Optimal consensus control of the Cucker-Smale model
This work addresses the challenge of numerically realizing optimal control for consensus in multi-agent systems, which is relevant for applications like flocking and swarm robotics.
The paper develops numerical methods for optimal consensus control in the Cucker-Smale multi-agent system, deriving first-order optimality conditions and approximating solutions via gradient descent for smooth penalties and heuristic methods for non-smooth penalties, with mean-field approximation for large agent numbers.
We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive first-order necessary optimality conditions. In the case of a smooth penalization fo the control energy, the optimality system is numerically approximated via a gradient-descent method. For sparsity promoting, non-smooth $\ell_1$-norm control penalizations, the optimal controllers are realised by means of heuristic methods. For an increasing number of agents, we discuss the approximation of the consensus control problem by following a mean-field modelling approach.