Nonlocal Problem for a System of Partial Differential Equations of Higher Order with Pulsed Actions

Assanova, A. T.; Tleulessova, A. B.

doi:10.1007/s11253-020-01750-9

Cited by 7 publications

(3 citation statements)

References 18 publications

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“…In this paper, we offered a modification of the parameterization method by Dzhumabaev for solving problem with impulse actions for system of nonlinear ODEs in the interval. This technique can be applied to various kinds of differential equations with discontinuities [18][19][20].…”

Section: Discussionmentioning

confidence: 99%

“…In present work we consider problem with impulse actions for nonlinear ODEs by parameterization method by Dulat Dzhumabaev [12] proposed for solving BVPs for ODEs and extended to different classes of differential equations [13][14][15][16][17][18][19][20]. We offer a modification of parameterization method for solving to problem with impulse actions for system of nonlinear ODEs.…”

Section: Introductionmentioning

confidence: 99%

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A problem with impulse actions for nonlinear ODEs

Mukash

Assanova

Stanzhytskyi

2023

ijmph

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In the paper, we consider problem with impulse actions for system of nonlinear ordinary differential equations (ODEs) in the interval. For solving this problem we use a modification of parameterization method by Dulat Dzhumabaev. In the modification of the method we introduce the parameters as the values of the unknown function at the middle of the subintervals of the partition of the considered interval. The problem with impulse actions transfers to an equivalent problem system of nonlinear ODEs with parameters. Conditions for an existence of solution to the equivalent problem are obtained. Existence theorem for solutions this problem is established by one generalizes a theorem of Hadamard. We also constructed an algorithm for finding of solution to this problem. Finally, we found conditions for solvability to the problem with impulse actions for system of nonlinear ODEs in terms of special matrix composed by the initial data. This method can be applied to various types of nonlinear problems with impulse actions for ODEs.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A problem with impulse actions for nonlinear ODEs

Mukash

Assanova

Stanzhytskyi

2023

ijmph

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“…In ref. [13], the algorithm for solving the nonlocal problem of second-order impulsive hyperbolic equations is constructed, and sufficient conditions for the existence of its unique solution are obtained. It provides a very valuable reference for the content of this paper.…”

Section: Introductionmentioning

confidence: 99%

Iterative learning tracking control for second‐order nonlinear hyperbolic impulsive partial differential systems

Dai

Zhang

et al. 2023

IET Control Theory & Appl

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This paper studies the iterative learning control (ILC) for a class of second‐order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow the discontinuous desired output, a P‐type learning law is adopted, and sufficient conditions for the convergence of the tracking error is established under identified initial state value. The rigorous analysis is also given using the impulsive Gronwall inequality. Secondly, the tracking error of output trajectory is considered in systems with state initial values shifting based on an initial learning algorithm. These results of this paper show that the tracking error on the finite time interval can uniform converge to 0 as the iteration index goes to infinity if impulse number of the systems is only a finite numbers. Finally, two numerical simulation examples are given to verify the effectiveness of the theoretical results.

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