An adaptive extension to robust data-driven predictive control under parametric uncertainty

TL;DR

This paper introduces an adaptive robust data-driven control method for stabilizing time-varying linear systems with parametric uncertainty, combining offline and online data to improve performance without requiring persistent excitation.

Contribution

It proposes a novel control synthesis approach that leverages both offline and online data within a data informativity framework, relaxing persistent excitation requirements and ensuring stability.

Findings

Effective stabilization of time-varying systems demonstrated

Upper bounds on cost-to-go established for systems consistent with data

Numerical experiments confirm improved control performance

Abstract

Robust data-driven controllers typically rely on datasets from previous experiments, which embed information on the variability of the system parameters across past operational conditions. Complementarily, data collected online can contribute to improving the feedback performance relative to the current system's conditions, but are unable to account for the overall -- possibly time-varying -- system operation. With this in mind, we consider the problem of stabilizing a time-varying linear system, whose parameters are only known to lie within a bounded polytopic set. Taking a robust data-driven approach, we synthesize the control law by simultaneously leveraging two sets of historical state and input measures: an offline dataset -- which covers the extreme variations of the system parameters -- and an online dataset consisting of a rolling window of the latest state and input samples. Our approach relies on the data informativity framework: we thus relax persistent excitation requirements (i.e., the collected samples need not be sufficient for system identification), while still allowing for the design of a stabilizing controller. The state feedback law is obtained from standard Lyapunov arguments, implemented via semi-definite optimization: this also yields an upper bound on the cost-to-go for the class of systems that are consistent with the online data, while guaranteeing a decreasing cost for all systems compatible with the offline data. Numerical experiments are presented to illustrate the effectiveness of the proposed controller.