Design of a robust H_∞ preview controller for a class of uncertain discrete-time systems

Abstract

The robust preview tracking control problem of uncertain discrete-time systems satisfying matching conditions is considered. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to derive an augmented error system that includes the future information on the reference signal and disturbance signal to transform the tracking problem into a regulator problem. Then, a robust preview controller of the augmented error system is proposed by integrating Lyapunov stability theory and LMI approach. Research shows that the preview controller gain matrix can be determined by solving a LMI. The proposed robust preview controller in this paper cannot only guarantee the asymptotic stability of the closed-loop system, but also enhance the interference rejection properties. An integrator is applied to make sure that the output tracks the reference signal with no static error. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.

Robust preview control for polytopic nonlinear control systems

“…However, it has been proven that the classical difference methods in Lan et al (2019), Li and Liao (2017), and Takaba (2000) attempt to find system matrices to be independent of time variables, which tends to give conservative results. To overcome the deficiencies, the difference between a system state and its steady-state value, instead of the usual difference between system states, was used to derive an augmented error system to transform the tracking problem into a robust H ∞ problem, and the robust preview controller was obtained by solving an LMI (Li and Liao, 2018; Liao and Li, 2016). In addition, the cooperative preview control methods were design for a class of linear multi agent systems (Lu et al, 2019a; Lu et al, 2019b).…”

Energy-based Hamiltonian approach in H∞ controller design for n-degree of freedom mechanical systems

“…Among them, the H ∞ controller is not only known in attenuating the effects of matched and unmatched disturbances, but it also is capable to attenuate the impacts of model uncertainties (Acho, Orlov, & Solis, 2001;Erol & Delibaşı, 2018;Orlov & Aguilar, 2014;van der Schaft, 2001). While, general solutions have been presented for H ∞ controllers (Gholami & Binazadeh, 2019a, 2019bLi & Liao, 2018;Orlov & Aguilar, 2014;van der Schaft, 2001), the major drawback is the difficulty of solving HJI inequalities where in the design procedure leads to an infinite dimension problem (Krstic & Deng, 1998;Subbotin, 1995). This fact causes local solutions for CONTACT T. Binazadeh binazadeh@sutech.ac.ir many problems (Orlov & Aguilar, 2004).…”