Continuous delay estimation with polynomial splines

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

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A Novel Adaptive Super-Twisting Sliding Mode Control Scheme with Time-Delay Estimation for a Single Ducted-Fan Unmanned Aerial Vehicle

Actuators ◽

10.3390/act10030054 ◽

2021 ◽

Vol 10 (3) ◽

pp. 54

Author(s):

Minh-Thien Tran ◽

Dong-Hun Lee ◽

Soumayya Chakir ◽

Young-Bok Kim

Keyword(s):

Time Delay ◽

Sliding Mode Control ◽

Unmanned Aerial Vehicle ◽

Sliding Mode ◽

Time Delay Estimation ◽

Delay Estimation ◽

Mode Control ◽

Ducted Fan ◽

Control Scheme ◽

Aerial Vehicle

This article proposes a novel adaptive super-twisting sliding mode control scheme with a time-delay estimation technique (ASTSMC-TDE) to control the yaw angle of a single ducted-fan unmanned aerial vehicle system. Such systems are highly nonlinear; hence, the proposed control scheme is a combination of several control schemes; super-twisting sliding mode, TDE technique to estimate the nonlinear factors of the system, and an adaptive sliding mode. The tracking error of the ASTSMC-TDE is guaranteed to be uniformly ultimately bounded using Lyapunov stability theory. Moreover, to enhance the versatility and the practical feasibility of the proposed control scheme, a comparison study between the proposed controller and a proportional-integral-derivative controller (PID) is conducted. The comparison is achieved through two different scenarios: a normal mode and an abnormal mode. Simulation and experimental tests are carried out to provide an in-depth investigation of the performance of the proposed ASTSMC-TDE control system.

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Even-order differential equation with continuous delay: nonexistence criteria of Kneser solutions

Advances in Difference Equations ◽

10.1186/s13662-021-03409-6 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Ali Muhib ◽

M. Motawi Khashan ◽

Osama Moaaz

Keyword(s):

Differential Equation ◽

Order Differential Equation ◽

Delay Argument ◽

Even Order ◽

Continuous Delay ◽

New Criteria

AbstractIn this paper, we study even-order DEs where we deduce new conditions for nonexistence Kneser solutions for this type of DEs. Based on the nonexistence criteria of Kneser solutions, we establish the criteria for oscillation that take into account the effect of the delay argument, where to our knowledge all the previous results neglected the effect of the delay argument, so our results improve the previous results. The effectiveness of our new criteria is illustrated by examples.

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