
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2 changes: 1 addition & 1 deletion _pages/resources.md
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Expand Up @@ -14,7 +14,7 @@ To share these execellent learning materials with others who are on a similar pa
- <span style="color:red">**Robotics Simulator**</span>

<i class="fa-brands fa-github"></i> [**Mujoco**](https://github.com/google-deepmind/mujoco) developed by <span style="color:blue">*Google DeepMind*</span>
- <i class="fa-brands fa-chrome"></i> [Mujoco Bootcamp [Website]](https://pab47.github.io/mujoco.html) and corresponding tutorials that programming in both <br> <i class="fab fa-youtube"></i> [C++ [YouTube]](https://www.youtube.com/watch?v=j1nCeqtfySQ&list=PLc7bpbeTIk758Ad3fkSywdxHWpBh9PM0G&index=6) and <i class="fab fa-youtube"></i> [Python [YouTube]](https://www.youtube.com/watch?v=u6tNfvLXK-I&list=PLc7bpbeTIk75dgBVd07z6_uKN1KQkwFRK) by Prof. Pranav Bhounsule.
- <i class="fa-brands fa-chrome"></i> [Mujoco Bootcamp](https://pab47.github.io/mujoco.html) and corresponding tutorials that programming in both <br> <i class="fab fa-youtube"></i> [C++](https://www.youtube.com/watch?v=j1nCeqtfySQ&list=PLc7bpbeTIk758Ad3fkSywdxHWpBh9PM0G&index=6) and <i class="fab fa-youtube"></i> [Python](https://www.youtube.com/watch?v=u6tNfvLXK-I&list=PLc7bpbeTIk75dgBVd07z6_uKN1KQkwFRK) by Prof. Pranav Bhounsule.

<i class="fa-brands fa-github"></i> [**Isaac Lab**](https://github.com/isaac-sim/IsaacLab) and <i class="fa-brands fa-chrome"></i> [**Isaac Sim**](https://docs.omniverse.nvidia.com/isaacsim/latest/overview.html) developed by <span style="color:blue">*Nvidia*</span>
- <i class="fa-brands fa-chrome"></i> [Official Tutorial [Self-Paced Course]](https://learn.nvidia.com/courses/course-detail?course_id=course-v1:DLI+S-OV-03+V1) and [many others](https://learn.nvidia.com/en-us/training/self-paced-courses) by <span style="color:blue">*Nvidia*</span>
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8 changes: 4 additions & 4 deletions _posts/2024-06-30-blog-1.md
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## References
- [Constrained Lagrangian mechanics: understanding Lagrange multipliers [YouTube]](https://www.youtube.com/watch?v=keMzpa_iWjs) (super excellent and enlightening explanation).
- [Introduction to Lagrangian Mechanics [YouTube]](https://www.youtube.com/watch?v=8UtnDaGHpq0) (succinct and clear intro with examples).
- [Introduction to Variational Calculus - Deriving the Euler-Lagrange Equation [YouTube]](https://www.youtube.com/watch?v=VCHFCXgYdvY) (another great explanation on derivation of Euler-Lagrange Equation).
- [H.J. Sussmann and J.C. Willems, "300 years of optimal control: from the brachystochrone to the maximum principle," _IEEE Control Systems Magazine_, vol. 17, no. 3, pp. 32-44, June 1997.](https://ieeexplore.ieee.org/document/588098)
- <i class="fab fa-youtube"></i> [Constrained Lagrangian mechanics: understanding Lagrange multipliers ](https://www.youtube.com/watch?v=keMzpa_iWjs) (super excellent and enlightening explanation).
- <i class="fab fa-youtube"></i> [Introduction to Lagrangian Mechanics ](https://www.youtube.com/watch?v=8UtnDaGHpq0) (succinct and clear intro with examples).
- <i class="fab fa-youtube"></i> [Introduction to Variational Calculus - Deriving the Euler-Lagrange Equation ](https://www.youtube.com/watch?v=VCHFCXgYdvY) (another great explanation on derivation of Euler-Lagrange Equation).
- <i class="fa-solid fa-book-open"></i> [H.J. Sussmann and J.C. Willems, "300 years of optimal control: from the brachystochrone to the maximum principle," _IEEE Control Systems Magazine_, vol. 17, no. 3, pp. 32-44, June 1997.](https://ieeexplore.ieee.org/document/588098)

<!-- - [Deriving the Adjoint Equation for Neural ODEs using Lagrange Multipliers](https://vaipatel.com/posts/deriving-the-adjoint-equation-for-neural-odes-using-lagrange-multipliers/#fn:2)
- [What Is the Adjoint of a Linear System?](https://dsbaero.engin.umich.edu/wp-content/uploads/sites/441/2020/05/Adjoints-21.pdf)(Prof. Omran Kouba and Prof. Dennis S. Bernstein) -->
16 changes: 8 additions & 8 deletions _posts/2024-07-31-blog-2.md
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Expand Up @@ -660,15 +660,15 @@ $$ u^* \neq \text{sat}(u_{\text{LQR}}) $$
- In contrast to the **Hamilton–Jacobi–Bellman equation**, which needs to hold over the entire state space to be valid, **PMP** is potentially more computationally efficient in that the conditions which it specifies only need to hold over a particular trajectory.
## References
1. [L7.1 Pontryagin's principle of maximum (minimum) and its application to optimal control [YouTube]](https://www.youtube.com/watch?v=Bxc4iy2xUjc&list=PLMLojHoA_QPmRiPotD_TnfdUkglTexuqm&index=16&t=1s) (Explains the difference of Control Hamiltonian formulation in both Maximum and Minimum Principle)
2. [Optimal Control (CMU 16-745) 2023 Lecture 6: Deterministic Optimal Control Intro [YouTube]](https://www.youtube.com/watch?v=U9zrNwMXktQ&list=PLZnJoM76RM6KugDT9sw5zhAmqKnGeoLRa&index=10) (Deriviation of PMP in discrete time setting, starting at 57 minutes and 15 seconds)
3. [Karush-Kuhn-Tucker (KKT) conditions: motivation and theorem [YouTube]](https://www.youtube.com/watch?v=K3L7UYnZuZ4&list=PLHAS_3-nESXV6XgW53wSkZHazVE7ZkHAV&index=38) (Part of Intro to Optimization Course by Prof.
1. <i class="fab fa-youtube"></i> [L7.1 Pontryagin's principle of maximum (minimum) and its application to optimal control](https://www.youtube.com/watch?v=Bxc4iy2xUjc&list=PLMLojHoA_QPmRiPotD_TnfdUkglTexuqm&index=16&t=1s) (Explains the difference of Control Hamiltonian formulation in both Maximum and Minimum Principle)
2. <i class="fab fa-youtube"></i> [Optimal Control (CMU 16-745) 2023 Lecture 6: Deterministic Optimal Control Intro](https://www.youtube.com/watch?v=U9zrNwMXktQ&list=PLZnJoM76RM6KugDT9sw5zhAmqKnGeoLRa&index=10) (Deriviation of PMP in discrete time setting, starting at 57 minutes and 15 seconds)
3. <i class="fab fa-youtube"></i> [Karush-Kuhn-Tucker (KKT) conditions: motivation and theorem](https://www.youtube.com/watch?v=K3L7UYnZuZ4&list=PLHAS_3-nESXV6XgW53wSkZHazVE7ZkHAV&index=38) (Part of Intro to Optimization Course by Prof.
Lewis Mitchell, also contains other great explanation including lagrange multipliers, Netwon's method, etc.)
4. [Hamiltonian Method of Optimization of Control Systems [YouTube]](https://www.youtube.com/watch?v=r-fscDKfeUs) (Clear example problem solved using Control Hamiltonian)
5. [Why the Riccati Equation Is important for LQR Control [YouTube]](https://www.youtube.com/watch?v=ZktL3YjTbB4) (Derivation of ARE using the approach of completing the square)
6. [Matrix Calculus [YouTube]](https://www.youtube.com/watch?v=IgAr5kzza78) (Great explanation on matrix and vector derivatives)
7. [Geomety of the Pontryagin Maximum Principle [YouTube]](https://www.youtube.com/watch?v=V04N9X3NxYA&t=9s) (Explanation of PMP from another persepctive)
8. D. E. Kirk, _Optimal Control Theory: An Introduction, 2004._
4. <i class="fab fa-youtube"></i> [Hamiltonian Method of Optimization of Control Systems ](https://www.youtube.com/watch?v=r-fscDKfeUs) (Clear example problem solved using Control Hamiltonian)
5. <i class="fab fa-youtube"></i> [Why the Riccati Equation Is important for LQR Control](https://www.youtube.com/watch?v=ZktL3YjTbB4) (Derivation of ARE using the approach of completing the square)
6. <i class="fab fa-youtube"></i> [Matrix Calculus](https://www.youtube.com/watch?v=IgAr5kzza78) (Great explanation on matrix and vector derivatives)
7. <i class="fab fa-youtube"></i> [Geomety of the Pontryagin Maximum Principle ](https://www.youtube.com/watch?v=V04N9X3NxYA&t=9s) (Explanation of PMP from another persepctive)
8. <i class="fa-solid fa-book-open"></i> D. E. Kirk, _Optimal Control Theory: An Introduction, 2004._
## Appendix
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12 changes: 6 additions & 6 deletions _posts/2024-08-15-blog-3.md
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- **HJB** provides a fundation for both value iteration and policy iteration in continuous action spaces in the filed of reinforcement learning. Using the neural network to approximate the Bellman value function is the key of **Approximate Dyanmic Programming**.

### References
- [Nonlinear Control: Hamilton Jacobi Bellman (HJB) and Dynamic Programming [YouTube]](https://www.youtube.com/watch?v=-hO-AnFYm6M&list=PLMrJAkhIeNNQe1JXNvaFvURxGY4gE9k74&index=8&t=929s) (Part of excellent series on optimal control and reinforcement learning by Prof. Steve Brunton.)
- [EE 564: Lecture 26 (Optimal Control): The Hamilton Jacobi Bellman Approach [YouTube]](https://www.youtube.com/watch?v=kDtcg6U49kY&t=1s) (Great lecture that include the derivation of ARE using HJB and connection with PMP.)
- [Explaining the Principle of Least Action: Physics Mini Lesson [YouTube]](https://www.youtube.com/watch?v=sUk9y23FPHk) (Include derivation of Newton's Second Law.)
- [The principle of least action [YouTube]](https://www.youtube.com/watch?v=xz7jLnWcxMs)
- [Hamiltonian Mechanics in 10 Minutes [YouTube]](https://www.youtube.com/watch?v=B6PCntP3cek) and [Understanding Hamiltonian mechanics: (1) The math [YouTube]](https://www.youtube.com/watch?v=FGQddvjP19w&list=PLmNMSMaNjnDd9Qj4VxNL8dijiWZCAzanl) (More in-depth explanation of Hamiltonian mechanics.)
- [Action principle: geometric and physical interpretation [YouTube]](https://www.youtube.com/watch?v=7M0BzJhw4wA)
- <i class="fab fa-youtube"></i> [Nonlinear Control: Hamilton Jacobi Bellman (HJB) and Dynamic Programming](https://www.youtube.com/watch?v=-hO-AnFYm6M&list=PLMrJAkhIeNNQe1JXNvaFvURxGY4gE9k74&index=8&t=929s) (Part of excellent series on optimal control and reinforcement learning by Prof. Steve Brunton.)
- <i class="fab fa-youtube"></i> [EE 564: Lecture 26 (Optimal Control): The Hamilton Jacobi Bellman Approach](https://www.youtube.com/watch?v=kDtcg6U49kY&t=1s) (Great lecture that include the derivation of ARE using HJB and connection with PMP.)
- <i class="fab fa-youtube"></i> [Explaining the Principle of Least Action: Physics Mini Lesson](https://www.youtube.com/watch?v=sUk9y23FPHk) (Include derivation of Newton's Second Law.)
- <i class="fab fa-youtube"></i> [The principle of least action](https://www.youtube.com/watch?v=xz7jLnWcxMs)
- <i class="fab fa-youtube"></i> [Hamiltonian Mechanics in 10 Minutes](https://www.youtube.com/watch?v=B6PCntP3cek) and <i class="fab fa-youtube"></i> [Understanding Hamiltonian mechanics: (1) The math](https://www.youtube.com/watch?v=FGQddvjP19w&list=PLmNMSMaNjnDd9Qj4VxNL8dijiWZCAzanl) (More in-depth explanation of Hamiltonian mechanics.)
- <i class="fab fa-youtube"></i> [Action principle: geometric and physical interpretation](https://www.youtube.com/watch?v=7M0BzJhw4wA)
2 changes: 1 addition & 1 deletion _publications/2024-09-30-pub1.md
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<u>Lihan Lian</u>, <span style="color: gray;">Uduak Inyang-Udoh</span><br>
<span style="color: blue;">*American Control Conference (ACC) (In Submission)*, 2025 </span><br>
[**[arXiv]**](https://arxiv.org/)
<i class="fa-solid fa-book-open"></i> [**[arXiv]**](https://arxiv.org/)

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