Towards a Constructive Interconnection and Damping Assignment Stabilization Methodology

Meng Zhang (1) , Romeo Ortega (2) , Zhitao Liu (1) , Hongye Su (1) , Jianping Cai (1)

1 Zhejiang University
2 L2S - Laboratoire des signaux et systèmes

Interconnection and damping assignment passivity-based control (IDA-PBC) relies on the solution of a partial differential equation (PDE) that identifies the assignable storage function [10] [12], thus the difficulties in solving the PDE are usually the main stumbling block that hampers the application of IDA-PBC. The main objective of this paper is to propose a new IDA-PBC to simplify the solution of the PDE, in particular, we extend this method in the following directions. Firstly, we allow the desired interconnection and damping matrices to depend on the control signal, giving the possibility to simplify the PDE to ensure its solvability. Secondly, the PDE directly generates the control signal that has, in general, a simpler expression. Thirdly, it is applicable for general nonlinear systems possibly not affine in the control. The methodology is validated with two illustrative examples.

Keywords: interconnection and damping assignment; nonlinear systems; passivity based control

Domains: Automatic Control Engineering

Meng Zhang, Romeo Ortega, Zhitao Liu, Hongye Su, Jianping Cai. Towards a Constructive Interconnection and Damping Assignment Stabilization Methodology. 55th IEEE Conference on Decision and Control (CDC), Dec 2016, Las Vegas, United States. ⟨10.1109/CDC.2016.7799255⟩. ⟨hal-02378515⟩