Geodesic
Invariant tracking
Martin, Philippe ; Rouchon, Pierre  ; Rudolph, Joachim1 
1 Institut fur Regelungs- und Steuerungstheorie, Technische Universität Dresden, Mommsenstr. 13, 01062 Dresden, Germany
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 1-13

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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.

DOI : 10.1051/cocv:2003037
Classification : 53A55, 93C10, 93D25, 70Q05
Keywords: symmetries, invariants, nonlinear control, output tracking, decoupling

Martin, Philippe  ; Rouchon, Pierre  ; Rudolph, Joachim 1

1 Institut fur Regelungs- und Steuerungstheorie, Technische Universität Dresden, Mommsenstr. 13, 01062 Dresden, Germany 
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Martin, Philippe; Rouchon, Pierre; Rudolph, Joachim. Invariant tracking. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 1-13. doi: 10.1051/cocv:2003037

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