Energy-Gain Control of Time-Varying Systems: Receding Horizon Approximation

Abstract: Standard formulations of prescribed worstcase disturbance energy-gain control policies for linear time-varying systems depend on all forward model data. In a discrete-time setting, this dependence arises through a backward Riccati recursion. The aim herein is to consider 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 establishes a sufficient number of preview steps for the performance loss to remain below any set tolerance, relative to the baseline gain bound of the associated infinite-preview controller. Aspects of the main result are explored in the context of a numerical example.