Predictor methods for decentralized control of large-scale systems with input delays

Abstract

This paper develops a decentralized predictor-based control for large-scale systems with large input delays under the premise that the interconnections between subsystems are not strong. The local controller operates independently. Given any large delays, the predictor which exponentially stabilizes each uncoupled system, will stabilize the coupled one provided that the coupling is not solid. We propose two methods for the delay compensation: the backstepping-based partial differential equation (PDE) approach and the reduction-based ordinary differential equation (ODE) approach. We present decentralized Lyapunov-based analysis under the two predictor methods. It appears that the first predictor method leads to simpler conditions and manages with larger delays, whereas the second is easily applied to decentralized asynchronous sampled-data implementation, both under continuous and under discrete-time measurements. Through a benchmark example of two coupled cart–pendulum systems, the proposed methods are demonstrated to be effective when the input delays are too large for the system to be stabilized without a predictor.