Computation of optimal controls of a stochastic van der Pol type oscillator

Using the example of van der Pol developed a mathematical model of frictional self-oscillations in topochemically kinetics. Marked qualitative correspondence of the results of calculation performed using the experimental data of researchers.

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Modal synchronization of coupled bistable van der Pol oscillators

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2020.110555 ◽

2021 ◽

Vol 143 ◽

pp. 110555

Author(s):

I.B. Shiroky ◽

O.V. Gendelman

Keyword(s):

Van Der Pol ◽

Van Der Pol Oscillators

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Statistical and physiologically analysis of using a Duffing-van der Pol oscillator to modeled ictal signals

2020 16th International Conference on Control, Automation, Robotics and Vision (ICARCV) ◽

10.1109/icarcv50220.2020.9305339 ◽

2020 ◽

Author(s):

Beata Szuflitowska ◽

Przemyslaw Orlowski

Keyword(s):

Van Der Pol Oscillator ◽

Van Der Pol

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Existence and optimal controls for nonlocal fractional evolution equations of order (1,2) in Banach spaces

Advances in Difference Equations ◽

10.1186/s13662-021-03430-9 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Denghao Pang ◽

Wei Jiang ◽

Azmat Ullah Khan Niazi ◽

Jiale Sheng

Keyword(s):

Banach Spaces ◽

Mild Solution ◽

Measure Of Noncompactness ◽

Evolution Equations ◽

Well Posedness ◽

Optimal Controls ◽

Lagrange Problem ◽

Fractional Differential ◽

Fractional Evolution Systems ◽

Definition Of

AbstractIn this paper, we mainly investigate the existence, continuous dependence, and the optimal control for nonlocal fractional differential evolution equations of order (1,2) in Banach spaces. We define a competent definition of a mild solution. On this basis, we verify the well-posedness of the mild solution. Meanwhile, with a construction of Lagrange problem, we elaborate the existence of optimal pairs of the fractional evolution systems. The main tools are the fractional calculus, cosine family, multivalued analysis, measure of noncompactness method, and fixed point theorem. Finally, an example is propounded to illustrate the validity of our main results.

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Optimal Controls that Maximize the Expectation of First Passage Time

Journal of the Franklin Institute ◽

10.1016/0016-0032(77)90002-3 ◽

1977 ◽

Vol 304 (6) ◽

pp. 231-242 ◽

Cited By ~ 3

Author(s):

Menahem Friedman ◽

Yaakov Yavin

Keyword(s):

First Passage Time ◽

Passage Time ◽

Optimal Controls ◽

First Passage

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A numerical method for computing optimal controls in feedback and digital forms and its application to the blowing-venting control system of manned submarines

Optimal Control Applications and Methods ◽

10.1002/oca.2024 ◽

2012 ◽

Vol 34 (2) ◽

pp. 236-252 ◽

Cited By ~ 1

Author(s):

R. Font ◽

P. Pedregal ◽

F. Periago

Keyword(s):

Control System ◽

Numerical Method ◽

Optimal Controls

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Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

Advances in Difference Equations ◽

10.1186/s13662-019-2356-1 ◽

2019 ◽

Vol 2019 (1) ◽

Author(s):

Yajie Li ◽

Zhiqiang Wu ◽

Guoqi Zhang ◽

Feng Wang ◽

Yuancen Wang

Keyword(s):

Time Delay ◽

White Noise ◽

Gaussian White Noise ◽

Singularity Theory ◽

Van Der Pol Oscillator ◽

Order System ◽

Damping Force ◽

Van Der Pol ◽

Restoring Force ◽

White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

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