arXiv subjects

Andreas Oliveira

Publications and source records attributed to Andreas Oliveira.

4 recordsLinked to original sources

arXiv2026

Time-Varying Perturbations of Contractive Systems With an Application to Safe Stabilization

Perturbation theory for asymptotically stable systems has received sustained attention, leading to many criteria that preserve stability under uncertainty. A limitation of classical stability analysis, however, is that it is inherently equilibrium-dependent. Contractive systems, by contrast, are defined independently of any equilibrium and admit a rich set of robustness bounds. In this letter, we develop new time-varying perturbation conditions for contractive dynamics that preserve incremental exponential stability of the perturbed system and, in specific regimes, guarantee asymptotic convergence to solutions of the nominal dynamics. As an application, we propose a safety filter for steering a nominally contractive system to a desired equilibrium while avoiding an unsafe set, and we present an example illustrating advantages of the proposed method over existing approaches.

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arXiv2026

On incremental and semi-global exponential stability of gradient flows satisfying generalized {\L}ojasiewicz inequalities

The {\L}ojasiewicz inequality characterizes objective-value convergence along gradient flows and, in special cases, yields exponential decay of the cost. However, such results do not directly give rates of convergence in the state. In this paper, we use contraction theory to derive state-space guarantees for gradient systems satisfying generalized {\L}ojasiewicz inequalities. We first show that, when the objective has a unique strongly convex minimizer, the generalized {\L}ojasiewicz inequality implies semi-global exponential stability; on arbitrary compact subsets, this yields exponential stability. We then give two curvature-based sufficient conditions, together with constraints on the {\L}ojasiewicz rate, under which the nonconvex gradient flow is globally incrementally exponentially stable.

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arXiv2025

Modeling Adaptive Tracking of Predictable Stimuli in Electric Fish

The weakly electric fish \emph{Eigenmannia virescens} naturally swims back and forth to stay within a moving refuge, tracking its motion using visual and electrosensory feedback. Previous experiments show that when the refuge oscillates as a low-frequency sinusoid (below about 0.5 Hz), the tracking is nearly perfect, but phase lag increases and gain decreases at higher frequencies. Here, we model this nonlinear behavior as an adaptive internal model principle (IMP) system. Specifically, an adaptive state estimator identifies the \emph{a priori} unknown frequency, and feeds this parameter estimate into a closed-loop IMP-based system built around a lightly damped harmonic oscillator. We prove that the closed-loop tracking error of the IMP-based system, where the online adaptive frequency estimate is used as a surrogate for the unknown frequency, converges exponentially to that of an ideal control system with perfect information about the stimulus. Simulations further show that our model reproduces the fish refuge tracking Bode plot across a wide frequency range. These results establish the theoretical validity of combining the IMP with an adaptive identification process and provide a basic framework in adaptive sensorimotor control.

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arXiv2025

Convex Data-Driven Contraction With Riemannian Metrics

The growing complexity of dynamical systems and advances in data collection necessitates robust data-driven control strategies without explicit system identification and robust synthesis. Data-driven stability has been explored in linear and nonlinear systems, often by turning the problem into a linear or positive semidefinite program. This paper focuses on a new emerging property called contractivity, which refers to the exponential convergence of all system trajectories toward each other under a specified metric. Data-driven closed loop contractivity has been studied for the case of the 2-norm and assuming nonlinearities are Lipschitz bounded in subsets of n dimensional euclidean space. We extend the analysis by considering Riemannian metrics for polynomial dynamics. The key to our derivation is to leverage the convex criteria for closed-loop contraction and duality results to efficiently check infinite dimensional membership constraints. Numerical examples demonstrate the effectiveness of the proposed method for both linear and nonlinear systems, highlighting its potential for robust data-driven contraction.

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