Risk Aware and Robust Nonlinear Planning

Calendar

LEC #	TOPICS	KEY DATES
1	Introduction and Overview of the Course
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	Problem set 1 out
3	Nonlinear Optimization Using the Theory of Nonnegative Polynomials Sum-of-Squares Formulation (SOS)	Problem set 1 due Problem set 2 out
4	Nonlinear Optimization Using the Theory of Measure and Moments	Problem set 2 due Problem set 3 out
5	Duality i) Duality of Moments and Polynomials ii) Duality of Measures and Continuous Functions	Problem set 3 due Problem set 4 out
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)	Problem set 4 due Problem set 5 out
7	Chance Optimization and Chance-Constrained Optimization i) Measure and Moments Formulation ii) Sum-of-Squares Formulation	Problem set 5 due
8	Part 1: Robust Optimization Using Sum-of-Squares Optimization Part 2: Distributionally Robust Chance-Constrained Optimization	Problem set 6 out
9	Algorithms for Large-Scale Semidefinite Programs (Guest Lecture)	Problem set 6 due  Problem set 7 out
10	Safety Verification of Probabilistic Systems i) Risk Estimation ii) Probabilistic Uncertainty Propagation iii) Uncertainty Set Construction iv) Forward-Reachable Sets	Problem set 7 due
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
12	Dynamical Systems with Gaussian Uncertainties i) Chance-Constrained Control ii) Safety Verification iii) Distributionally Robust Chance Constraints
13	Occupation Measure-Based Analysis and Control i) Safety Verification ii) Region-of-Attraction Set iii) Optimal Control
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
15	Final Project Presentation