Prescribed Performance Tracking of Uncertain MIMO Nonlinear Systems in the Presence of Delays

Bikas, Lampros N.; Rovithakis, George A.

doi:10.1109/tac.2021.3135276

Cited by 22 publications

(18 citation statements)

References 42 publications

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“…From Figures 4 and 5, it is observed that the system is more sensitive to the amplitude of the delay function than the frequency. This outcome agreed with previous results 36,50 that the tracking performance degrades with larger delays applied to the system. Moreover, to validate the superiority of our proposed method, we conducted two sets of comparative simulations against the method referenced in Reference 14.…”

Section: F I G U R Esupporting

confidence: 93%

“…To guarantee steady‐state and transient performance, a new control design and synthesis method has been developed by Bechlioulis and Rovithakis in Reference 49, in which a tracking error transformation is performed by introducing an appropriate performance function so that if the stability of the transformed system is guaranteed, then the stability of the original system can be guaranteed, and both transient and steady‐state performance can be quantitatively examined and analytically studied. This concept has been extended in Reference 50 to uncertain multi‐input multi‐output (MIMO) strict‐feedback nonlinear systems with time‐varying state measurement delay and input delay. However, the state measurement delay is considered to be known, and the steady is achieved as

t\to \infty

but not in finite time.…”

Section: Introductionmentioning

confidence: 99%

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Finite‐time tracking control for time‐delayed pure‐feedback systems with guaranteed performance

Dai,

Wang,

Wang

2023

Intl J Robust & Nonlinear

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This article investigates the finite‐time tracking control problem with guaranteed performance for a class of nonlinear pure‐feedback systems subject to both time‐varying state delays and control input delays. Both the state delays and control input delays are assumed to be unknown yet bounded by some known constants. A new performance function is introduced that ensures the finite‐time convergence of tracking errors and guaranteed performance. The key to handling both the states and input delays lies in a novel construction of the Lyapunov–Krasovskii (LK) function, which also avoids the reconstruction of the LK function in stability analysis. In addition, a continuous package function is introduced, which allows the unknown nonlinear terms arising from the uncertain perturbation and the derivation of the LK function to be eliminated. Under the proposed method, the semi‐global uniform ultimate boundedness of all signals in the closed‐loop system can also be ensured. Simulation examples are provided to demonstrate the effectiveness of the proposed approach in this article.

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Section: F I G U R Esupporting

confidence: 93%

t\to \infty

but not in finite time.…”

Section: Introductionmentioning

confidence: 99%

Finite‐time tracking control for time‐delayed pure‐feedback systems with guaranteed performance

Dai,

Wang,

Wang

2023

Intl J Robust & Nonlinear

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“…Then, ζ n (t) = 0 for all z n (t). Differentiating V n (t) along the solution of closed-loop system (29) yields…”

Section: B Control Schemesmentioning

confidence: 99%

“…Via uniting control [26], the global prescribed performance of the output tracking error is achieved, improving the semi-global stability [11]- [14], [20], [21], [24], [25], [27]. Moreover, significant modifications on the standard prescribed performance control methodology are provided to successfully handle discontinuities in desired trajectory [28], and time-varying delays in both state measurements and control inputs [29].…”

Section: Introductionmentioning

confidence: 99%

“…(A1) To well define the error transformation function at the initial time, the initial value of the prescribed performance function depends on the initial value of the tracking error [11]- [14], [19]- [24], [26], [28], [29], [34]- [38], [43]. (A2) To suppress the influence of the error surface defined in dynamic surface control on the energy function, derivatives of virtual controllers are bounded or defined on a compact set [31], [34], [39].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Fuzzy Tracking Control with Global Prescribed-Time Prescribed Performance for Uncertain Strict-Feedback Nonlinear Systems

Mao¹,

Wu²,

Liu³

et al. 2022

Preprint

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Adaptive fuzzy control strategies are established to achieve global prescribed performance for uncertain strictfeedback nonlinear systems with prescribed time. Firstly, a class of prescribed-time prescribed performance function is designed to quantify the transient and steady performance constraints of the tracking error. Secondly, based on dynamic surface control methods, controllers with or without approximating structures are established to guarantee that the tracking error satisfies prescribed transient performance and converges into a prescribed bounded set within prescribed time. In particular, the settling time and initial value of the prescribed performance function are completely independent of initial conditions of the tracking error and system parameters, which improves existing results. Moreover, with a novel Lyapunov-like energy function, not only the differential explosion problem frequently occurring in backstepping techniques is solved, but the drawback of the semiglobal boundedness of tracking error induced by dynamic surface control can be overcome. The validity and effectiveness of the main results are verified by numerical simulations on practical examples.

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Asymptotic tracking control of uncertain MIMO nonlinear systems with extended condition for controllability

Zhou,

Huang,

Song

et al. 2024

Intl J Robust & Nonlinear

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For uncertain multiple‐inputs multi‐outputs nonlinear systems, it is nontrivial to achieve asymptotic tracking due to the intrinsic coupling among inputs, while the controllability conditions in most existing methods are rather restrictive or even impractical especially when unexpected actuator faults are involved. In this article, we focus on extending such controllability condition by resorting to the existence (instead of a priori knowledge) of some feasible auxiliary matrix, upon which a robust adaptive control scheme is first presented in the absence of actuator faults that is not only able to achieve asymptotic tracking even in the presence of non‐parametric uncertainties with all the closed‐loop signals globally ultimately uniformly bounded, but also able to deal with a larger class of system models. Furthermore, for the case with intermittent actuator faults, we develop a fault‐tolerant control scheme with extended condition for controllability that is able to accommodate such faults automatically without using any fault detection or fault diagnosis unit. The effectiveness and benefits of the proposed method are verified via simulation on robotic systems.

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Prescribed Performance Tracking of Uncertain MIMO Nonlinear Systems in the Presence of Delays

Cited by 22 publications

References 42 publications

Finite‐time tracking control for time‐delayed pure‐feedback systems with guaranteed performance

Finite‐time tracking control for time‐delayed pure‐feedback systems with guaranteed performance

Adaptive Fuzzy Tracking Control with Global Prescribed-Time Prescribed Performance for Uncertain Strict-Feedback Nonlinear Systems

Asymptotic tracking control of uncertain MIMO nonlinear systems with extended condition for controllability

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