Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs
This paper investigates the problem of fixed-time distributed time-varying optimization of a nonlinear fractional-order multiagent system (FOMAS) over a weight-unbalanced directed graph (digraph), where the heterogeneous unknown nonlinear functions and disturbances are involved. The aim is to cooper...
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MDPI AG
2023-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/11/813 |
| _version_ | 1797459295131926528 |
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| author | Kun Wang Ping Gong Zhiyao Ma |
| author_facet | Kun Wang Ping Gong Zhiyao Ma |
| author_sort | Kun Wang |
| collection | DOAJ |
| description | This paper investigates the problem of fixed-time distributed time-varying optimization of a nonlinear fractional-order multiagent system (FOMAS) over a weight-unbalanced directed graph (digraph), where the heterogeneous unknown nonlinear functions and disturbances are involved. The aim is to cooperatively minimize a convex time-varying global cost function produced by a sum of time-varying local cost functions within a fixed time, where each time-varying local cost function does not have to be convex. Using a three-step design procedure, a fully distributed fixed-time optimization algorithm is constructed to achieve the objective. The first step is to design a fully distributed fixed-time estimator to estimate some centralized optimization terms within a fixed time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>0</mn></msub></semantics></math></inline-formula>. The second step is to develop a novel discontinuous fixed-time sliding mode algorithm with nominal controller to derive all the agents to the sliding-mode surface within a fixed time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>1</mn></msub></semantics></math></inline-formula>, and meanwhile the dynamics of each agent is described by a single-integrator MAS with nominal controller. In the third step, a novel estimator-based fully distributed fixed-time nominal controller for the single-integrator MAS is presented to guarantee all agents reach consensus within a fixed time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>2</mn></msub></semantics></math></inline-formula>, and afterwards minimize the convex time-varying global cost function within a fixed time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>3</mn></msub></semantics></math></inline-formula>. The upper bound of each fixed time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mspace width="3.33333pt"></mspace><mrow><mo>(</mo><mi>m</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is given explicitly, which is independent of the initial states. Finally, a numerical example is provided to validate the results. |
| first_indexed | 2024-03-09T16:49:25Z |
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| id | doaj.art-f4d97a837fdf414087eb0d8fbcc9832b |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T16:49:25Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
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| series | Fractal and Fractional |
| spelling | doaj.art-f4d97a837fdf414087eb0d8fbcc9832b2023-11-24T14:43:04ZengMDPI AGFractal and Fractional2504-31102023-11-0171181310.3390/fractalfract7110813Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced DigraphsKun Wang0Ping Gong1Zhiyao Ma2School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, ChinaSchool of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, ChinaCollege of Science, Liaoning University of Technology, Jinzhou 121001, ChinaThis paper investigates the problem of fixed-time distributed time-varying optimization of a nonlinear fractional-order multiagent system (FOMAS) over a weight-unbalanced directed graph (digraph), where the heterogeneous unknown nonlinear functions and disturbances are involved. The aim is to cooperatively minimize a convex time-varying global cost function produced by a sum of time-varying local cost functions within a fixed time, where each time-varying local cost function does not have to be convex. Using a three-step design procedure, a fully distributed fixed-time optimization algorithm is constructed to achieve the objective. The first step is to design a fully distributed fixed-time estimator to estimate some centralized optimization terms within a fixed time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>0</mn></msub></semantics></math></inline-formula>. The second step is to develop a novel discontinuous fixed-time sliding mode algorithm with nominal controller to derive all the agents to the sliding-mode surface within a fixed time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>1</mn></msub></semantics></math></inline-formula>, and meanwhile the dynamics of each agent is described by a single-integrator MAS with nominal controller. In the third step, a novel estimator-based fully distributed fixed-time nominal controller for the single-integrator MAS is presented to guarantee all agents reach consensus within a fixed time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>2</mn></msub></semantics></math></inline-formula>, and afterwards minimize the convex time-varying global cost function within a fixed time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>3</mn></msub></semantics></math></inline-formula>. The upper bound of each fixed time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mspace width="3.33333pt"></mspace><mrow><mo>(</mo><mi>m</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is given explicitly, which is independent of the initial states. Finally, a numerical example is provided to validate the results.https://www.mdpi.com/2504-3110/7/11/813fixed-time distributed optimizationfractional-order multiagent systemsweight-unbalanced digraphtime-varying cost functions |
| spellingShingle | Kun Wang Ping Gong Zhiyao Ma Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs Fractal and Fractional fixed-time distributed optimization fractional-order multiagent systems weight-unbalanced digraph time-varying cost functions |
| title | Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs |
| title_full | Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs |
| title_fullStr | Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs |
| title_full_unstemmed | Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs |
| title_short | Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs |
| title_sort | fixed time distributed time varying optimization for nonlinear fractional order multiagent systems with unbalanced digraphs |
| topic | fixed-time distributed optimization fractional-order multiagent systems weight-unbalanced digraph time-varying cost functions |
| url | https://www.mdpi.com/2504-3110/7/11/813 |
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