Measures and LMIs for Adaptive Control Validation

TL;DR

This paper extends occupation measure and LMI relaxation methods to validate complex adaptive control laws, specifically MRAC configurations in aircraft, using a nonlinear F-16 model and comparing with Monte-Carlo simulations.

Contribution

It introduces a validation scheme tailored for MRAC control laws, leveraging their specific nonlinearities and structure, and demonstrates its effectiveness on a nonlinear aircraft model.

Findings

LMI relaxations outperform Monte-Carlo in validation efficiency.

The method effectively handles nonlinearities in MRAC control laws.

Validation scheme is applicable to complex aerospace control systems.

Abstract

Occupation measures and linear matrix inequality (LMI) relax-ations (called the moment sums of squares or Lasserre hierarchy) have been used previously as a means for solving control law verification and validation (VV) problems. However, these methods have been restricted to relatively simple control laws and a limited number of states. In this document, we extend these methods to model reference adaptive control (MRAC) configurations typical of the aircraft industry. The main contribution is a validation scheme that exploits the specific nonlinearities and structure of MRAC. A nonlinear F-16 plant is used for illustration. LMI relaxations solved by off-the-shelf-software are compared to traditional Monte-Carlo simulations.