Estimating the Lyapunov Function and Stability of Motion of a System with Equations of Motion with an Asymptotically Expanded Right-Hand Side

Martynyuk, À. À.; Chernienko, V. A.

doi:10.1007/s10778-021-01064-8

Cited by 2 publications

(2 citation statements)

References 6 publications

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“…However, the difculty lies in the fact that there are no general recommendations or general approaches on how to fnd such a solution. Existing works mostly provide analysis rather than synthesis of such motions [23]. Most often, stability at a point is ensured, and not stability of movement because the difculty here is that the stability of movement must be ensured in time.…”

Section: Extended Statement Of the Optimal Control Problemmentioning

confidence: 99%

Extended Statement of the Optimal Control Problem and Machine Learning Approach to Its Solution

Shmalko

Diveev

2022

Mathematical Problems in Engineering

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Engineers strive to realize the goal of control in the best possible way based on a given quality criterion when developing control system. The well-known optimal control problem requires finding a solution as a function of time. Such a function cannot be directly used to control a real object because its application corresponds to an open-loop control system and engineers usually complete it with a feedback stabilization system. Hence, there is an obvious need to reformulate the optimal control problem so that its solution can be directly applied to real objects. The paper presents a new extended statement of the optimal control problem. An additional requirement for the control function is introduced to give the system describing the control object properties that will ensure the stability of solutions. The desired control function must provide for the optimal trajectory given the properties of the attractor in the neighbourhood. The solution to the extended optimal control problem can be directly used to control a real object. The paper presents a computational machine learning approach to solving the extended problem of optimal control based on the application of a synthesized optimal control technique. Examples of the practical solution to the stated problem are given to illustrate the efficiency of the approach, where the solution to the conventional optimal control problem is compared with the proposed extended one in the presence of perturbations in models and initial conditions.

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Section: Extended Statement Of the Optimal Control Problemmentioning

confidence: 99%

Extended Statement of the Optimal Control Problem and Machine Learning Approach to Its Solution

Shmalko

Diveev

2022

Mathematical Problems in Engineering

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“…The present article further examines the main provisions of the method of optimal Lyapunov functions, formulated in [5,12,21] at relation to dynamic systems, which are described by ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

Optimal Stabilization in Systems of Linear Differential Equations

Khusainov,

Diblik,

Shatyrko

et al. 2024

JODEA

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This article considers the optimal stabilization problems for complex dynamical systems, which can be described in terms of linear differential equations. At the beginning of the article, general provisions on optimal stabilization and the application of the apparatus of optimal Lyapunov functions for the purpose of solving the formulated problem are given. To ensure consistency and easier understanding of the obtained results, the systems with scalar control are considered first. The main results were obtained for systems with n-dimensional control and the presence of a diagonal matrix in the quality criteria. Finally, the conditions are extended to the case when a matrix of the general form is used in the quality criterion.

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Estimating the Lyapunov Function and Stability of Motion of a System with Equations of Motion with an Asymptotically Expanded Right-Hand Side

Cited by 2 publications

References 6 publications

Extended Statement of the Optimal Control Problem and Machine Learning Approach to Its Solution

Extended Statement of the Optimal Control Problem and Machine Learning Approach to Its Solution

Optimal Stabilization in Systems of Linear Differential Equations

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