Formation tracking for interconnected networks with interaction silence and minimum total energy restriction

Abstract

The minimum‐energy formation tracking design and analysis problems for interconnected networks with distributed tracking protocols are addressed, where the effects of the total energy restriction and the interaction silence on the formation tracking are discussed, respectively. The key characteristic of this article is that the value of the energy restriction is required to be minimum, while the guaranteed‐cost tracking strategy and the energy‐constraint tracking strategy cannot ensure the minimum property of the total energy restriction. For interconnected networks without the interaction silence, sufficient conditions for minimum‐energy formation tracking are presented, whose effectiveness can be checked by the optimization procedure associated with the generalized eigenvalue method. Then, for interconnected networks with the interaction silence, by constructing the specific constraint associated with the maximum silent rate and two inhibition parameters, sufficient conditions for minimum‐energy formation tracking are proposed. Finally, numerical examples are shown to illustrate the efficacy of main results.