Stabilization of Nonlinear Systems with State-Dependent Representation: From Model-Based to Direct Data-Driven Control
Year: 2025
Type: preprint
Abstract: This paper presents a framework for stabilizing nonlinear systems in state-dependent form. We first develop a model-based formulation that constructs a polytope enclosing the state-dependent system matrices over a prescribed state region and then synthesizes the controller by solving linear matrix inequalities (LMIs) at the polytope vertices. To establish stability and region of attraction (ROA) guarantees from the vertex LMIs, we develop a model-based mechanism and then apply it to direct data-driven control. In the data-driven setting, we use a known library of basis functions to represent the dynamics with unknown coefficients. A polytope captures the basis-function variation over a state region, and a data-consistent set characterizes the noise-induced coefficient uncertainty. This data-consistent set is incorporated directly into the vertex LMIs via Petersen's lemma. Building on our model-based mechanism, the resulting vertex LMIs yield a controller that guarantees stability and provides a certified ROA. The data-driven formulation further establishes disturbance-robustness guarantees and ROA estimates under input saturation. Numerical simulations and physical experiments demonstrate the effectiveness of the proposed controller.
Source: arXiv (Cornell University)
Authors: Li, Lidong, Huang, Rui, Zhao, Lin
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415953474
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