A Minimax Linear Quadratic Gaussian Method for Antiwindup Control Synthesis

In this paper, a dynamic antiwindup compensator design is proposed which augments the main controller and guarantees robust performance in the event of input saturation. This is a two stage process in which first a robust optimal controller is designed for an uncertain linear system which guarantees the internal stability of the closed loop system and provides robust performance in the absence of input saturation. Then a minimax linear quadratic Gaussian (LQG) compensator is designed to guarantee the performance in certain domain of attraction, in the presence of input saturation. This antiwindup augmentation only comes into action when plant is subject to input saturation. In order to illustrate the effectiveness of this approach, the proposed method is applied to a tracking control problem for an air-breathing hypersonic flight vehicle (AHFV).

💡 Research Summary

The paper introduces a systematic two‑stage design methodology for anti‑windup compensation in uncertain linear systems that are subject to actuator input saturation. In the first stage, a robust optimal controller is synthesized by ignoring saturation and treating model uncertainties as integral quadratic constraints (IQCs). This yields a guaranteed‑cost linear‑quadratic regulator (LQR) whose gain Gτ is obtained from a Riccati equation (4) parameterized by positive scalars τi. Theorem 1 guarantees internal stability and a bound on the quadratic cost for all admissible uncertainties.

In the second stage, the saturation nonlinearity is modeled as a sector‑bounded (dead‑zone) uncertainty. Each saturated input component ui is expressed as ui = ui_sat + φi(ui), where φi satisfies 0 ≤ φi ui ≤ εi ui². By defining a new uncertainty input ŵi = φi − εi ui², the original plant is rewritten to include additional uncertainty terms (16)–(19). This reformulation leads to an augmented closed‑loop model (22) that incorporates both the original IQC uncertainties and the saturation‑induced uncertainties.

The anti‑windup compensator is then designed using the minimax linear‑quadratic‑Gaussian (LQG) framework, which is equivalent to a risk‑sensitive H∞ control problem. The performance index J (23) is the time‑averaged expected value of a quadratic form in the state x and the compensator output v, maximized over all admissible uncertainties. By introducing ψ =