Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games
Abstract This paper proposes a distributed adaptive dynamic programming scheme to investigate the optimal tracking control problem for finite‐horizon non‐linear interconnected systems with constraint inputs under aperiodic sampling. A N‐player nonzero‐sum differential game system is constructed with...
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| Format: | Article |
| Language: | English |
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Wiley
2021-06-01
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| Series: | IET Control Theory & Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1049/cth2.12116 |
| _version_ | 1811223237441355776 |
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| author | Dandan Duan Chunsheng Liu |
| author_facet | Dandan Duan Chunsheng Liu |
| author_sort | Dandan Duan |
| collection | DOAJ |
| description | Abstract This paper proposes a distributed adaptive dynamic programming scheme to investigate the optimal tracking control problem for finite‐horizon non‐linear interconnected systems with constraint inputs under aperiodic sampling. A N‐player nonzero‐sum differential game system is constructed with the presented non‐linear interconnected system and the tracking error system by introducing the augment vectors. To address the problems of constrained‐input and finite‐horizon control, a non‐quadratic utility function and a finite‐horizon cost function are utilized which will arise in the time‐varying Hamilton–Jacobi (HJ) equation. Then, a periodic event‐triggered scheme is designed to realize aperiodic sampling, where the consumption of communication resources is reduced and the Zeno behavior is avoided. Under the designed periodic event‐triggered scheme, the time‐varying HJ equation is almost impossible to get an analytical solution due to its hybrid properties and non‐linearity. Therefore, the critic neural networks are used to estimate the optimal solution of the HJ equation, and the weight update law is constructed to guarantee the uniformly ultimate bounded of approximated errors. Further, the hybrid nonzero‐sum differential game is confirmed to be uniformly ultimate bounded by using the Lyapunov theory. Finally, the obtained distributed PET control strategy is successfully applied to dispose the missile‐target intercepter problem. |
| first_indexed | 2024-04-12T08:29:34Z |
| format | Article |
| id | doaj.art-57f5bd02f3064e5684ecbbcb93796f1a |
| institution | Directory Open Access Journal |
| issn | 1751-8644 1751-8652 |
| language | English |
| last_indexed | 2024-04-12T08:29:34Z |
| publishDate | 2021-06-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Control Theory & Applications |
| spelling | doaj.art-57f5bd02f3064e5684ecbbcb93796f1a2022-12-22T03:40:16ZengWileyIET Control Theory & Applications1751-86441751-86522021-06-011591199121310.1049/cth2.12116Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum gamesDandan Duan0Chunsheng Liu1College of Automation Engineering Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 210016 People's Republic of ChinaCollege of Automation Engineering Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 210016 People's Republic of ChinaAbstract This paper proposes a distributed adaptive dynamic programming scheme to investigate the optimal tracking control problem for finite‐horizon non‐linear interconnected systems with constraint inputs under aperiodic sampling. A N‐player nonzero‐sum differential game system is constructed with the presented non‐linear interconnected system and the tracking error system by introducing the augment vectors. To address the problems of constrained‐input and finite‐horizon control, a non‐quadratic utility function and a finite‐horizon cost function are utilized which will arise in the time‐varying Hamilton–Jacobi (HJ) equation. Then, a periodic event‐triggered scheme is designed to realize aperiodic sampling, where the consumption of communication resources is reduced and the Zeno behavior is avoided. Under the designed periodic event‐triggered scheme, the time‐varying HJ equation is almost impossible to get an analytical solution due to its hybrid properties and non‐linearity. Therefore, the critic neural networks are used to estimate the optimal solution of the HJ equation, and the weight update law is constructed to guarantee the uniformly ultimate bounded of approximated errors. Further, the hybrid nonzero‐sum differential game is confirmed to be uniformly ultimate bounded by using the Lyapunov theory. Finally, the obtained distributed PET control strategy is successfully applied to dispose the missile‐target intercepter problem.https://doi.org/10.1049/cth2.12116Optimisation techniquesInterpolation and function approximation (numerical analysis)AlgebraGame theoryOther topics in statisticsCombinatorial mathematics |
| spellingShingle | Dandan Duan Chunsheng Liu Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games IET Control Theory & Applications Optimisation techniques Interpolation and function approximation (numerical analysis) Algebra Game theory Other topics in statistics Combinatorial mathematics |
| title | Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games |
| title_full | Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games |
| title_fullStr | Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games |
| title_full_unstemmed | Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games |
| title_short | Finite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games |
| title_sort | finite horizon optimal tracking control for constrained input nonlinear interconnected system using aperiodic distributed nonzero sum games |
| topic | Optimisation techniques Interpolation and function approximation (numerical analysis) Algebra Game theory Other topics in statistics Combinatorial mathematics |
| url | https://doi.org/10.1049/cth2.12116 |
| work_keys_str_mv | AT dandanduan finitehorizonoptimaltrackingcontrolforconstrainedinputnonlinearinterconnectedsystemusingaperiodicdistributednonzerosumgames AT chunshengliu finitehorizonoptimaltrackingcontrolforconstrainedinputnonlinearinterconnectedsystemusingaperiodicdistributednonzerosumgames |