Learning bang-bang regulators

A continuous-time algorithm for learning a stable bang-bang regulator is developed. It is assumed that a Liapunov function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V(x)</tex> is known such that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V̇</tex> is negative definite for some bang-bang control The plant may be unstable since a simple condition (that a constant be large enough) on the learning algorithm guarantees stability of the closed-loop system during the learning phase. Derivative computation is required, but a significant time delay and an error are permissible in such computation.