# An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

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## Abstract

**:**

## 1. Introduction

## 2. Problem Statement

## 3. The Cost-Functional Increment Formulas

## 4. Variational Maximum Principle

**Theorem**

**1.**

- We choose an arbitrary admissible control $u=u\left(t\right)$. Then, we calculate $y(t,u)$ and $\psi (s,t)$.

## 5. Illustrative Example

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ODE | ordinary differential equation |

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**MDPI and ACS Style**

Arguchintsev, A.; Poplevko, V.
An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations. *Games* **2021**, *12*, 23.
https://doi.org/10.3390/g12010023

**AMA Style**

Arguchintsev A, Poplevko V.
An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations. *Games*. 2021; 12(1):23.
https://doi.org/10.3390/g12010023

**Chicago/Turabian Style**

Arguchintsev, Alexander, and Vasilisa Poplevko.
2021. "An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations" *Games* 12, no. 1: 23.
https://doi.org/10.3390/g12010023