I am looking for some lecture notes or a textbook for time-optimal trajectories.
Any help is greatly appreciated. I am having plenty of trouble with understanding switching $C^+$ and $C^-$ curves.
2026-02-23 06:33:14.1771828394
Reference request: Time-optimal trajectories
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One very good resource that is available for free online (legally, from the author's website) is Daniel Liberzon's book on calculus of variations and optimal control which you can find here. On page $107$ of the book (which is page $117$ when you look at it in a PDF viewer), he solves an optimal control problem for a double integrator system subject to the constraint $u \in [-1,1]$. The switching curves are explicitly derived an then the principles of bang-bang control are discussed after that.
In addition, Bryson and Ho's optimal control book (it's not available for free, but here is a link to Amazon) goes over similar material, including deriving switching curves for a system known as the Bushaw oscillator (and these switching curves are actually what's pictured on the cover of the book).