Design of structured dynamic output-feedback controllers for interconnected systems

Abstract

Abstract We address the design of structured controllers for networks of interconnected multivariable discrete-time subsystems. Different from existing approaches, where the structure of the controller is fixed a priori, we aim to design decentralised controllers such that each subsystem has a controller, which may not only use the output of its own associated subsystem, but also selected outputs of other subsystems. The total number of all those additional outputs used is to be minimised, while satisfying a guaranteed level of ℋ∞-performance. For the resulting non-convex optimisation problem, we first present a novel characterisation of the ℋ∞-performance of the closed-loop system by means of a system augmentation approach. Then, stimulated from compressive sensing theory, we propose a weighted ℓ1-minimisation to relax the ℓ0 objective function for structure optimisation. We develop an algorithm to deal with the relaxed decentralisation control problem, where the controller is obtained by iteratively solving convex optimisation problems. In addition, an iterative algorithm is developed to optimise the initial values such that the solvability of the decentralised control problem is further improved. Finally, an example is given to show the effectiveness of the proposed approaches. Keywords: compressive sensingconvex relaxationdecentralised controlℓ0-minimisationsystem augmentation approach Acknowledgements This study was partially supported by HKU CRCG 200907176129 and the Priority Programme 1305 Control Theory of Digitally Networked Dynamical Systems of the German Research Foundation (DFG).