An alternative method for optimal consensus protocol design for scalar single-integrators using krotov conditions

This article proposes a novel alternative approach for optimal consensus protocol design for scalar single-integrator multi-agent systems based on the Krotov methodology. The problem under consideration generally turns out to be non-convex due to the desired diffusive nature (i.e. using only relative information from the neighboring agents) of the control input. This work employs the Krotov framework which transforms the optimal control problem into another equivalent optimization problem via the selection of so-called Krotov function whose selection is ad-hoc. The formulation of this equivalent optimization problem provides sufficient conditions for the existence of globally optimal control law(s) and it is generally solved using iterative methods because of non-convex characteristics. In this work, these conditions are used to solve the optimal consensus protocol design problem for the single-integrator multi-agent systems by choosing the Krotov function in such a way the equivalent optimization problem can be solved non-iteratively and at the same time, the obtained optimal control law has the desired structure (as necessitated by the communication topology). The proposed method is demonstrated by a numerical example.