Observer‐based decentralized robust H_∞ output tracking control with preview action for uncertain and disturbed nonlinear interconnected systems

Abstract

The problem of observer‐based decentralized robust H∞ output tracking control with preview action in a class of uncertain and disturbed nonlinear interconnected systems is investigated in this study. The considered interconnected system consists of several subsystems with nonlinear interconnections, parametric uncertainties, and external disturbances. Based on the augmented error system approach combined with Lyapunov stability theory and special matrix inequality linearization techniques, a sufficient condition for the existence of a decentralized observer‐based robust H∞ output feedback preview controller is derived for the original interconnected system in terms of linear matrix inequality (LMI) formulations. The gain matrices of the tracking controller and state observer are derived using only a one‐step LMI procedure, which overcomes the drawbacks of some multistep iterative algorithms. Finally, the effectiveness of the proposed control scheme is validated using a numerical example.

Adaptive nonlinear information fusion preview control for autonomous surface vessels subject to measurement noises and unknown input saturations

“…The system uncertainty and measurement noise in system dynamics (15) are assumed to have the following distribution characteristics…”

“…Preview control can improve the dynamic response and tracking accuracy of the actual system by using the previewed reference trajectory information and disturbance information [14,15]. For ASV system, its reference trajectory can generally be planned in advance and which is previewed.…”

“…Based on the above research works, for the tracking problem of the underactuated ASV subject to system uncertainty and measurement noise, the traditional LQG-based preview control method needs to establish an augmented error system and solve the complex Riccati equation [14][15][16][17][18][19][20][21]. Different from the LQG-based preview control, the information fusion preview control obtains control input by fusing the system's future reference trajectory information, noise information, performance index requirements, and system dynamic model, without the need to construct an augmented error system or solve the optimization problems.…”

Design of distributed preview tracking controller for nonlinear interconnected systems with time‐delay

“…Remark The existing literature requires restrictions on the nonlinear function $$$ {f}_{ij}\left(t,{x}_i(t),{x}_j(t),{x}_i\left(t-{\mu}_{ij}\right),{x}_j\left(t-{\tau}_{ij}\right)\right) $$$ when investigating nonlinear interconnected systems by means of decentralized control. For example, the References 27 and 28 requires that the nonlinear function satisfies the Lipschitz condition. However, in our article, as long as the form of the nonlinear function is known, it can be used to design the controller without any additional restrictions.…”

“…Reference 26 investigated the problem of preview control for a class of discrete‐time interconnected systems by using decentralized control. In References 27 and 28, the observer‐based decentralized output feedback preview tracking control methods were proposed for nonlinear interconnected systems. Reference 29 tackled the design problem of preview tracking controller for singular interconnected systems.…”