# Research of Trajectory Optimization Approaches in Synthesized Optimal Control

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## Abstract

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## 1. Introduction

## 2. Problem of Optimal Movement on Trajectory Determined by a Set of Points

## 3. Synthesized Optimal Control

## 4. Numerical Methods

#### 4.1. Methods for the Control Synthesis Problem

#### 4.2. Methods for the Optimal Control Problem

## 5. Computational Example

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Optimal trajectory ${x}_{1}\left(t\right)$ (black) and optimal control ${x}_{1}^{*}\left(t\right)$ (red).

**Figure 3.**Optimal trajectory ${x}_{2}\left(t\right)$ (black) and optimal control ${x}_{2}^{*}\left(t\right)$ (red).

**Figure 4.**Optimal trajectory ${x}_{3}\left(t\right)$ (black) and optimal control ${x}_{3}^{*}\left(t\right)$ (red).

**Figure 6.**Optimal trajectory ${x}_{1}\left(t\right)$ (black) and optimal control ${x}_{1}^{*}\left(t\right)$ (red) for movement on square.

**Figure 7.**Optimal trajectory ${x}_{2}\left(t\right)$ (black) and optimal control ${x}_{2}^{*}\left(t\right)$ (red) for movement on square.

**Figure 8.**Optimal trajectory ${x}_{3}\left(t\right)$ (black) and optimal control ${x}_{3}^{*}\left(t\right)$ (red) for movement on square.

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Diveev, A.; Shmalko, E. Research of Trajectory Optimization Approaches in Synthesized Optimal Control. *Symmetry* **2021**, *13*, 336.
https://doi.org/10.3390/sym13020336

**AMA Style**

Diveev A, Shmalko E. Research of Trajectory Optimization Approaches in Synthesized Optimal Control. *Symmetry*. 2021; 13(2):336.
https://doi.org/10.3390/sym13020336

**Chicago/Turabian Style**

Diveev, Askhat, and Elizaveta Shmalko. 2021. "Research of Trajectory Optimization Approaches in Synthesized Optimal Control" *Symmetry* 13, no. 2: 336.
https://doi.org/10.3390/sym13020336