2022/04/12 by Stratoglou, Efstratios, Colombo, Leonardo, Ohsawa, Tomoki
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2204.06050
In this paper we study reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles. Specifically, we recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Hamiltonian and obtain the reduced optimality conditions from a reduced variational principle via Pontryagin Maximum Principle. We apply the results to a collision avoidance problem for multiple unicycles in the presence of an obstacle.