H<inf>2</inf> analysis and synthesis of networked dynamic systems

Abstract

This work provides a general framework for the analysis and synthesis of a class of linear networked dynamic systems (NDS). We focus our attention on NDS where the underlying connection topology couples the agents at their outputs. A distinction is made between NDS with homogeneous agent dynamics and NDS with heterogeneous agent dynamics. In the homogeneous setting, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm expression reduces to the Frobenius norm of the underlying connection topology incidence matrix, E(G), scaled by the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm of the agents comprising the NDS. In the heterogeneous case, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm becomes the weighted Frobenius norm of the incidence matrix, where the weights appear on the nodes of the graph. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm characterization is then used to synthesize NDS with certain H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance. Specifically, a semi-definite programming solution is presented to design a local controller for each agent when the underlying topology is fixed. A solution using Kruskal's algorithm for finding a minimum weight spanning tree is used to design the optimal NDS topology given fixed agent dynamics.