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Browse materialsMIT 16.S498 · Fall 2019

Risk Aware and Robust Nonlinear Planning

Art: Claude Louis Desrais, Montgolfiere 1783, 18th… · Public domain

Instructor: Dr. Ashkan Jasour
Term: Fall 2019
Level: Graduate
What's inside: 1 lecture note · 21 other files · 3 web pages
Materials open: MIT OCW

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Source: MIT OpenCourseWare 16.S498 Risk Aware and Robust Nonlinear Planning, Fall 2019, Dr. Ashkan Jasour — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

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MIT OpenCourseWare, Dr. Ashkan Jasour, 16.S498 Risk Aware and Robust Nonlinear Planning, Fall 2019.

License: CC BY-NC-SA 4.0 · Edition: Fall 2019 · Open the original course on OCW ↗

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Risk Aware and Robust Nonlinear Planning

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Lecture 1: Introduction and Overview of the Course

Lecture 2: Overview of Nonlinear and Convex Optimization: i) Optimality Conditions ii) Newton’s Method iii) Interior Point Method iv) Dual Optimization v) Convex Optimization vi) Linear Program vii) Semidefinite Program

Lecture 3: Nonlinear Optimization Using the Theory of Nonnegative Polynomials Sum-of-Squares Formulation (SOS)

Lecture 4: Nonlinear Optimization Using the Theory of Measure and Moments

Lecture 5: Duality i) Duality of Moments and Polynomials ii) Duality of Measures and Continuous Functions

Lecture 6: Modified Sum-of-Squares Optimization i) Spars Sum-of-Squares Optimization (SOS) ii) Bounded Degree Sum-of-Squares Optimization (BSOS) iii) (Scaled) Diagonally Dominant Sum-of-Squares Optimization (SDSOS, DSOS)

Lecture 7: Chance Optimization and Chance-Constrained Optimization i) Measure and Moments Formulation ii) Sum-of-Squares Formulation

Lecture 8: Part 1: Robust Optimization Using Sum-of-Squares Optimization Part 2: Distributionally Robust Chance-Constrained Optimization

Lecture 9: Algorithms for Large-Scale Semidefinite Programs (Guest Lecture)

Lecture 10: Safety Verification of Probabilistic Systems i) Risk Estimation ii) Probabilistic Uncertainty Propagation iii) Uncertainty Set Construction iv) Forward-Reachable Sets

Lecture 11: Risk Aware Planning and Control i) Risk-Bounded Trajectory Planning ii) Risk Aware Nonlinear Control iii) Flow-Tube–Based Control iv) Backward-Reachable Sets

Lecture 12: Dynamical Systems with Gaussian Uncertainties i) Chance-Constrained Control ii) Safety Verification iii) Distributionally Robust Chance Constraints

Lecture 13: Occupation Measure-Based Analysis and Control i) Safety Verification ii) Region-of-Attraction Set iii) Optimal Control

Lecture 14: Sum-of-Squares Optimization for Uncertain Nonlinear Systems i) Lyapunov-Based Stability and Region-of-Attraction Set ii) Barrier-Function–Based Safety Verification iii) Robust Control

Lecture 15: Final Project Presentation