The Decoupling Cooperative Control With Dominant Poles Assignment
Jilie Zhang, Tao Feng, Huaguang Zhang, Xiaomin Wang
Abstract
This article studies a decoupling cooperative control (DCC) with state feedback. It solves the output consensus problem on heterogeneous multiagent systems (MASs) over the input graph whose all nodes are reachable from the external reference signal. In light of the communication topology, the DCC forces each agent to reach a consensus on the given trajectory, which is from the reference signal of the common exosystem. Here, the output consensus problem is first equivalently converted into a stabilization one. Second the DCC involves a mapping <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ L}}_{d}$ </tex-math></inline-formula> of Laplacian matrix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ L}}$ </tex-math></inline-formula> , i.e., every diagonal element of the Laplacian matrix is multiplied by a parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d_{i}$ </tex-math></inline-formula> . <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ L}}_{d}$ </tex-math></inline-formula> moves Ger <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">š</i> gorin circles of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ L}}$ </tex-math></inline-formula> . By the merit of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal{ L}}_{d}$ </tex-math></inline-formula> , the equivalent stabilization problem is solved by the strictly positive real (SPR). In fact, the DCC is an approximate distributed decoupling control, when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d_{i}$ </tex-math></inline-formula> is sufficiently large. In addition, under the framework of the DCC, the assignment problem of the dominant poles for each agent is also solved by inverse optimal regulator technology in this article. Finally, several simulation examples verify the effectiveness of our method.