Open loop solution for the linear quadratic generalized consensus control problem

摘要

The Linear Quadratic Optimal Consensus (LQOC) control problemrnis a relaxation of the classical Linear Quadratic Regulation (LQR) prob-rnlem, that consists of assymptotically driving the state of the system to arn"consensus" point in which all coordinates are equal, in such a way thatrna quadratic cost function on the transient of the state trajectory andrnthe input is minimized. The generalized version of this problem requiresrnthe state of the system to converge assymptotically to a given subspacernof the state space. This paper shows that, if the associated standardrnLQR problem has a regular optimal solution, then the the existence ofrnthe open loop solution of the generalized LQOC can be readily veriu001cedrnand, if it exists, the solution can be readily computed by simple algebraicrnmanipulations.