Optimal tracking consensus for swarm systems with leader-following switching topologies

For swarm systems with leader-following switching topologies, optimal tracking consensus achievement problems are investigated. First, by these errors of the cooperative states among neighboring agents, a new tracking strategy with an optimization index is proposed to realize the optimal tracking consensus. The optimization index contains a tracking consensus performance term and a control energy consumption term. Then, by introducing a local interaction matrix and a dual nonsingular transformation, sufficient conditions for optimal tracking consensus are proposed. A constraint relationship between topology switching and control parameters of the optimal tracking strategy is determined. Furthermore, an explicit expression of the minimum value of the optimization index is given. The minimum value is completely determined by initial conditions and is independent of the operation process of the whole system and switching movements. Finally, a numerical simulation with seven agents is implemented to demonstrate the effectiveness of main results.