We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems. with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Lagrangian and obtain the reduced optimalit... https://parisnaturalfoodes.shop/product-category/ylang-ylang-extra/