Optimal Control Theory

doi:10.1007/0-387-29903-3

Cited by 3 publications

(2 citation statements)

References 203 publications

(286 reference statements)

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“…It was proposed by Bellman in the 1950s and is an extension of Hamilton-Jacobi theory. A number of books exist on these topics including [31,18,32]. A general overview of the optimal control methods for dynamical systems can be found in [17].…”

Section: Methodsmentioning

confidence: 99%

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Explainable Machine Learning Control -- robust control and stability analysis

Quade¹,

Isele²,

Abel³

2020

Preprint

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Recently, the term explainable AI became known as an approach to produce models from artificial intelligence which allow interpretation. Since a long time, there are models of symbolic regression in use that are perfectly explainable and mathematically tractable: in this contribution we demonstrate how to use symbolic regression methods to infer the optimal control of a dynamical system given one or several optimization criteria, or cost functions. In previous publications, network control was achieved by automatized machine learning control using genetic programming. Here, we focus on the subsequent analysis of the analytical expressions which result from the machine learning. In particular, we use AUTO to analyze the stability properties of the controlled oscillator system which served as our model. As a result, we show that there is a considerable advantage of explainable models over less accessible neural networks.

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Section: Methodsmentioning

confidence: 99%

“…If the control is useful is decided heavily by the stability of the controlled system. This stability can be determined by standard mathematical methods for linear theory can be used [18,19]. However, for nonlinear, extended and consequently complex systems, linear theory to determine a control may fail.…”

Section: Introductionmentioning

confidence: 99%

Explainable Machine Learning Control -- robust control and stability analysis

Quade¹,

Isele²,

Abel³

2020

Preprint

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Linear Interpolation of Program Control with Respect to a Multidimensional Parameter in the Convergence Problem

Ushakov,

Ershov,

Ershova

et al. 2023

Communications in Computer and Information Science

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On a Discrete Model of Optimal Advertising

Adukov

Adukova²,

Kudryavtsev³

2015

JCEM

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The continuous models are considered in the most works on optimal advertising. Articles on the discrete-time models are more rare because in this case it is dicult to obtain an explicit solution. In this paper a new discrete model of optimal advertising for a monopolist-seller of a new goods is proposed. In the model, the dynamics is given by a nonlinear dierence equation. The non-linearity depends on a parameter σ, 0 < σ < 1, i.e. a continuous family of the models is considered. The discrete versions of the Vidale Wolfe model and the Sethi model are particular cases of this model. The seller's problem is to maximize its prot up to the nite horizon T by the optimal advertising expenditure. This problem is a discrete multistep optimal control problem, where an advertising expenditure is a control variable. For our model the optimal control problem can be solved explicitly. The Bellman method of dynaming programming is used to study the problem. Explicit recurrence relations for the optimal control and the market share up to the step t, t = 1,. .. , T , are obtained under the assumption that the dierence equation of the model has a solution. Sucient conditions on the parameters of the model, which ensure the existence of a solution, are found. The proposed algorithm is implemented as the procedure OptimalAdvertising in the package Maple. Numerical experiments with the procedure were carried out.

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Optimal Control Theory

Cited by 3 publications

References 203 publications

Explainable Machine Learning Control -- robust control and stability analysis

Explainable Machine Learning Control -- robust control and stability analysis

Linear Interpolation of Program Control with Respect to a Multidimensional Parameter in the Convergence Problem

On a Discrete Model of Optimal Advertising

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