Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle
This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of the target being detected by...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/19/2386 |
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| author | Andrey A. Galyaev Pavel V. Lysenko Evgeny Y. Rubinovich |
| author_facet | Andrey A. Galyaev Pavel V. Lysenko Evgeny Y. Rubinovich |
| author_sort | Andrey A. Galyaev |
| collection | DOAJ |
| description | This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of the target being detected by the search vehicle exceeds a certain threshold value. Interception was carried out by a controlled vehicle (defender) protecting the target. An analytical estimation of this detection probability is proposed. The interception problem was formulated as an optimal stochastic control problem, which was transformed to a deterministic optimization problem. As a result, the optimal control law of the defender was found, and the optimal interception time was estimated. The deterministic problem is a simplified version of the problem whose optimal solution provides a suboptimal solution to the stochastic problem. The obtained control law was compared with classic guidance methods. All the results were obtained analytically and validated with a computer simulation. |
| first_indexed | 2024-03-10T06:54:52Z |
| format | Article |
| id | doaj.art-45858aa7b5214150849d6ed0088b1649 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:54:52Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-45858aa7b5214150849d6ed0088b16492023-11-22T16:29:35ZengMDPI AGMathematics2227-73902021-09-01919238610.3390/math9192386Optimal Stochastic Control in the Interception Problem of a Randomly Tacking VehicleAndrey A. Galyaev0Pavel V. Lysenko1Evgeny Y. Rubinovich2Institute of Control Sciences of RAS, 117997 Moscow, RussiaInstitute of Control Sciences of RAS, 117997 Moscow, RussiaInstitute of Control Sciences of RAS, 117997 Moscow, RussiaThis article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of the target being detected by the search vehicle exceeds a certain threshold value. Interception was carried out by a controlled vehicle (defender) protecting the target. An analytical estimation of this detection probability is proposed. The interception problem was formulated as an optimal stochastic control problem, which was transformed to a deterministic optimization problem. As a result, the optimal control law of the defender was found, and the optimal interception time was estimated. The deterministic problem is a simplified version of the problem whose optimal solution provides a suboptimal solution to the stochastic problem. The obtained control law was compared with classic guidance methods. All the results were obtained analytically and validated with a computer simulation.https://www.mdpi.com/2227-7390/9/19/2386optimal stochastic controlpath planning2D random searchinterception |
| spellingShingle | Andrey A. Galyaev Pavel V. Lysenko Evgeny Y. Rubinovich Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle Mathematics optimal stochastic control path planning 2D random search interception |
| title | Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle |
| title_full | Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle |
| title_fullStr | Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle |
| title_full_unstemmed | Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle |
| title_short | Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle |
| title_sort | optimal stochastic control in the interception problem of a randomly tacking vehicle |
| topic | optimal stochastic control path planning 2D random search interception |
| url | https://www.mdpi.com/2227-7390/9/19/2386 |
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