Optimal Consensus Protocol Design for Scalar Single Integrators using Krotov Conditions

Abstract

This article proposes a new approach to consensus protocol design for scalar single integrator multi-agent systems based on Krotov framework in optimal control theory. The problem under consideration is generally non-convex due to the distributed nature of the control input to be designed. To tackle this problem, this work employs the Krotov framework which transforms the optimal control problem into another optimization problem via the usage of a so-called Krotov function whose selection is ad-hoc. This equivalent optimization problem provides the sufficient conditions, called Krotov conditions, for the existence of optimal control laws. In this work, these conditions are used to solve the distributed optimal control problem for single integrator multi-agent system by choosing the Krotov function such that the equivalent optimization problem turns out to be convex and the at the same time the designed control law (which results upon solving the equivalent optimization problem) has the desired distributed structure. The proposed method is demonstrated by numerical examples.