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General symmetries in optimal control
M. de León, J. Cortés, D. Martín de Diego, S. Martínez
Reports on Mathematical Physics 53 (1) (2004), 55-78

Abstract

Making use of the geometric setting proposed in [J. Cortés, M. de León, D. Martín de Diego, S. Martínez, "Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions", SIAM Journal on Control and Optimization 41 (5) (2003), 1389-1412] to formulate optimal control problems, we address here the treatment of general symmetries. This viewpoint allows us to reduce the number of equations associated with optimal control problems with symmetry and compare the solutions of the original system with the solutions of the reduced one. The reconstruction of the optimal controls starting from the reduced problem is also explored.

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