arXiv subjects

Nicolas Espitia

Publications and source records attributed to Nicolas Espitia.

6 recordsLinked to original sources

arXiv2026

Event-Triggered Gain Scheduling of 2 x 2 Linear Hyperbolic PDEs via Neural Operators (Full Version)

This paper introduces a new framework for event-triggered gain scheduling applied to linear hyperbolic Partial Differential Equations (PDEs) with time- and space-varying coefficients. The approach leverages neural operators to address the challenges of real-time control in such systems. At each triggering time, the control input is designed using the classical static backstepping control law, while the gains of the boundary controller are updated according to the triggering mechanism and the spatial variation of the coefficients. Neural operators are employed to learn the mapping between the system parameters in the PDEs and the corresponding backstepping kernels. By integrating neural operators into the event-triggered framework, we eliminate the need to repeatedly solve complex kernel equations at every triggering instant, thereby reducing computational overhead while ensuring closed-loop stability. The proposed method is validated through theoretical analysis and numerical simulations, demonstrating its effectiveness and strong potential for real-time control of time-varying hyperbolic PDE systems.

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arXiv2025

Prescribed-Time Newton Extremum Seeking using Delays and Time-Periodic Gains

We study prescribed-time extremum seeking (PT-ES) for scalar maps in the presence of time delays. The PT-ES problem has been studied by Yilmaz and Krstic in 2023 using chirpy probing and time-varying gains that grow unbounded. To alleviate the gain singularity, in this paper we present an alternative approach, employing delays with bounded time-periodic gains, for achieving prescribed-time convergence to the extremum. Our results are not extensions or refinements of earlier works, but a new methodological direction --applicable even when the map has no delay. The main PT-ES algorithm compensates the map's delay and uses perturbation-based and the Newton (rather than gradient) approaches. With the help of averaging theorems in infinite dimension, specifically Retarded Functional Differential Equations (RFDEs), we conduct a prescribed-time convergence analysis on a suitable averaged target ES system, which contains the time-periodic gains of the map and feedback delays. We further extend our method to multivariable static maps and illustrate our results through numerical simulations.

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arXiv2023

Prescribed-Time Control in Switching Systems with Resets: A Hybrid Dynamical Systems Approach

We consider the problem of achieving prescribed-time stability (PT-S) in a class of hybrid dynamical systems that incorporate switching nonlinear dynamics, exogenous inputs, and resets. By "prescribed-time stability", we refer to the property of having the states converge to a particular compact set of interest before a given time defined a priori by the user. We focus on dynamical systems that achieve this property via time-varying gains. For continuous-time systems, this approach has received significant attention in recent years, with various applications in control, optimization, and estimation problems. However, its extensions beyond continuous-time systems have been limited. This gap motivates this paper, which introduces a novel class of switching conditions for switching systems with resets that incorporate time-varying gains, ensuring the PT-S property even in the presence of unstable modes. The analysis leverages tools from hybrid dynamical system's theory, and a contraction-dilation property that is established for the hybrid time domains of the solutions of the system. We present the model and main results in a general framework and subsequently apply them to three novel applications: (a) PT regulation of switching plants with no common Lyapunov functions; (b) PT control of dynamic plants with uncertainty and intermittent feedback; and (c) PT decision-making in non-cooperative switching games via hybrid Nash seeking dynamics.

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arXiv2021

Observer-based Event-triggered Boundary Control of a Class of Reaction-Diffusion PDEs

This paper presents an observer-based event-triggered boundary control strategy for a class of reaction-diffusion PDEs with Robin actuation. The observer only requires boundary measurements. The control approach consists of a backstepping output feedback boundary controller, derived using estimated states, and a dynamic triggering condition, which determines the time instants at which the control input needs to be updated. It is shown that under the proposed observer-based event-triggered boundary control approach, there is a minimal dwell-time between two triggering instants independent of initial conditions. Furthermore, the well-posedness and the global exponential convergence of the closed-loop system to the equilibrium point are established. A simulation example is provided to validate the theoretical developments.

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arXiv2020

Event-triggered gain scheduling of reaction-diffusion PDEs

This paper deals with the problem of boundary stabilization of 1D reaction-diffusion PDEs with a time- and space- varying reaction coefficient. The boundary control design relies on the backstepping approach. The gains of the boundary control are scheduled under two suitable event-triggered mechanisms. More precisely, gains are computed/updated on events according to two state-dependent event-triggering conditions: static-based and dynamic-based conditions, under which, the Zeno behavior is avoided and well-posedness as well as exponential stability of the closed-loop system are guaranteed. Numerical simulations are presented to illustrate the results.

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arXiv2019

Event-triggered boundary control of constant-parameter reaction-diffusion PDEs: a small-gain approach

This paper deals with an event-triggered boundary control of constant-parameters reaction-diffusion PDE systems. The approach relies on the emulation of backstepping control along with a suitable triggering condition which establishes the time instants at which the control value needs to be sampled/updated. In this paper, it is shown that under the proposed event-triggered boundary control, there exists a minimal dwell-time (independent of the initial condition) between two triggering times and furthermore the well-posedness and global exponential stability are guaranteed. The analysis follows small-gain arguments and builds on recent papers on sampled-data control for this kind of PDE. A simulation example is presented to validate the theoretical results.

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