Abstract
Optimal control problems on a Lie group G make an interesting link between modern control theory and its classical past through the problems of elastica [6], and its geometric counterpart the problem of Radon ([1]). The first of these problems consists of minimizing \( \frac{1} {2}\int_0^\ell {\left( {{C_1}u_1^2 + {C_2}u_2^2 + {C_3}u_3^2} \right)dt} \) over the trajectories g(t) in the group of motions of R 3 which satisfy.
Keywords
- Optimal Control Problem
- Integral Curve
- Elastic Problem
- Prescribe Boundary Condition
- Hamiltonian Vector Field
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© 1991 Birkhäuser Boston
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Jurdjevic, V. (1991). Optimal Control Problems on Lie groups. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_24
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_24
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7835-1
Online ISBN: 978-1-4612-3214-8
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