Invariant tracking

Martin, Philippe; Rouchon, Pierre; Rudolph, Joachim

ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 1-13.

The problem of invariant output tracking is considered: given a control system admitting a symmetry group $G$, design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of $G$. Invariant output errors are defined as a set of scalar invariants of $G$; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the required “symmetry-preserving” feedback.

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