TWO-POINT BOUNDARY PROBLEM SOLUTION BY NON-GRADIENT RANDOM SEARCH METHOD
The numerical solution of two-point boundary problem when determining optimal control of dynamical system by means of Pontryagin’s maximum principle is considered. The initial conditions of conjugate set of equations are determined by use of non-gradient random search method.The non-gradient random...
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Belarusian National Technical University
2016-03-01
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| Series: | Системный анализ и прикладная информатика |
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| Online Access: | https://sapi.bntu.by/jour/article/view/87 |
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| author | V. A. Malkin |
| author_facet | V. A. Malkin |
| author_sort | V. A. Malkin |
| collection | DOAJ |
| description | The numerical solution of two-point boundary problem when determining optimal control of dynamical system by means of Pontryagin’s maximum principle is considered. The initial conditions of conjugate set of equations are determined by use of non-gradient random search method.The non-gradient random search method based on application of stochastic procedures for range of problems solving, including the deterministic ones. When solving the task of optimal control estimation of dynamical system by means of Pontryagin’s maximum principle the initial conditions of conjugate set of equations must be determined, provided that dynamical system’s variables values meet the known terminal conditions Y(tk).The problem’s solution lie in random selection of vector of initial conditions in some actual range, numerical integration of basic and conjugate systems and subsequent processing of findings. Statistic processing gives the mean and RMS estimations of initial conditions values, providing terminal conditions values hit in some domain Q0 relative to Y(tk) point. For the purpose of ensuring of representative sampling for mean and RMS values estimation the adaptive recurrent search procedure with stepby-step domain Q0 contraction is introduced. The initial conditions of conjugate set of equations on the next search stage are determined on a base of sample estimates of distribution’s parameters.The example problem solution for thirst-order control object is given. The findings confirm the possibility of proposed approach utilization for optimal control synthesis of dynamical system by means of Pontryagin’s maximum principle. |
| format | Article |
| id | doaj-art-8ac268770ac54121a4a364ddac0f6f84 |
| institution | Kabale University |
| issn | 2309-4923 2414-0481 |
| language | English |
| publishDate | 2016-03-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Системный анализ и прикладная информатика |
| spelling | doaj-art-8ac268770ac54121a4a364ddac0f6f842025-02-03T05:16:55ZengBelarusian National Technical UniversityСистемный анализ и прикладная информатика2309-49232414-04812016-03-0101293478TWO-POINT BOUNDARY PROBLEM SOLUTION BY NON-GRADIENT RANDOM SEARCH METHODV. A. Malkin0Military Academy of the Republic of BelarusThe numerical solution of two-point boundary problem when determining optimal control of dynamical system by means of Pontryagin’s maximum principle is considered. The initial conditions of conjugate set of equations are determined by use of non-gradient random search method.The non-gradient random search method based on application of stochastic procedures for range of problems solving, including the deterministic ones. When solving the task of optimal control estimation of dynamical system by means of Pontryagin’s maximum principle the initial conditions of conjugate set of equations must be determined, provided that dynamical system’s variables values meet the known terminal conditions Y(tk).The problem’s solution lie in random selection of vector of initial conditions in some actual range, numerical integration of basic and conjugate systems and subsequent processing of findings. Statistic processing gives the mean and RMS estimations of initial conditions values, providing terminal conditions values hit in some domain Q0 relative to Y(tk) point. For the purpose of ensuring of representative sampling for mean and RMS values estimation the adaptive recurrent search procedure with stepby-step domain Q0 contraction is introduced. The initial conditions of conjugate set of equations on the next search stage are determined on a base of sample estimates of distribution’s parameters.The example problem solution for thirst-order control object is given. The findings confirm the possibility of proposed approach utilization for optimal control synthesis of dynamical system by means of Pontryagin’s maximum principle.https://sapi.bntu.by/jour/article/view/87dynamical system, optimal control, pontryagin’s maximum principle, non-gradient random search method |
| spellingShingle | V. A. Malkin TWO-POINT BOUNDARY PROBLEM SOLUTION BY NON-GRADIENT RANDOM SEARCH METHOD Системный анализ и прикладная информатика dynamical system, optimal control, pontryagin’s maximum principle, non-gradient random search method |
| title | TWO-POINT BOUNDARY PROBLEM SOLUTION BY NON-GRADIENT RANDOM SEARCH METHOD |
| title_full | TWO-POINT BOUNDARY PROBLEM SOLUTION BY NON-GRADIENT RANDOM SEARCH METHOD |
| title_fullStr | TWO-POINT BOUNDARY PROBLEM SOLUTION BY NON-GRADIENT RANDOM SEARCH METHOD |
| title_full_unstemmed | TWO-POINT BOUNDARY PROBLEM SOLUTION BY NON-GRADIENT RANDOM SEARCH METHOD |
| title_short | TWO-POINT BOUNDARY PROBLEM SOLUTION BY NON-GRADIENT RANDOM SEARCH METHOD |
| title_sort | two point boundary problem solution by non gradient random search method |
| topic | dynamical system, optimal control, pontryagin’s maximum principle, non-gradient random search method |
| url | https://sapi.bntu.by/jour/article/view/87 |
| work_keys_str_mv | AT vamalkin twopointboundaryproblemsolutionbynongradientrandomsearchmethod |