An algebraic approach to hierarchical LQR synthesis for large-scale dynamical systems

This paper considers a linear quadratic optimal hierarchical control problem for large-scale dynamical systems modeled by an interconnected system under multi-scale information exchange networks. We first propose an algebraic characterization of hierarchies by using semigroups the Kronecker product. The multiplication rule of the Kronecker product quite fits to the property of semigroups. As a result, a condition under which the stabilizing solution of the Riccati equation inherits the hierarchy is obtained with the aid of the previous result. Furthermore, the proposed framework makes it possible to understand several previous results on decentralized optimal control from a unified viewpoint.