OPTIMAL CONTROL OF NON-HOLONOMIC 3-STEP NILPOTENT SYSTEMS
Alfonso Anzaldo-Meneses, Felipe Monroy-Perez
We study the optimal control problem for control affine driftless
systems with quadratic cost, than further satisfy the property that
the Lie algebra generated by the vector fields defining the system is
3-step nilpotent. The Pontryagin Maximum Principle provides necessary
conditions for the extremal trajectories and in some low dimensions
explicit integration for the adjoint system can be carried out. The
explicit integration of these cases yields the elements for completing
the optimal synthesis. In dimension five these systems are related
with the so called cross-chained form.