Synthesis of Control and State Observer for Weakly Nonlinear Systems Based on the Pseudo-Linearization Technique
In this paper, an approach to the construction of nonlinear output tracking control on a finite time interval for a class of weakly nonlinear systems with state-dependent coefficients is considered. The proposed method of control synthesis consists of two main stages. At the first stage, a nonlinear...
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Yaroslavl State University
2017-12-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/616 |
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| author | Dmitry A. Makarov |
| author_facet | Dmitry A. Makarov |
| author_sort | Dmitry A. Makarov |
| collection | DOAJ |
| description | In this paper, an approach to the construction of nonlinear output tracking control on a finite time interval for a class of weakly nonlinear systems with state-dependent coefficients is considered. The proposed method of control synthesis consists of two main stages. At the first stage, a nonlinear state feedback regulator is constructed by using a previously proposed control algorithm based on the State Dependent Riccati Equation (SDRE). At the second stage, the problem of fullorder observer construction is formulated and then it is reduced to the differential game problem. The form of its solution is obtained with the help of the guaranteed (minimax) control principle, which allows to find the best observer coefficients with respect to a given functional considering the worstcase uncertainty realization. The form of the obtained equations made it possible to use the algorithm from the first stage to determine the observer matrix. The proposed approach is characterized by the nonapplicability of the estimation and control separation principle used for linear systems, since the matrix of observer coefficients turned out to be dependent on the feedback coefficients matrix. The use of numerical-analytical procedures for determination of observer and feedback coefficients matrices significantly reduces the computational complexity of the control algorithm. |
| format | Article |
| id | doaj-art-b4e0a7262903471b8701c78a54e5eb7b |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2017-12-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-b4e0a7262903471b8701c78a54e5eb7b2025-08-20T04:00:19ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172017-12-0124680281010.18255/1818-1015-2017-6-802-810450Synthesis of Control and State Observer for Weakly Nonlinear Systems Based on the Pseudo-Linearization TechniqueDmitry A. Makarov0«Technologies Of System Analysis» Ltd, Institute for Systems Analysis, Federal Research Center «Computer Science and Control» of Russian Academy of SciencesIn this paper, an approach to the construction of nonlinear output tracking control on a finite time interval for a class of weakly nonlinear systems with state-dependent coefficients is considered. The proposed method of control synthesis consists of two main stages. At the first stage, a nonlinear state feedback regulator is constructed by using a previously proposed control algorithm based on the State Dependent Riccati Equation (SDRE). At the second stage, the problem of fullorder observer construction is formulated and then it is reduced to the differential game problem. The form of its solution is obtained with the help of the guaranteed (minimax) control principle, which allows to find the best observer coefficients with respect to a given functional considering the worstcase uncertainty realization. The form of the obtained equations made it possible to use the algorithm from the first stage to determine the observer matrix. The proposed approach is characterized by the nonapplicability of the estimation and control separation principle used for linear systems, since the matrix of observer coefficients turned out to be dependent on the feedback coefficients matrix. The use of numerical-analytical procedures for determination of observer and feedback coefficients matrices significantly reduces the computational complexity of the control algorithm.https://www.mais-journal.ru/jour/article/view/616tracking problemnonlinear controlstate-dependent riccati equationminimax control |
| spellingShingle | Dmitry A. Makarov Synthesis of Control and State Observer for Weakly Nonlinear Systems Based on the Pseudo-Linearization Technique Моделирование и анализ информационных систем tracking problem nonlinear control state-dependent riccati equation minimax control |
| title | Synthesis of Control and State Observer for Weakly Nonlinear Systems Based on the Pseudo-Linearization Technique |
| title_full | Synthesis of Control and State Observer for Weakly Nonlinear Systems Based on the Pseudo-Linearization Technique |
| title_fullStr | Synthesis of Control and State Observer for Weakly Nonlinear Systems Based on the Pseudo-Linearization Technique |
| title_full_unstemmed | Synthesis of Control and State Observer for Weakly Nonlinear Systems Based on the Pseudo-Linearization Technique |
| title_short | Synthesis of Control and State Observer for Weakly Nonlinear Systems Based on the Pseudo-Linearization Technique |
| title_sort | synthesis of control and state observer for weakly nonlinear systems based on the pseudo linearization technique |
| topic | tracking problem nonlinear control state-dependent riccati equation minimax control |
| url | https://www.mais-journal.ru/jour/article/view/616 |
| work_keys_str_mv | AT dmitryamakarov synthesisofcontrolandstateobserverforweaklynonlinearsystemsbasedonthepseudolinearizationtechnique |