Optimal distributed control of multi agents: Generalization of consensus algorithms for high-order state derivatives of SISO and MIMO systems

Abstract

This paper studies optimal consensus and formation coordination algorithms for both Single-input Single-output (SISO) and Multi-input Multi output (MIMO) multi-agent systems with high-order integral dynamics from a Linear Quadratic Regulator (LQR) perspective. Firstly, as a new approach using partitioning method, the high-order linear differential dynamic is modeled for SISO multi-agent systems. Then, the consensus algorithm based on Laplacian matrix corresponding to interaction graph between agents is derived for the system under consideration. After that, optimal consensus problem is defined in a LQR problem setting. In addition, a part from most of the similar works, Laplacian matrix which is one of the important elements in consensus algorithms is supposed to be unknown, and optimal Laplacian matrix is derived. Then, optimal consensus algorithm for high-order SISO systems with high-order-integrator dynamics is derived, and extended for MIMO systems. Moreover, to provide the formation algorithm for SISO and MIMO multi-agent systems, necessary terms are added to the derived optimal consensus algorithms.