Robust linear static anti-windup with probabilistic certificates
Simone Formentin, Fabrizio Dabbene, Roberto Tempo, Luca Zaccarian and, Sergio M. Savaresi

TL;DR
This paper introduces a probabilistic approach for designing robust static anti-windup controllers in saturated linear systems with uncertainties, utilizing a novel scenario with certificates method and a sequential randomized algorithm.
Contribution
It develops a new scenario with certificates framework for robust anti-windup design, enabling implicit Lyapunov function synthesis and reducing computational complexity.
Findings
Effective robust anti-windup design under probabilistic uncertainties.
The scenario with certificates approach removes convexity restrictions.
Numerical examples demonstrate the method's practicality and efficiency.
Abstract
In this paper, we address robust static anti-windup compensator design and performance analysis for saturated linear closed loops in the presence of nonlinear probabilistic parameter uncertainties via randomized techniques. The proposed static anti-windup analysis and robust performance synthesis correspond to several optimization goals, ranging from minimization of the nonlinear input/output gain to maximization of the stability region or maximization of the domain of attraction. We also introduce a novel paradigm accounting for uncertainties in the energy of the disturbance inputs. Due to the special structure of linear static anti-windup design, wherein the design variables are decoupled from the Lyapunov certificates, we introduce a significant extension, called scenario with certificates (SwC), of the so-called scenario approach for uncertain optimization problems. This extension…
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