arXiv subjects

Diego Gutiérrez-Oribio

Publications and source records attributed to Diego Gutiérrez-Oribio.

8 recordsLinked to original sources

arXiv2026

Zero-Crossing Time Lower Bounds for the Homogeneous Super-Twisting Algorithm

High-frequency switching and chattering are well-known problems in sliding-mode control. Although the super-twisting algorithm produces a continuous control input, the sliding variable may still cross zero repeatedly near the sliding manifold. This paper studies how fast these crossings can occur and whether they can accumulate in finite time for the scalar homogeneous super-twisting algorithm. Two lower bounds on the time required to return to zero are derived, together with a bound on the time needed to complete a full excursion. These results give minimum separation times and upper bounds on the number of crossings associated with excursions above a prescribed amplitude. Although zero crossings may accumulate in finite time, the amplitudes of the complete excursions considered here must vanish and satisfy a summability condition. Thus, crossings associated with excursions above any prescribed nonzero amplitude cannot accumulate in finite time. When the perturbation-rate bound is zero, the estimates recover the scaling imposed by homogeneity. For the classical super-twisting algorithm, the square-root scaling also holds for nonzero perturbation-rate bounds. Numerical simulations illustrate the results.

eess.SY↗

arXiv2026

Modular Sign Compensation for MIMO Systems with Unknown Control Direction: An Exact Nominal Recovery Approach

This paper addresses stabilization of MIMO systems with uncertain time-varying diagonal input direction. We propose a modular switching sign-compensation layer acting as an outer wrapper around a nominal controller. Unlike Nussbaum-type gains, monitoring functions, or binary adaptive mechanisms, the method uses only bounded sign changes that preserve the nominal control magnitude and its properties. The compensation layer uses adaptive variables built from nominal Lyapunov quantities to search for the unknown input-sign configuration based on schedulers. Two schedulers are developed: a vector scheduler, where each input channel explores its own sign compensation and admits an online trapping certificate, and a scalar pattern scheduler, where one variable visits all diagonal sign matrices and gives a design-time recovery guarantee on sufficiently long constant-sign intervals. Once the correct sign configuration is set, the actual closed loop coincides with the nominal closed loop and the original nominal stability property is recovered. The approach is illustrated on a flight roll-reversal problem, a visual-servoing benchmark, and an underground-reservoir control example motivated by human induced-seismicity mitigation.

eess.SY↗

arXiv2026

A Control Framework for Induced Seismicity Mitigation in Groningen Gas Reservoir

Induced seismicity associated with gas production poses major operational and societal challenges, as illustrated by the Groningen field in the Netherlands. While many studies have focused on forecasting seismicity under prescribed production scenarios, fewer works address the inverse problem: designing operational strategies that minimize seismicity while maintaining production objectives. In this paper, we propose a control-oriented methodology for operating Groningen under induced-seismicity mitigation constraints. We employ a cascade model coupling pore-pressure diffusion with seismicity rate (SR) dynamics, and complement it with a stochastic event-generation procedure to convert the continuous SR field into a synthetic earthquake catalog with event times, locations, and magnitudes. From this catalog, we estimate regional SR measurements and design a robust feedback controller that computes well-rate commands to regulate the SR toward a desired reference while satisfying operational requirements, including prescribed production constraints. The proposed control architecture explicitly accounts for injection and extraction flux limits (actuator saturation). The well fluxes generated by the controller are updated at discrete-time intervals (digital control). We validate the modeling components against Groningen data and illustrate the approach through numerical experiments under different scenarios, including various control update periods and gain selections, as well as combined production with compensating injection (e.g., reinjection of nitrogen). The results illustrate how the proposed framework can reduce seismicity levels in a controlled manner while maximizing production targets.

eess.SY↗

arXiv2026

Control of Human-Induced Seismicity in Underground Reservoirs Governed by a Nonlinear 3D PDE-ODE System

Induced seismicity caused by fluid extraction or injection in underground reservoirs is a major challenge for safe energy production and storage. This paper presents a robust output-feedback controller for induced seismicity mitigation in geological reservoirs described by a coupled 3D PDE-ODE model. The controller is nonlinear and robust (MIMO Super-Twisting design), producing a continuous control signal and requiring minimal model information, while accommodating parameter uncertainties and spatial heterogeneity. Two operational outputs are regulated simultaneously: regional pressures and seismicity rates computed over reservoir sub-regions. Closed-loop properties are established via explicit bounds on the solution and its time derivative for both the infinite-dimensional dynamics and the nonlinear ODE system, yielding finite-time or exponential convergence of the tracking errors. The method is evaluated on the Groningen gas-field case study in two scenarios: gas production while not exceeding the intrinsic seismicity of the region, and combined production with CO$_2$ injection toward net-zero carbon operation. Simulations demonstrate accurate tracking of pressure and seismicity targets across regions under significant parameter uncertainty, supporting safer reservoir operation while preserving production objectives.

eess.SY↗

arXiv2025

Reinforcement learning-based adaptive time-integration for nonsmooth dynamics

Numerical time integration is fundamental to the simulation of initial and boundary value problems. Traditionally, time integration schemes require adaptive time-stepping to ensure computational speed and sufficient accuracy. Although these methods are based on mathematical derivations related to the order of accuracy for the chosen integrator, they also rely on heuristic development to determine optimal time steps. In this work, we use an alternative approach based on Reinforcement Learning (RL) to select the optimal time step for any time integrator method, balancing computational speed and accuracy. To explore the potential of our RL-based adaptive time-stepping approach, we choose a challenging model problem involving set-valued frictional instabilities at various spatiotemporal scales. This problem demonstrates the robustness of our strategy in handling nonsmooth problems, which present a demanding scenario for numerical integration. Specifically, we apply RL to the simulation of a seismic fault with Coulomb friction. Our findings indicate that RL can learn an optimal strategy for time integration, achieving up to a fourfold speed-up. Our RL-based adaptive integrator offers a new approach for time integration in various other problems in mechanics.

physics.comp-ph↗

arXiv2025

Slip, Differentiate, Observe: State and Parameter Estimation for Rate and State Friction from Noisy Data

Quantifying frictional properties of interfaces remains a major challenge in both terrestrial and extraterrestrial geomechanics, where available samples, laboratory apparatuses, and geophysical observations are inherently limited. We introduce an analytic and numerical framework, grounded in nonlinear control theory, to infer the emergent frictional behavior of seismic faults. From noisy slip measurements, we first reconstruct the slip rate and frictional response in finite time using a Robust Exact Filtering Differentiator (REFD) that attenuates measurement noise. Building on these reconstructions, we design an exponentially convergent adaptive-gain observer that estimates the internal state variable and the key parameters (a - b) and dc of the rate-and-state friction (RSF) law, widely used in fault mechanics. Numerical experiments show that, in fast slip regimes where data are sufficiently rich, the method recovers RSF parameters with errors on the order of 20% and accurately tracks the RSF state variable despite noise contamination, whereas slowly varying sliding periods lack the observability required for reliable estimation. We also establish observability and identifiability conditions for the extended system, enabling the determination of additional parameters and outlining pathways for more advanced control-theoretic approaches to friction and state identification in fault systems. Although we apply the approach to a reduced spring-slider analogue, it improves on classical RSF calibration methods that depend on laboratory access to shear and normal stress. It also offers convergence guarantees and explicit error bounds, and it can further support model-based inversions that embed RSF in forward simulations.

physics.geo-ph↗

arXiv2023

Earthquake Control: An Emerging Application for Robust Control. Theory and Experimental Tests

This paper addresses the possibility of using robust control theory for preventing earthquakes through fluid injections in the earth's crust. The designed robust controllers drive aseismically a fault system to a new equilibrium point of lower energy by tracking a slow reference signal. The control design is based on a reduced-order nonlinear model able to reproduce earthquake-like instabilities. Uncertainties related to the frictional and mechanical properties of the underlying physical process and external perturbations are considered. Two types of controllers are derived. The first one is based on sliding-mode theory and leads to local finite-time convergence of the tracking error and rejection of Lipschitz w.r.t. time perturbations. The second controller is based on LQR control and presents global exponential stability of the tracking error and rejection of Lipschitz w.r.t. states perturbations. Both controllers generate a continuous control signal, attenuating the chattering effect in the case of the sliding-mode algorithms. The developed controllers are tested extensively and compared on the basis of numerical simulations and experiments in the laboratory. The present work opens new perspectives for the application of robust nonlinear control theory to complex geosystems, earthquakes and sustainable energy production.

math.OC↗

arXiv2022

Motion Planning and Robust Tracking for the Heat Equation using Boundary Control

Robust output tracking is addressed in this paper for a heat equation with Neumann boundary conditions and anti-collocated boundary input and output. The desired reference tracking is solved using the well-known flatness and Lyapunov approaches. The reference profile is obtained by solving the motion planning problem for the nominal plant. To robustify the closed-loop system in the presence of the disturbances and uncertainties, it is then augmented with PI feedback plus a discontinuous component responsible for rejecting matched disturbances with \textit{a priori} known magnitude bounds. Such control law only requires the information of the system at the same boundary as the control input is located. The resulting dynamic controller globally exponentially stabilizes the error dynamics while also attenuating the influence of Lipschitz-in-time external disturbances and parameter uncertainties. For the case when the motion planning is performed over the uncertain plant, an exponential Input-to-State Stability is obtained, preserving the boundedness of the tracking error norm. The proposed controller relies on a discontinuous term that however passes through an integrator, thereby minimizing the chattering effect in the plant dynamics. The performance of the closed-loop system, thus designed, is illustrated in simulations under different kinds of reference trajectories in the presence of external disturbances and parameter uncertainties.

math.OC↗