Energy-Gain Control of Time-Varying Systems: Receding Horizon Approximation
For control engineers dealing with time-varying systems, this work offers a practical approximation method with guaranteed performance bounds, though the result is incremental as it extends existing contraction-based analysis to a specific preview constraint.
The paper addresses the problem of designing energy-gain control policies for linear time-varying systems when only finite receding-horizon preview of model parameters is available. It provides a sufficient number of preview steps to keep performance loss below any desired tolerance relative to the infinite-preview baseline.
Standard formulations of prescribed worst-case disturbance energy-gain control policies for linear time-varying systems depend on all forward model data. In discrete time, this dependence arises through a backward Riccati recursion. This article is about the infinite-horizon $\ell_2$ gain performance of state feedback policies with only finite receding-horizon preview of the model parameters. The proposed synthesis of controllers subject to such a constraint leverages the strict contraction of lifted Riccati operators under uniform controllability and observability. The main approximation result is a sufficient number of preview steps for the incurred performance loss to remain below any set tolerance, relative to the baseline gain bound of the associated infinite-preview controller. Aspects of the result are explored in a numerical example.