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American Institute of Aeronautics and Astronautics

    Course Outline

    Emerging Principles in Fast Trajectory Optimization



    Course Outline:

    I. Emerging perspectives in mathematical analysis and trajectory optimization
    II. What kinds of trajectory optimization problems are solvable today and why
    III. A Modern perspective on classical optimality conditions
    IV. Modern terminologies; illustrative examples
    V. Pontryagin’s Principle and the Curse of Complexity
    VI. Bellman’s Principle and the Curse of Dimensionality
    VII. The Covector Mapping Principle
    VIII. Quick review of the “forgotten” methods of Bernoulli and Euler
    IX. Sequences, limits and convergences
    X. Illustrative counter examples
    XI. How to commute discretization with dualization and why
    XII. Introduction to pseudospectral optimal control
    XIII. Pseudospectral methods on arbitrary grids
    XIV. How to choose discretization grids
    XV. Analysis on computational properties
    XVI. Putting it all together: CMP, PMP and HJB
    XVII. Optimality test through Covector Mapping Principle
    XVIII. Quantifying suboptimality via Bellman’s Principle
    XIX. Anti-aliasing in trajectory optimization
    XX. Bellman methods to improve feasibility
    XXI. Real-time optimal control
    XXII. Closed-form solution vs. closed-loop solution
    XXIII. What is real time?
    XXIV. Closed-loop optimal control structures and examples