Backstepping Design for Incremental Input-to-State Stabilization of Unknown Systems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916466287181824 |
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| author | Sundarsingh, David Smith Dey, Bhabani Shankar Jagtap, Pushpak |
| author_facet | Sundarsingh, David Smith Dey, Bhabani Shankar Jagtap, Pushpak |
| contents | Incremental stability of dynamical systems ensures the convergence of trajectories from different initial conditions towards each other rather than a fixed trajectory or equilibrium point. Here, we introduce and characterize a novel class of incremental Lyapunov functions, an incremental stability notion known as Incremental Input-to-State practical Stability (δ-ISpS). Using Gaussian Process, we learn the unknown dynamics of a class of control systems. We then present a backstepping control design scheme that provides state-feedback controllers that render the partially unknown control system δ-ISpS. To show the effectiveness of the proposed controller, we implement it in two case studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01872 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Backstepping Design for Incremental Input-to-State Stabilization of Unknown Systems Sundarsingh, David Smith Dey, Bhabani Shankar Jagtap, Pushpak Systems and Control Dynamical Systems Incremental stability of dynamical systems ensures the convergence of trajectories from different initial conditions towards each other rather than a fixed trajectory or equilibrium point. Here, we introduce and characterize a novel class of incremental Lyapunov functions, an incremental stability notion known as Incremental Input-to-State practical Stability (δ-ISpS). Using Gaussian Process, we learn the unknown dynamics of a class of control systems. We then present a backstepping control design scheme that provides state-feedback controllers that render the partially unknown control system δ-ISpS. To show the effectiveness of the proposed controller, we implement it in two case studies. |
| title | Backstepping Design for Incremental Input-to-State Stabilization of Unknown Systems |
| topic | Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2411.01872 |