arXiv subjects

Tiago Roux Oliveira

Publications and source records attributed to Tiago Roux Oliveira.

At least 19 recordsLinked to original sources

arXiv2026

Safe Newton-Based Extremum Seeking for Static Maps with Delayed Output Measurements

This work presents a delayed safe Newton-based extremum seeking (SANES) framework for minimizing an unknown static map subject to an unknown safety constraint. The objective and safety measurements are assumed to be affected by the same constant time delay. To compensate for delayed measurements, a model-free predictor is developed to construct the quantities required for optimization, including the nominal Newton-based extremum-seeking control input and the gradient information used to formulate control Lyapunov function (CLF) and control barrier function (CBF) conditions. Robust CLF--CBF quadratic programs (QPs), subject to parameter-update constraints, are then formulated to account explicitly for derivative-estimation and prediction errors. For the delay-free case, robustness margins are derived from bounds on the extremum-seeking estimation errors, whereas for the delayed case, the margins incorporate both estimation and prediction errors. Practical stability of the nominal Newton-based extremum-seeking dynamics is established directly through a Lyapunov analysis, thereby providing convergence guarantees over the admissible parameter set without relying exclusively on local averaging arguments. Robust CLF and CBF conditions are subsequently derived to establish practical convergence and forward invariance of a robust subset of the prescribed safe set. A numerical case study demonstrates the effectiveness of the proposed SANES framework in achieving constrained optimization despite unknown objective and safety maps and delayed measurements.

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arXiv2026

Resilient Extremum Seeking Control for Cyber-Physical Systems Under Denial-of-Service Attacks

Extremum seeking control (ESC) relies on deliberately injected excitation to extract optimization information from measured outputs, making its networked implementation particularly vulnerable to denial-of-service (DoS) attacks. This paper develops a resilient discrete-time ESC architecture for cyber-physical systems subject to DoS attacks. By holding the most recently successfully transmitted signals during DoS intervals, the proposed mechanism yields averaged error dynamics with an exponentially contracting mode under successful communication and a neutral mode under attack. For deterministic DoS attacks, practical exponential convergence to the extremum is established under an average bound on the attack duration, with an explicit convergence rate depending on the fraction of time under attack. For probabilistic DoS attacks, almost-sure and in-probability convergence properties are established via stochastic averaging, with the attack success probability explicitly entering the convergence rate. A key finding is that a seemingly natural zero-input strategy can fundamentally compromise ESC: attacks synchronized with the dither generate an $\mathcal{O}(1/a)$ bias in the averaged dynamics, where $a$ is the dither amplitude, and can displace the equilibrium from the true optimizer. Thus, under the proposed hold-based architecture, increasingly severe DoS attacks primarily slow the optimization process rather than destroy its stability, provided that communication is not permanently blocked. Numerical simulations illustrate the theoretical guarantees and the failure mechanism induced by dither-synchronized attacks.

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arXiv2026

Extremum Seeking Control: Three Revolutions and the Road Ahead

The history of extremum seeking is not merely the history of an algorithm; it is the history of an idea. Few ideas in control engineering have demonstrated the remarkable longevity of extremum seeking control (ESC). Invented more than one hundred years ago, ESC has continually reinvented itself while remaining faithful to its original objective: enabling systems to optimize their performance without relying on accurate mathematical models. This perspective article proposes that the evolution of ESC is best understood through three scientific revolutions. The first Engineering Revolution (1922-1999) established the engineering principles of model-free optimization; the second Mathematical Revolution (2000-2010) provided the rigorous mathematical foundations that transformed ESC into a mature discipline of nonlinear control; and the third ongoing Infinite-Dimensional and Cyber-Physical Revolution (2010-present) continues to expand its scope toward delays, partial differential equations, distributed optimization, event-triggered implementations, and increasingly complex cyber-physical systems. Beyond recounting this historical evolution, we offer a personal perspective on why ESC has remained relevant across successive technological eras. We argue that its enduring influence arises because the fundamental engineering challenge has never changed: "how can a dynamical system learn to improve its own performance when the optimum is unknown?" As optimization, learning, and feedback control become increasingly intertwined, ESC appears uniquely positioned to contribute to a new generation of intelligent autonomous systems, pointing toward what may become the field's fourth scientific revolution.

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arXiv2026

Multi-Observer Output Feedback Stabilization of a Class of Uncertain Nonminimum-Phase Systems

This paper addresses the challenging problem of output feedback stabilization for nonlinear nonminimum phase (NMP) systems in the presence of parametric uncertainties and external disturbances. The proposed framework integrates three distinct observers: a reduced-order observer for reconstructing the unmeasured states of the internal (zero) dynamics, a high-gain observer for estimating output derivatives, and an observer for estimating the aggregated effect of parametric uncertainties and disturbances. Leveraging these estimates, a sliding mode control law is synthesized to ensure global asymptotic stability of the entire system using only output measurements. The control design requires only partial model knowledge, significantly relaxing the restrictive assumptions common in existing literature. Numerical simulations illustrate the effectiveness of the proposed output-feedback strategy and corroborate the theoretical developments.

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arXiv2026

Towards Co-Designed Event-Triggered Extremum Seeking

This paper studies event-triggered gradient-based multivariable extremum seeking for nonlinear maps with polytopic Hessian uncertainty. Unlike existing event-triggered extremum-seeking methods, which first fix the controller (typically diagonal) and then design the triggering mechanism, the proposed approach jointly synthesizes the controller and the triggering mechanism through a co-design framework that admits both diagonal and full controller gain matrices. The co-design problem is formulated as a convex optimization problem with linear matrix inequality constraints. Its solution guarantees exponential convergence of the average closed-loop system with a prescribed decay rate while maximizing the admissible triggering threshold to reduce communication. Lyapunov and averaging analyses establish exponential stability of the event-triggered system, and Zeno-freeness is proved to guarantee implementability. Numerical results illustrate that diagonal gains cannot achieve the same triggering thresholds and decay rates as the full controller gain matrices, highlighting the benefits of exploiting Hessian coupling information.

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arXiv2026

Estimated-State Adaptive Sliding Mode Control and Disturbance Observation Using Second-Order Surfaces for Spacecraft Formation Reconfiguration

This paper presents a two-phase relative orbit control framework for spacecraft formation flying that combines analytic energy-optimal transfer with robust adaptive sliding mode tracking. In the first phase, a chaser is transferred from an arbitrary initial relative state to a projected circular orbit (PCO) under the Clohessy--Wiltshire dynamics. Rather than selecting the PCO entry phase by numerical sweeping, the transfer cost is parameterized by the phase angle, and the stationarity condition is reduced to a quartic polynomial whose real roots yield all candidate entry phases. In the second phase, the chaser maintains the PCO in the presence of external disturbances. An adaptive sliding mode controller (ASMC) and a sliding mode disturbance observer (SMDO) are employed in both phases to provide robust tracking and disturbance compensation. The observer reduces the lumped disturbance to a bounded residual, while the controller updates its adaptive gain from an estimated-state second-order sliding variable. The second-order surface tightens the ultimate tracking error bound, and a practical derivative estimation method reuses available reference velocity and acceleration signals, avoiding finite-difference noise amplification and additional differentiator tuning. Simulations demonstrate accurate tracking, effective disturbance rejection, and a smooth transition between the two phases.

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arXiv2026

Event-Triggered Discrete-Time Multivariable Extremum Seeking Systems

This paper introduces a discrete-time event-triggered extremum seeking framework for real-time optimization of multivariable nonlinear systems. In contrast to conventional discrete-time extremum seeking implementations that rely on periodic input updates, the proposed scheme updates the control action only when a state-dependent triggering condition is met, enabling aperiodic execution and substantial reduction of actuation and communication effort. The resulting closed-loop architecture reconciles two structurally different paradigms: the periodic excitation required for gradient recovery in extremum seeking and the aperiodic philosophy of event-triggered control. By combining discrete-time averaging arguments with Lyapunov-based analysis, we prove practical convergence of the system trajectories to a neighborhood of the unknown extremum and exponential stability of the corresponding average dynamics despite the loss of uniform sampling. The results show that appropriately designed triggering rules preserve the essential optimization mechanisms of classical extremum seeking while drastically reducing the number of input updates. Numerical simulations demonstrate that comparable optimization performance can be achieved with significantly fewer actuation events, highlighting the suitability of the method for resource-aware digital and networked control implementations.

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arXiv2026

Discrete-Time Event-Triggered Extremum Seeking

This paper proposes a discrete-time event-triggered extremum seeking control scheme for real-time optimization of nonlinear systems. Unlike conventional discrete-time implementations relying on periodic updates, the proposed approach updates the control input only when a state-dependent triggering condition is satisfied, reducing unnecessary actuation and communication. The resulting closed-loop system combines extremum seeking with an event-triggering mechanism that adaptively determines the input update instants. Using discrete-time averaging and Lyapunov analysis, we establish practical convergence of the trajectories to a neighborhood of the unknown extremum point and show exponential stability of the associated average dynamics. The proposed method preserves the optimization capability of classical extremum seeking while significantly reducing the number of input updates. Simulation results illustrate the effectiveness of the approach for resource-aware real-time optimization.

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arXiv2026

Event-Triggered Newton Extremum Seeking for Multivariable Optimization

This paper presents a static event-triggered control strategy for multivariable Newton-based extremum seeking. The proposed method integrates event-triggered actuation into the Newton-based optimization framework to reduce control updates while maintaining rapid convergence to the extremum. Unlike traditional gradient-based extremum seeking, where the convergence rate depends on the unknown Hessian of the cost function, the proposed approach employs a dynamic estimator of the Hessian inverse, formulated as a Riccati equation, enabling user-assignable convergence rates. The event-triggering mechanism is designed to minimize unnecessary actuation updates while preserving stability and performance. Using averaging theory, we establish local stability results and exponential convergence to a neighborhood of the unknown extremum point. Additionally, numerical simulations illustrate the benefits of the proposed approach over gradient-based and continuously actuated Newton-based extremum seeking, showing improved convergence rates and reduced control update frequency, leading to more efficient implementation in real-time optimization scenarios.

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arXiv2026

Extremum Seeking Control for Wave-PDE Actuation with Distributed Effects

This paper deals with the gradient-based extremum seeking control (ESC) with actuation dynamics governed by distributed wave partial differential equations (PDEs). To achieve the control objective of real-time optimization for this class of infinite-dimensional systems, we first solve the trajectory generation problem to re-design the additive perturbation signal of the ESC system. Then, we develop a boundary control law through the backstepping method to compensate for the wave PDE with distributed effects, which ensures the exponential stability of the average closed-loop system by means of a Lyapunov-based analysis. At last, by employing the averaging theory for infinite-dimensional systems, we prove that the closed-loop trajectories converge to a small neighborhood surrounding the optimal point. Numerical simulations are presented to illustrate the effectiveness of the proposed method.

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arXiv2025

Extremum-Seeking Boundary Control for Schrödinger-Type PDEs

This paper addresses the design and analysis of an extremum-seeking (ES) controller for scalar static maps in the context of infinite-dimensional dynamics governed by complex-valued partial differential equations (PDEs) of Schrodinger type. The system is actuated at one boundary, and the map input is defined as a real-valued quadratic functional corresponding to the squared norm of the complex state at the uncontrolled boundary. An isomorphism between the complex Hilbert space and its two-dimensional real-valued representation is established to enable the use of the standard multivariable Newton-based ES method. To compensate for the PDE actuation dynamics, a boundary control strategy based on a two-step backstepping procedure is employed. With a perturbation-based estimate of the Hessian inverse, the local exponential stability to a small neighborhood of the unknown extremum point is proved. A numerical example illustrates the effectiveness of the proposed extremum-seeking methodology.

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arXiv2025

Multivariable Gradient-Based Extremum Seeking Control with Saturation Constraints

This paper addresses the multivariable gradient-based extremum seeking control (ESC) subject to saturation. Two distinct saturation scenarios are investigated here: saturation acting on the input of the function to be optimized, which is addressed using an anti-windup compensation strategy, and saturation affecting the gradient estimate. In both cases, the unknown Hessian matrix is represented using a polytopic uncertainty description, and sufficient conditions in the form of linear matrix inequalities (LMIs) are derived to design a stabilizing control gain. The proposed conditions guarantee exponential stability of the origin for the average closed-loop system under saturation constraints. With the proposed design conditions, non-diagonal control gain matrices can be obtained, generalizing conventional ESC designs that typically rely on diagonal structures. Stability and convergence are rigorously proven using the Averaging Theory for dynamical systems with Lipschitz continuous right-hand sides. Numerical simulations illustrate the effectiveness of the proposed ESC algorithms, confirming the convergence even in the presence of saturation.

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arXiv2025

Gradient- and Newton-Based Unit Vector Extremum Seeking Control

This paper presents novel methods for achieving stable and efficient convergence in multivariable extremum seeking control (ESC) using sliding mode techniques. Drawing inspiration from both classical sliding mode control and more recent developments in finite-time and fixed-time control, we propose a new framework that integrates these concepts into Gradient- and Newton-based ESC schemes based on sinusoidal perturbation signals. The key innovation lies in the use of discontinuous "relay-type" control components, replacing traditional proportional feedback to estimate the gradient of unknown quadratic nonlinear performance maps with Unit Vector Control (UVC). This represents the first attempt to address real-time, model-free optimization using sliding modes within the classical extremum seeking paradigm. In the Gradient-based approach, the convergence rate is influenced by the unknown Hessian of the objective function. In contrast, the Newton-based method overcomes this limitation by employing a dynamic estimator for the inverse of the Hessian, implemented via a Riccati equation filter. We establish finite-time convergence of the closed-loop average system to the extremum point for both methods by leveraging Lyapunov-based analysis and averaging theory tailored to systems with discontinuous right-hand sides. Numerical simulations validate the proposed method, illustrating significantly faster convergence and improved robustness compared to conventional ESC strategies, which typically guarantee only exponential stability. The results also demonstrate that the Gradient-based method exhibits slower convergence and higher transients since the gradient trajectory follows the curved and steepest-descent path, whereas the Newton-based method achieves faster convergence and improved overall performance going straightly to the extremum.

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arXiv2025

Sliding Mode Control for Uncertain Systems with Time-Varying Delays via Predictor Feedback and Super-Twisting Observer

This paper introduces a novel stabilization control strategy for linear time-invariant systems affected by known time-varying measurement delays and matched unknown nonlinear disturbances, which may encompass actuator faults. It is considered that part of the state vector is not available for real-time measurement. To address this, the proposed approach combines an open-loop predictor with a state observer designed using the Super-Twisting Algorithm, aiming to compensate for the delays and estimate the unmeasured state components. Specifically, the nonlinear observer-based framework enables the reconstruction of unmodeled fault signals without assuming that they originate from a known exogenous system, offering robustness against parametric uncertainties. Meanwhile, the predictor forwards the delayed output in time. Subsequently, a sliding mode control law is formulated to enforce an ideal sliding mode and ensure global stabilization, even under a broader class of perturbations, unmodeled disturbances, parametric uncertainties, and delays, owing to the integration of the Super-Twisting observer. Numerical simulations illustrate the efficiency of the proposed approach.

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arXiv2025

Extremum Seeking for PDE Systems using Physics-Informed Neural Networks

Extremum Seeking (ES) is an effective real-time optimization method for PDE systems in cascade with nonlinear quadratic maps. To address PDEs in the feedback loop, a boundary control law and a re-design of the additive probing signal are mandatory. The latter, commonly called "trajectory generation" or "motion planning," involves designing perturbation signals that anticipate their propagation through PDEs. Specifically, this requires solving motion planning problems for systems governed by parabolic and hyperbolic PDEs. Physics-Informed Neural Networks (PINN) is a powerful tool for solving PDEs by embedding physical laws as constraints in the neural network's loss function, enabling efficient solutions for high-dimensional, nonlinear, and complex problems. This paper proposes a novel construction integrating PINN and ES, automating the motion planning process for specific PDE systems and eliminating the need for case-by-case analytical derivations. The proposed strategy efficiently extracts perturbation signals, optimizing the PDE system.

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arXiv2025

Distributed Event-Triggered Nash Equilibrium Seeking for Noncooperative Games

We propose locally convergent Nash equilibrium seeking algorithms for $N$-player noncooperative games, which use distributed event-triggered pseudo-gradient estimates. The proposed approach employs sinusoidal perturbations to estimate the pseudo-gradients of unknown quadratic payoff functions. This is the first instance of noncooperative games being tackled in a model-free fashion with event-triggered extremum seeking. Each player evaluates independently the deviation between the corresponding current pseudo-gradient estimate and its last broadcasted value from the event-triggering mechanism to tune individually the player action, while they preserve collectively the closed-loop stability/convergence. We guarantee Zeno behavior avoidance by establishing a minimum dwell-time to avoid infinitely fast switching. In particular, the stability analysis is carried out using Lyapunov's method and averaging for systems with discontinuous right-hand sides. We quantify the size of the ultimate small residual sets around the Nash equilibrium and illustrate the theoretical results numerically on an oligopoly setting.

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arXiv2025

Extremum Seeking Boundary Control for Euler-Bernoulli Beam PDEs

This paper presents the design and analysis of an extremum seeking (ES) controller for scalar static maps in the context of infinite-dimensional dynamics governed by the 1D Euler-Bernoulli (EB) beam Partial Differential Equation (PDE). The beam is actuated at one end (using position and moment actuators). The map's input is the displacement at the beam's uncontrolled end, which is subject to a sliding boundary condition. Notably, ES for this class of PDEs remains unexplored in the existing literature. To compensate for PDE actuation dynamics, we employ a boundary control law via a backstepping transformation and averaging-based estimates for the gradient and Hessian of the static map to be optimized. This compensation controller leverages a Schrödinger equation representation of the EB beam and adapts existing backstepping designs to stabilize the beam. Using the semigroup and averaging theory in infinite dimensions, we prove local exponential convergence to a small neighborhood of the unknown optimal point. Finally, simulations illustrate the effectiveness of the design in optimizing the unknown static map.

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arXiv2025

Event-Triggered Source Seeking Control for Nonholonomic Systems

This paper introduces an event-triggered source seeking control (ET-SSC) for autonomous vehicles modeled as the nonholonomic unicycle. The classical source seeking control is enhanced with static-triggering conditions to enable aperiodic and less frequent updates of the system's input signals, offering a resource-aware control design. Our convergence analysis is based on time-scaling combined with Lyapunov and averaging theories for systems with discontinuous right-hand sides. ET-SSC ensures exponentially stable behavior for the resulting average system, leading to practical asymptotic convergence to a small neighborhood of the source point. We guarantee the avoidance of Zeno behavior by establishing a minimum dwell time to prevent infinitely fast switching. The performance optimization is aligned with classical continuous-time source seeking algorithms while balancing system performance with actuation resource consumption. Our ET-SSC algorithm, the first of its kind, allows for arbitrarily large inter-sampling times, overcoming the limitations of classical sampled-data implementations for source seeking control.

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