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American Institute of Aeronautics and Astronautics

    Course Outline

    Course Outline

    Emerging perspectives in mathematical analysis and trajectory optimization

    What kinds of trajectory optimization problems are solvable today and why.


    A Modern Perspective on Classical Optimality Conditions

    • Modern terminologies; illustrative examples
    • Pontryagin’s Principle and the Curse of Complexity
    • Bellman’s Principle and the Curse of Dimensionality

    The Covector Mapping Principle

    • Quick review of the “forgotten” methods of Bernoulli and Euler
    • Sequences, limits and convergences
    • Illustrative counter examples
    • How to commute discretization with dualization and why

    Introduction to Pseudospectral Optimal Control

    • Pseudospectral methods on arbitrary grids
    • How to choose discretization grids
    • Analysis on computational properties

    Putting it All Together: CMP, PMP and HJB

    • Optimality test through Covector Mapping Principle
    • Quantifying suboptimality via Bellman’s Principle
    • Anti-aliasing in trajectory optimization
    • Bellman methods to improve feasibility

    Real-Time Optimal Control

    • Closed-form solution vs. closed-loop solution
    • What is real time?
    • Closed-loop optimal control structures and examples