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

TL;DR

This paper proposes a receding horizon approach to control linear time-varying systems with finite preview, ensuring near-optimal energy-gain performance with a quantifiable approximation bound.

Contribution

It introduces a controller synthesis method leveraging Riccati operator contraction to achieve near-infinite horizon performance with limited preview.

Findings

Finite preview steps can approximate infinite-horizon performance within a specified tolerance.

Controller synthesis leverages strict contraction of Riccati operators under controllability and observability.

Numerical example demonstrates the effectiveness of the proposed approximation.

Abstract

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.