Data-Driven Synthesis of Configuration-Constrained Robust Invariant Sets for Linear Parameter-Varying Systems

TL;DR

This paper introduces a data-driven approach to synthesize robust control invariant sets for LPV systems using finite data, avoiding explicit system identification, and solving a single LP for the invariant set and controller.

Contribution

It proposes a novel data-based method for RCI set synthesis for LPV systems that does not require system identification and uses a single LP formulation.

Findings

RCI sets comparable in size to model-based methods

Effective with limited data if excitation conditions are met

Single LP problem suffices for set and controller computation

Abstract

We present a data-driven method to synthesize robust control invariant (RCI) sets for linear parameter-varying (LPV) systems subject to unknown but bounded disturbances. A finite-length data set consisting of state, input, and scheduling signal measurements is used to compute an RCI set and invariance-inducing controller, without identifying an LPV model of the system. We parameterize the RCI set as a configuration-constrained polytope whose facets have a fixed orientation and variable offset. This allows us to define the vertices of the polytopic set in terms of its offset. By exploiting this property, an RCI set and associated vertex control inputs are computed by solving a single linear programming (LP) problem, formulated based on a data-based invariance condition and system constraints. We illustrate the effectiveness of our approach via two numerical examples. The proposed method can generate RCI sets that are of comparable size to those obtained by a model-based method in which exact knowledge of the system matrices is assumed. We show that RCI sets can be synthesized even with a relatively small number of data samples, if the gathered data satisfy certain excitation conditions.