On dynamical input reconstruction in a distributed second order equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yury S. Osipov ◽  
Vyacheslav I. Maksimov
Keyword(s):  
Differential Equation ◽  
Feedback Control ◽  
Control Theory ◽  
Nonlinear Differential Equation ◽  
Order Equation ◽  
Second Order ◽  
Ill Posed ◽  
Computational Errors ◽  
Input Reconstruction ◽  
Feedback Control Theory

Abstract A second order nonlinear differential equation is considered. An algorithm for reconstructing an input from inaccurate measurements of the solution at discrete times is designed. The algorithm based on the constructions of feedback control theory and theory of ill-posed problems is stable with respect to informational noises and computational errors.

The methods of dynamical reconstruction of an input in a system of ordinary differential equations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Vyacheslav I. Maksimov
Keyword(s):  
Feedback Control ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Reconstruction Algorithm ◽  
System A ◽  
Ill Posed ◽  
Computational Errors ◽  
Combination Of Methods ◽  
Input Reconstruction ◽  
Dynamical Reconstruction

AbstractIn the paper, for systems described by ordinary differential equations a review of algorithms of dynamical input reconstruction by results of inaccurate observations of its solutions is given. The problem under discussion is referred to the class of dynamical inverse problems. The proposed algorithms are stable with respect to informational noises and computational errors. They are based on the combination of methods of the theory of ill-posed problems and the theory of feedback control. The essence of the methodology underlying the algorithms suggested in the paper consists in the representation of a reconstruction algorithm in the form of a feedback control algorithm for a certain artificial dynamical system, a model; such an algorithm, whose output is the realization of the control in the model, is dynamical by its definition.

Tips on Stochastic Optimal Feedback Control and Bayesian Spatiotemporal Models: Applications to Robotics

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Jongeun Choi ◽  
Dejan Milutinović
Keyword(s):  
Sensor Networks ◽  
Feedback Control ◽  
Control Theory ◽  
Mobile Sensor Networks ◽  
Optimal Feedback Control ◽  
Mobile Sensor ◽  
Optimal Feedback ◽  
Spatiotemporal Models ◽  
Feedback Control Theory

This tutorial paper presents the expositions of stochastic optimal feedback control theory and Bayesian spatiotemporal models in the context of robotics applications. The presented material is self-contained so that readers can grasp the most important concepts and acquire knowledge needed to jump-start their research. To facilitate this, we provide a series of educational examples from robotics and mobile sensor networks.

scholarly journals Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongwei Shi ◽  
Yuzhen Bai
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Order Nonlinear Differential Equation

AbstractIn this paper, we present several new oscillation criteria for a second order nonlinear differential equation with mixed neutral terms of the form $$ \bigl(r(t) \bigl(z'(t)\bigr)^{\alpha }\bigr)'+q(t)x^{\beta } \bigl(\sigma (t)\bigr)=0,\quad t\geq t_{0}, $$(r(t)(z′(t))α)′+q(t)xβ(σ(t))=0,t≥t0, where $z(t)=x(t)+p_{1}(t)x(\tau (t))+p_{2}(t)x(\lambda (t))$z(t)=x(t)+p1(t)x(τ(t))+p2(t)x(λ(t)) and α, β are ratios of two positive odd integers. Our results improve and complement some well-known results which were published recently in the literature. Two examples are given to illustrate the efficiency of our results.

Implications of Optimal Feedback Control Theory for Sport Coaching and Motor Learning: A Systematic Review

Motor Control ◽  
2021 ◽  
pp. 1-24
Author(s):  
Steven van Andel ◽  
Robin Pieper ◽  
Inge Werner ◽  
Felix Wachholz ◽  
Maurice Mohr ◽  
...  
Keyword(s):  
Feedback Control ◽  
Motor Learning ◽  
Control Theory ◽  
Skill Acquisition ◽  
Best Practice ◽  
Optimal Feedback Control ◽  
Optimal Feedback ◽  
Different Types ◽  
Novel Theory ◽  
Feedback Control Theory

Best practice in skill acquisition has been informed by motor control theories. The main aim of this study is to screen existing literature on a relatively novel theory, Optimal Feedback Control Theory (OFCT), and to assess how OFCT concepts can be applied in sports and motor learning research. Based on 51 included studies with on average a high methodological quality, we found that different types of training seem to appeal to different control processes within OFCT. The minimum intervention principle (founded in OFCT) was used in many of the reviewed studies, and further investigation might lead to further improvements in sport skill acquisition. However, considering the homogenous nature of the tasks included in the reviewed studies, these ideas and their generalizability should be tested in future studies.

scholarly journals General boundedness theorems to some second order nonlinear differential equation with integrable forcing term

1995 ◽  
Vol 18 (4) ◽  
pp. 823-824 ◽  
Author(s):  
Allan Kroopnick
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Real Line ◽  
Integrable Function ◽  
Second Order ◽  
Boundedness Theorem ◽  
Forcing Term ◽  
Order Nonlinear Differential Equation

In this note we present a boundedness theorem to the equationx″+c(t,x,x′)+a(t)b(x)=e(t)wheree(t)is a continuous absolutely integrable function over the nonnegative real line. We then extend the result to the equationx″+c(t,x,x′)+a(t,x)=e(t). The first theorem provides the motivation for the second theorem. Also, an example illustrating the theory is then given.

A Qualitative Look at Feedback Control Theory as a Style of Describing Behavior

1977 ◽  
Vol 19 (4) ◽  
pp. 331-347 ◽  
Author(s):  
Richard J. Jagacinski
Keyword(s):  
Feedback Control ◽  
Control Theory ◽  
Social Groups ◽  
Emotional Behavior ◽  
Level Measurement ◽  
Tracking Behavior ◽  
Changes Over Time ◽  
Feedback Control Theory ◽  
Ordinal Level ◽  
Over Time

The present paper reviews several ways feedback control theory has been used to describe tracking behavior and several qualitative experimental techniques. These techniques require only ordinal-level measurement and may aid any researcher investigating behavior whose temporal patterning is critical and which involves fairly continuous changes over time. One possible application in the area of stuttering behavior is presented in detail to show how these techniques can provide useful insights and hypotheses. Other suggested areas of application include the behavior of human social groups, motivational behavior, and emotional behavior.

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