Fixed-time safe tracking control of uncertain high-order nonlinear pure-feedback systems via unified transformation functions

Guo, Chaoqun; Hu, Jiangping; Jiang, Hao; Čelikovský, Sergej; Hu, Xiaoming

doi:10.14736/kyb-2023-3-0342

Cited by 32 publications

(9 citation statements)

References 28 publications

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“…If the nonlinear second-order neutral differential equation satisfies the Conditions (1)-( 3), there is a solution to the initial problem [24][25][26][27]. From Condition (1), it can be found that ∃ε > 0 makes f bounded on [0, ε ] × B(x 0 , ε) × B(x 0 , ε), so there is a constant M 0 , which makes:…”

Section: Solution Of Nonlinear Second Order Neutral Differential Equa...mentioning

confidence: 99%

Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations

2023

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Differential equations are useful mathematical tools for solving complex problems. Differential equations include ordinary and partial differential equations. Nonlinear equations can express the nonlinear relationship between dependent and independent variables. The nonlinear second-order neutral differential equations studied in this paper are a class of quadratic differentiable equations that include delay terms. According to the t-value interval in the differential equation function, a basis is needed for selecting the initial values of the differential equations. The initial value of the differential equation is calculated with the initial value calculation formula, and the existence of the solution of the nonlinear second-order neutral differential equation is determined using the condensation mapping fixed-point theorem. Thus, the oscillation analysis of nonlinear differential equations is realized. The experimental results indicate that the nonlinear neutral differential equation can analyze the oscillation behavior of the circuit in the Colpitts oscillator by constructing a solution equation for the oscillation frequency and optimizing the circuit design. It provides a more accurate control for practical applications.

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Section: Solution Of Nonlinear Second Order Neutral Differential Equa...mentioning

confidence: 99%

Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations

2023

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“…However, developing numerical and exact solutions to these equations is crucial in applied mathematics and theoretical physics [19][20][21]. Consequently, innovative methods have been developed for analytical solutions that closely approximate the exact solutions [22,23]. Differential equations were often solved using integral transforms.…”

Section: Introductionmentioning

confidence: 99%

A comparative analytical investigation for some linear and nonlinear time-fractional partial differential equations in the framework of the Aboodh transformation

Noor,

Albalawi,

Shah

et al. 2024

Front. Phys.

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This article discusses two simple, complication-free, and effective methods for solving fractional-order linear and nonlinear partial differential equations analytically: the Aboodh residual power series method (ARPSM) and the Aboodh transform iteration method (ATIM). The Caputo operator is utilized to define fractional order derivatives. In these methods, the analytical approximations are derived in series form. We calculate the first terms of the series and then estimate the absolute error resulting from leaving out the remaining terms to ensure the accuracy of the derived approximations and determine the accuracy and efficiency of the suggested methods. The derived approximations are discussed numerically using some values for the relevant parameters to the subject of the study. Useful examples are thought to illustrate the practical application of current approaches. We also examine the fractional order results that converge to the integer order solutions to ensure the accuracy of the derived approximations. Many researchers, particularly those in plasma physics, are anticipated to gain from modeling evolution equations describing nonlinear events in plasma systems.

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“…The research articles cited encompass a diverse range of topics within the field of control systems, vibration isolation, and neural network approximation. Guo et al delve into fixed-time safe tracking control and nonsingular fixed-time tracking control of uncertain nonlinear systems [16,17] 3. Lu et al focus on nonlinear vibration isolation systems with high-static-low-dynamic stiffness [18,19].…”

Section: Introductionmentioning

confidence: 99%

On the approximations to fractional nonlinear damped Burger’s-type equations that arise in fluids and plasmas using Aboodh residual power series and Aboodh transform iteration methods

Noor,

Albalawi,

Shah

et al. 2024

Front. Phys.

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Damped Burger’s equation describes the characteristics of one-dimensional nonlinear shock waves in the presence of damping effects and is significant in fluid dynamics, plasma physics, and other fields. Due to the potential applications of this equation, thus the objective of this investigation is to solve and analyze the time fractional form of this equation using methods with precise efficiency, high accuracy, ease of application and calculation, and flexibility in dealing with more complicated equations, which are called the Aboodh residual power series method and the Aboodh transform iteration method (ATIM) within the Caputo operator framework. Also, this study intends to further our understanding of the dynamic characteristics of solutions to the Damped Burger’s equation and to assess the effectiveness of the proposed methods in addressing nonlinear fractional partial differential equations. The two proposed methods are highly effective mathematical techniques for studying more complicated nonlinear differential equations. They can produce precise approximate solutions for intricate evolution equations beyond the specific examined equation. In addition to the proposed methods, the fractional derivatives are processed using the Caputo operator. The Caputo operator enhances the representation of fractional derivatives by providing a more accurate portrayal of the underlying physical processes. Based on the proposed two approaches, a set of approximations to damped Burger’s equation are derived. These approximations are discussed graphically and numerically by presenting a set of two- and three-dimensional graphs. In addition, these approximations are analyzed numerically in several tables, including the absolute error for each approximate solution compared to the exact solution for the integer case. Furthermore, the effect of the fractional parameter on the behavior of the derived approximations is examined and discussed.

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Fixed-time safe tracking control of uncertain high-order nonlinear pure-feedback systems via unified transformation functions

Cited by 32 publications

References 28 publications

Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations

Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations

A comparative analytical investigation for some linear and nonlinear time-fractional partial differential equations in the framework of the Aboodh transformation

On the approximations to fractional nonlinear damped Burger’s-type equations that arise in fluids and plasmas using Aboodh residual power series and Aboodh transform iteration methods

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