Learning Quasi-LPV Models and Robust Control Invariant Sets with Reduced Conservativeness

TL;DR

This paper introduces a method to identify quasi-LPV models with guaranteed robust control invariant sets, reducing conservativeness by bounding the system with an uncertain LTI model and solving a nonlinear robust optimization problem.

Contribution

It presents a novel approach to reduce conservativeness in qLPV model identification and RCI set computation using bound propagation and differentiable optimization.

Findings

Demonstrates improved results over benchmark approaches

Reduces conservativeness in RCI set estimation

Provides a scalable optimization framework

Abstract

We present an approach to identify a quasi Linear Parameter Varying (qLPV) model of a plant, with the qLPV model guaranteed to admit a robust control invariant (RCI) set. It builds upon the concurrent synthesis framework presented in [1], in which the requirement of existence of an RCI set is modeled as a control-oriented regularization. Here, we reduce the conservativeness of the approach by bounding the qLPV system with an uncertain LTI system, which we derive using bound propagation approaches. The resulting regularization function is the optimal value of a nonlinear robust optimization problem that we solve via a differentiable algorithm. We numerically demonstrate the benefits of the proposed approach over two benchmark approaches.