Suboptimal Consensus Protocol Design for a Class of Multiagent Systems

TL;DR

This paper introduces a novel suboptimal consensus protocol design method for multiagent systems using an extension of linear-quadratic optimal control conditions within the Krotov framework, avoiding the need for identical feedback gains.

Contribution

It develops a new noniterative solution technique for suboptimal consensus control, formulating the problem as a convex optimization without requiring identical feedback gains.

Findings

The proposed method effectively computes suboptimal control laws.

It provides an explicit upper bound on the control cost.

Numerical examples validate the approach and compare favorably with existing methods.

Abstract

This article presents a new technique for suboptimal consensus protocol design for a class of multiagent systems. The technique is based upon the extension of newly developed sufficient conditions for suboptimal linear-quadratic optimal control design, which are derived in this paper by an explication of a noniterative solution technique of the infinite-horizon linear quadratic regulation problem in the Krotov framework. For suboptimal consensus protocol design, the structural requirements on the overall feedback gain matrix, which are inherently imposed by agents dynamics and their interaction topology, are recast on a specific matrix introduced in a suitably formulated convex optimization problem. As a result, preassigning the identical feedback gain matrices to a network of homogeneous agents, which acts on the relative state variables with respect to their neighbors is not required. The suboptimality of the computed control laws is quantified by implicitly deriving an upper bound on the cost in terms of the solution of a convex optimization problem and initial conditions instead of specifying it a priori. Numerical examples are provided to demonstrate the implementation of proposed approaches and their comparison with existing methods in the literature.