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IEEE Transactions on Automatic Control, Vol.52, No.10, 2005-2012, 2007
Flatness-based extremum-seeking control over periodic orbits
In this note, an extremum-seeking controller is developed to steer a periodic system to orbits that maximize a functional of interest for a class of differentially flat nonlinear systems. The problem is posed as a real-time optimal trajectory generation problem in which the optimal orbit is computed using an extremum-seeking approach. Using the flatness property of the dynamics, the original dynamic optimization problem is transformed to a parameterized optimization problem which can be solved in real-time to approximate the optimal orbit. The control algorithm provides tracking of the optimal orbit. A drug delivery control problem is considered to demonstrate the application of the technique.