A Novel Delay-Independent Robust Adaptive Controller Design for Uncertain Nonlinear Systems With Time-Varying State Delay

Abstract

In this paper, two novel adaptive control strategies are presented based on the linear matrix inequality for nonlinear Lipschitz systems. The proposed approaches are developed by creatively using Krasovskii stability theory to compensate parametric uncertainty, unknown time-varying internal delay, and bounded matched or mismatched disturbance effects in closed-loop system of nonlinear systems. The online adaptive tuning controllers are designed such that reference input tracking and asymptotic stability of the closed-loop system are guaranteed. A novel structural algorithm is developed based on linear matrix inequality (LMI) and boundaries of the system delay or uncertainty. The capabilities of the proposed tracking and regulation methods are verified by simulation of three physical uncertain nonlinear system with real practical parameters subject to internal or state time delay and disturbance.

Fault‐tolerant controller design for nonlinear systems with multiple input and state delays based on sliding mode algorithm

“…Then, this assumption will not be a limitation for practical applications. 6,7,15 Lipschitz lemmas in Reference 7 suggest simple ways for computing the Lipschitz constant. Assumption 2 is mentioned the controllability condition of the proposed system, which is quite natural and is common in the robust FTC literature.…”

“…Remark In fact, a major class of physical and practical nonlinear systems does satisfy the Lipschitz continuity condition globally or at least locally in a given neighborhood. Then, this assumption will not be a limitation for practical applications 6,7,15 . Lipschitz lemmas in Reference 7 suggest simple ways for computing the Lipschitz constant.…”

“…K ∈ R n×n is a constant matrix and will be computed later by using LMI. From (6), it is assumed the initial positions of states are known and on sliding surface, it will be satisfied S (x (0) , x d (0) , 0) = 0 then the reaching process will be canceled. However, if there are any given initial positions out of ISS, the system reaches to the surface by using SMC law.…”

“…This limitation in some of the published articles has led many scientists to offer more comprehensive solutions by assuming the different state and input delays. 2,6 An innovative method that meets the following conditions is the primary motive for authors to study nonlinear systems such that 1. Each of the control inputs (actuators) has an independent and non-uniform delay compared to the other control inputs.…”

“…Assuming the same time delay in systems inputs and states is unrealistic practically. This limitation in some of the published articles has led many scientists to offer more comprehensive solutions by assuming the different state and input delays 2,6 …”