An Algebraic Approach to Hierarchical Optimal Control of Large-scale Dynamical Systems

Abstract

Large-scale dynamical systems often consist of a number of subsystems that are interconnected according to a hierarchical multi-scale network. This paper introduces a hierarchical control scheme as an efficient strategy to handle such systems and proposes a method for designing a hierarchical linear quadratic optimal regulator. The proposed framework employs an algebraic approach. We first characterize a hierarchy of systems as an algebra based on semigroups, the Kronecker product, and the linear combination. This allows us to prove that the stabilizing solution of the Riccati equation inherits a hierarchy if system matrices and weights in the cost function belong to the corresponding common algebra that characterizes the hierarchy. A couple of classes of systems that can be treated by our algebraic framework are also provided in the paper. We will see that the derived result gives a unified insight into several related previous works.

Internet-based Control Experiments for Simultaneous Stabilization of Inverted Pendulums at Two Remote Locations

“…1. This is achieved using the HOC method (1) . An overview of the inverted pendulum control equipment is shown on the left side of Fig.…”

“…In this study, we intend to conduct an experiment for the stabilization control of an unstable system, and because it is a class, it aims to enable not only the leader/follower operation but also individual experiments for each participant while maintaining the same control system. To achieve this, the hierarchical optimal control (HOC) method proposed by Tsubakino et al was used (1) . This optimal control method evaluated the degree of goal achievement in a hierarchical structure.…”