A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential Games
This paper investigates three-dimensional pursuit problems in noncooperative stochastic differential games. By introducing a novel polynomial value function capable of addressing high-dimensional dynamic systems, the forward–backward stochastic differential equations (FBSDEs) for optimal strategies...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Aerospace |
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| Online Access: | https://www.mdpi.com/2226-4310/12/1/50 |
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| author | Yu Bai Di Zhou Zhen He |
| author_facet | Yu Bai Di Zhou Zhen He |
| author_sort | Yu Bai |
| collection | DOAJ |
| description | This paper investigates three-dimensional pursuit problems in noncooperative stochastic differential games. By introducing a novel polynomial value function capable of addressing high-dimensional dynamic systems, the forward–backward stochastic differential equations (FBSDEs) for optimal strategies are derived. The uniqueness of the value function under bounded control inputs is rigorously established as a theoretical foundation. The proposed methodology constructs optimal closed-loop feedback strategies for both pursuers and evaders, ensuring state convergence and solution uniqueness. Furthermore, the Lebesgue measure of the barrier surface is computed, enabling the design of strategies for scenarios involving multiple pursuers and evaders. To validate its applicability, the method is applied to missile interception games. Simulations confirm that the optimal strategies enable pursuers to consistently intercept evaders under stochastic dynamics, demonstrating the robustness and practical relevance of the approach in pursuit–evasion problems. |
| format | Article |
| id | doaj-art-22e1a0742e7543cb9897641102954df3 |
| institution | Kabale University |
| issn | 2226-4310 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Aerospace |
| spelling | doaj-art-22e1a0742e7543cb9897641102954df32025-01-24T13:15:37ZengMDPI AGAerospace2226-43102025-01-011215010.3390/aerospace12010050A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential GamesYu Bai0Di Zhou1Zhen He2School of Astronautics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Astronautics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Astronautics, Harbin Institute of Technology, Harbin 150001, ChinaThis paper investigates three-dimensional pursuit problems in noncooperative stochastic differential games. By introducing a novel polynomial value function capable of addressing high-dimensional dynamic systems, the forward–backward stochastic differential equations (FBSDEs) for optimal strategies are derived. The uniqueness of the value function under bounded control inputs is rigorously established as a theoretical foundation. The proposed methodology constructs optimal closed-loop feedback strategies for both pursuers and evaders, ensuring state convergence and solution uniqueness. Furthermore, the Lebesgue measure of the barrier surface is computed, enabling the design of strategies for scenarios involving multiple pursuers and evaders. To validate its applicability, the method is applied to missile interception games. Simulations confirm that the optimal strategies enable pursuers to consistently intercept evaders under stochastic dynamics, demonstrating the robustness and practical relevance of the approach in pursuit–evasion problems.https://www.mdpi.com/2226-4310/12/1/50pursuit dynamicsstochastic differential gamesoptimal closed-loop strategiesforward–backward stochastic differential equations (FBSDEs)Lebesgue measure of barrier surfaces |
| spellingShingle | Yu Bai Di Zhou Zhen He A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential Games Aerospace pursuit dynamics stochastic differential games optimal closed-loop strategies forward–backward stochastic differential equations (FBSDEs) Lebesgue measure of barrier surfaces |
| title | A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential Games |
| title_full | A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential Games |
| title_fullStr | A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential Games |
| title_full_unstemmed | A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential Games |
| title_short | A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential Games |
| title_sort | class of pursuit problems in 3d space via noncooperative stochastic differential games |
| topic | pursuit dynamics stochastic differential games optimal closed-loop strategies forward–backward stochastic differential equations (FBSDEs) Lebesgue measure of barrier surfaces |
| url | https://www.mdpi.com/2226-4310/12/1/50 |
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