Robust output‐based controller design for enlarging the region of attraction of input saturated linear systems

Abstract

The aim of this study was to design a constrained robust output feedback control strategy for stabilizing linear systems affected by uncertainties and output perturbations. The input is constrained by a saturation function. A classical Luenberger observer reconstructed the states from output observations. The state feedback control employed the estimated states given by the observer. This work proposed a Barrier Lyapunov Function (BLF) to manage the saturation problem in the control input. Moreover, an extended version of the attractive ellipsoid method (AEM) characterized the zone of convergence due the presence of perturbations in the output. A convex optimization procedure, formulated as a set of matrix inequalities, yielded the control parameters and the region of attraction for the close‐loop system as well as a minimal ultimately bounded set for the system trajectories. Numerical simulations supported the theoretical results formulated in this study.

Terminal angle constrained time‐varying sliding mode guidance law with autopilot dynamics and input saturation

“…According to the sliding mode surface in (16) and the convergence region of the LOS angle error x 1 in (39), the value k x should satisfy r 𝑓 ≪ k x ≪ r (0), since r (0) = 10000 √ 2 in the simulation and r 𝑓 is a small constant and usually satisfies r 𝑓 < 1. Hence, we select k x = 200.…”

“…Finally, from the definition of the sliding mode variable in (16), we obtain that V q converges to the region…”

“…Nonlinear saturation often exists in practical systems as well as the guidance and control system [7]. The saturation problem would severely deteriorate the system performance, resulting in undesirable inaccuracy even instability [16][17][18][19][20][21]. Zhou et al designed a three-dimensional guidance law considering the input saturation and the second-order autopilot dynamics based on the adaptive dynamic surface control, which is designed for intercepting maneuvering targets [22].…”

Robust output‐regulation for uncertain linear systems with input saturation

“…Such an approach is based on a Luenberger observer and the attractive ellipsoid method (AEM). Based also on the AEM, in [18] a robust output feedback controller is proposed for enlarging the attraction region of uncertain linear systems with input saturation constraints. It is worth highlighting that most of the above mentioned robust output control approaches are based on linear observers.…”