Stanford AA203 Optimal and Learning-Based Control | Spring 2026 | Lecture 12: Feasibility of MPC

Value of the Information & Strength of the Argument

The lecture provides high-value information by rigorously deriving key theoretical results in MPC, such as the persistent feasibility lemma and the stability theorem. The argumentation is solid, with clear logical progression from definitions to proofs, and the instructor effectively connects theoretical concepts to practical implications, such as the trade-off between feasibility and control effort. The use of examples and intuitive explanations enhances understanding, though the presentation assumes a strong background in linear algebra and optimization.

The title accurately reflects the lecture content, which focuses on feasibility and stability of Model Predictive Control.

8/10

Lecture by a renowned expert in robotics and control, with rigorous mathematical derivations and references to a companion textbook. The content is well-structured and based on established theory, though it lacks peer review and external validation.

Markers derived by PSI from the transcript: the creator did not define chapters.

• 00:00Introduction and overview of the lecture topics: persistent feasibility, stability, and practical aspects of MPC.
• 02:00Review of previous lecture concepts: one-step controllable set, control invariant set, and feasibility set.
• 05:00Proof of the persistent feasibility lemma, showing that if the one-step feasible set is control invariant, then MPC is persistently feasible.
• 10:00Discussion on the choice of terminal constraint set, emphasizing that the origin is a trivial but often suboptimal choice.
• 15:00Proof of the theorem linking persistent feasibility to the terminal set being control invariant.
• 20:00Introduction to Lyapunov stability theory, with intuitive examples and the formal theorem.
• 25:00Statement of the celebrated MPC stability theorem, providing sufficient conditions for asymptotic stability.
• 30:00Discussion on the practical implications of terminal constraints and the trade-off between feasibility and performance.

• AA203 Optimal and Learning-Based Control course page — Course information and enrollment details.
• Principles of Robot Autonomy (companion textbook) — Free online textbook referenced as companion material for the course.
• AA203 course schedule and syllabus — Course schedule and syllabus for Spring 2026.
• Lecture slides (Lecture 1) — Slides for the first lecture, provided as reference.
• Full playlist of AA203 lectures — Playlist containing all lectures of the course.

• Principles of Robot Autonomy — Companion textbook that aligns with the lecture content.