Robust switching control design for matrix second order systems: Application to robotic cane platform
This paper addresses the switching control design problem for a class of nonlinear matrix second-order systems that characterize the dynamics of robotic and multibody systems. These systems are inherently characterized by significant nonlinearities and are subject to uncertainties, parameter variati...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-09-01
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| Series: | Results in Control and Optimization |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666720725000839 |
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| author | Ivan Yupanqui Macarena Vilca Renzo Mendoza Alain Chupa Diego Arce Jesús Alan Calderón Bryan Bastidas Miguel Badillo |
| author_facet | Ivan Yupanqui Macarena Vilca Renzo Mendoza Alain Chupa Diego Arce Jesús Alan Calderón Bryan Bastidas Miguel Badillo |
| author_sort | Ivan Yupanqui |
| collection | DOAJ |
| description | This paper addresses the switching control design problem for a class of nonlinear matrix second-order systems that characterize the dynamics of robotic and multibody systems. These systems are inherently characterized by significant nonlinearities and are subject to uncertainties, parameter variations, and external disturbances, which pose substantial challenges for control design. Analytical solutions for such control problems are often intractable, necessitating the use of numerical optimization techniques. This study presents sufficient conditions, derived from Lyapunov stability theory, for synthesizing switching feedback controllers that ensure system stability with guaranteed H∞ performance. The approach leverages the Linear Parameter Varying (LPV) representation of the nonlinear dynamics through Takagi–Sugeno (T-S) modeling methodology. The proposed stability conditions are formulated as Linear Matrix Inequalities (LMIs), enabling efficient computation using standard convex optimization software. Comprehensive simulation studies demonstrate that the proposed switching control strategy, applicable to a broad class of nonlinear matrix second-order systems, significantly outperforms conventional weighted gain-scheduling approaches in terms of feasibility regions and H∞ performance indices. Experimental validation on a robotic cane platform confirms the practical effectiveness of the proposed methodology, achieving nice dynamic performance and robust disturbance rejection capabilities. |
| format | Article |
| id | doaj-art-dcb618a0b258424daf1baae0d883f5ec |
| institution | DOAJ |
| issn | 2666-7207 |
| language | English |
| publishDate | 2025-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj-art-dcb618a0b258424daf1baae0d883f5ec2025-08-20T03:12:56ZengElsevierResults in Control and Optimization2666-72072025-09-012010059710.1016/j.rico.2025.100597Robust switching control design for matrix second order systems: Application to robotic cane platformIvan Yupanqui0Macarena Vilca1Renzo Mendoza2Alain Chupa3Diego Arce4Jesús Alan Calderón5Bryan Bastidas6Miguel Badillo7Corresponding author.; Engineering Department, Pontificia Universidad Católica del Perú, San Miguel, Lima 15088, PeruEngineering Department, Pontificia Universidad Católica del Perú, San Miguel, Lima 15088, PeruEngineering Department, Pontificia Universidad Católica del Perú, San Miguel, Lima 15088, PeruEngineering Department, Pontificia Universidad Católica del Perú, San Miguel, Lima 15088, PeruEngineering Department, Pontificia Universidad Católica del Perú, San Miguel, Lima 15088, PeruEngineering Department, Pontificia Universidad Católica del Perú, San Miguel, Lima 15088, PeruEngineering Department, Pontificia Universidad Católica del Perú, San Miguel, Lima 15088, PeruEngineering Department, Pontificia Universidad Católica del Perú, San Miguel, Lima 15088, PeruThis paper addresses the switching control design problem for a class of nonlinear matrix second-order systems that characterize the dynamics of robotic and multibody systems. These systems are inherently characterized by significant nonlinearities and are subject to uncertainties, parameter variations, and external disturbances, which pose substantial challenges for control design. Analytical solutions for such control problems are often intractable, necessitating the use of numerical optimization techniques. This study presents sufficient conditions, derived from Lyapunov stability theory, for synthesizing switching feedback controllers that ensure system stability with guaranteed H∞ performance. The approach leverages the Linear Parameter Varying (LPV) representation of the nonlinear dynamics through Takagi–Sugeno (T-S) modeling methodology. The proposed stability conditions are formulated as Linear Matrix Inequalities (LMIs), enabling efficient computation using standard convex optimization software. Comprehensive simulation studies demonstrate that the proposed switching control strategy, applicable to a broad class of nonlinear matrix second-order systems, significantly outperforms conventional weighted gain-scheduling approaches in terms of feasibility regions and H∞ performance indices. Experimental validation on a robotic cane platform confirms the practical effectiveness of the proposed methodology, achieving nice dynamic performance and robust disturbance rejection capabilities.http://www.sciencedirect.com/science/article/pii/S2666720725000839Nonlinear matrix second order systemsT-S modelingSwitching controlLinear matrix inequalities |
| spellingShingle | Ivan Yupanqui Macarena Vilca Renzo Mendoza Alain Chupa Diego Arce Jesús Alan Calderón Bryan Bastidas Miguel Badillo Robust switching control design for matrix second order systems: Application to robotic cane platform Results in Control and Optimization Nonlinear matrix second order systems T-S modeling Switching control Linear matrix inequalities |
| title | Robust switching control design for matrix second order systems: Application to robotic cane platform |
| title_full | Robust switching control design for matrix second order systems: Application to robotic cane platform |
| title_fullStr | Robust switching control design for matrix second order systems: Application to robotic cane platform |
| title_full_unstemmed | Robust switching control design for matrix second order systems: Application to robotic cane platform |
| title_short | Robust switching control design for matrix second order systems: Application to robotic cane platform |
| title_sort | robust switching control design for matrix second order systems application to robotic cane platform |
| topic | Nonlinear matrix second order systems T-S modeling Switching control Linear matrix inequalities |
| url | http://www.sciencedirect.com/science/article/pii/S2666720725000839 |
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