An Efficient Decomposition-based Approach for Hierarchical Optimal Controller Computation

Abstract

A fast method for computing controllers designed with hierarchical optimal control (HOC) is proposed. Algebras, which are the mathematical algebraic structures utilized in HOC, are decomposed to achieve the finest possible block-diagonalization of the algebraic Riccati equations that should be solved in controller computation. Furthermore, to reduce computational complexity, the block-diagonalization process is divided into several minor steps by using the property that hierarchies in HOC are characterized by Kronecker products. The computational complexity of the method is analyzed. For the hierarchies expected in HOC, notable reductions in complexity are anticipated. The proposed method facilitates the application of HOC to large-scale systems.