Class 03

[andrewrosemberg]

📘 Class 03 Topics

• 🚀 Pontryagin’s Maximum Principle
• 🎯 Shooting & Multiple Shooting
• 📐 LQR, Riccati, QP viewpoint (finite / infinite horizon)

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📚 Useful References

• 📖 JOÃO PEDRO HESPANHA’s Linear Systems Theory (Ch. 21–24) (Available at GT Library)
• 🎥 CMU 16-745 Lectures 7–9

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🙏 Acknowledgement

Huge thanks to @joaquimg for the suggestions! 🎉

Tasks

• Presentation
• Chapter

[andrewrosemberg]

These proofs seem interesting: https://arxiv.org/abs/2509.01744

[andrewrosemberg]

For the chapter:

• It is good to make continuous parallels, but our focus is discrete.

• (Important) You should be connecting a lot with lecture 2, making the mappings from the methods you present (e.g slide 8 in your presentation) to optimization methods.

• When you are presenting the solution methods using LQR as an example:

  • start with single shooting
  • Then present it as QP and how to solve it using newton method from lecture 2.
  • Then open up the linear system we are solving when posing as QP and show how this can be done more efficiently than a naive linear solve: -> use this to present the Riccati recursion.
  • Intuition and numbers that indicate why this is more performant then the generic way to solve QPs (complexity of the algorithms)

• Only now you present the continuous versions of riccati (briefly) and compare to the discrete.

• now make the transition from deterministic open loop policy to close loop coming out of the Riccati recursion.

• (Important) For each afirmation, create an code example that shows your argument: e.g if you are saying that single shooting has vanishing gradients, then show an example where this happens.

• show an example of Riccati recursion working for a stochastic version of LQR.

• (Not shown in class but part of the scope of this chapter):

  • End of horizon effect; infinite horizon LQR and the riccati version for it

  • Controlability