Backstepping Design for Incremental Input-to-State Stabilization of Unknown Systems

David Smith Sundarsingh; Bhabani Shankar Dey; Pushpak Jagtap

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arXiv · 2411.01872

Backstepping Design for Incremental Input-to-State Stabilization of Unknown Systems

David Smith Sundarsingh·Bhabani Shankar Dey·Pushpak Jagtap

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Abstract

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.

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David Smith Sundarsingh, Bhabani Shankar Dey, Pushpak Jagtap. 2024-11-04. Backstepping Design for Incremental Input-to-State Stabilization of Unknown Systems. https://arxiv.org/abs/2411.01872

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