2022/03/06 by Angrisani, Francesca, Rampazzo, Franco · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2203.03070
Higher order necessary conditions for a minimizer of an optimal control problem are generally obtained for systems whose dynamics is continuously differentiable in the state variable. Here, by making use of the notion of set-valued Lie bracket we obtain a Goh-type condition for a control affine system with Lipschitz continuous dynamics and unbounded controls. In order to manage the simultaneous lack of smoothness of the adjoint equation and of the Lie bracket-like variations we make use of the notion of Quasi Differential Quotient. We conclude the paper with a worked out example where the established higher order condition is capable to rule out the optimality of a control verifying the standard maximum principle.