arXiv subjects

Mamadou Diagne

Publications and source records attributed to Mamadou Diagne.

At least 19 recordsLinked to original sources

arXiv2026

Distributed Time-Varying Optimization via Unbiased Extremum Seeking

This paper proposes a novel distributed optimization framework that addresses time-varying optimization problems without requiring explicit derivative information of the objective functions. Traditional distributed methods often rely on derivative computations, limiting their applicability when only real-time objective function measurements are available. Leveraging unbiased extremum seeking, we develop continuous-time algorithms that utilize local measurements and neighbor-shared data to collaboratively track time-varying optima. Key advancements include compatibility with directed communication graphs, customizable convergence rates (asymptotic, exponential, or prescribed-time), and the ability to handle dynamically evolving objectives. By integrating chirpy probing signals with time-varying frequencies, our unified framework achieves accelerated convergence while maintaining stability under mild assumptions. Theoretical guarantees are established through Lie bracket averaging and Lyapunov-based analysis, with linear matrix inequality conditions ensuring rigorous convergence. Numerical simulations validate the effectiveness of the algorithms.

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arXiv2026

When classical predictors fail: an exact network outflowpredictor for heterogeneous multi-agent systems with communication delays

This paper develops an information outflow predictor-feedback framework for the exact compensation of constant but nonuniform communication delays in the output synchronization problem of discrete-time heterogeneous multi-agent systems. The delays considered here act exclusively on communication channels between neighboring agents, rather than on the plant state, input or output, and thus fall outside the scope of classical predictor-feedback formulations. We show that standard approaches based on time inversion and variational construction of predictor states are insufficient, since even for simple directed acyclic communication graphs the required prediction horizon exceeds the delay window. We further illustrate that exact predictor-based compensation is achievable only in the discrete-time setting, while in continuous-time configuration the predictor state becomes non-computable due to the need for a continuum inaccessible future neighboring-agent information. Motivated by these observations, we propose a distributed prediction architecture in which a prediction-based distributed observer exactly reconstructs the flow of information exchanged between agents across the network. Furthermore, the layer-by-layer information flow eliminates the effect of communication delays after a finite number of steps. Based on this structure, we design prediction-based distributed state-feedback and dynamic output-feedback controllers by combining standard feedback designs with prediction-based distributed observers serving as feedforward components, such that the output of each agent asymptotically tracks the trajectory generated by the exosystem, thereby ensuring output synchronization.

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arXiv2026

Switched Event-Triggered Adaptive Control of Reaction-Diffusion PDE-ODE with Neural Operator Implementation

This paper develops a switched event-triggered adaptive boundary control for a class of reaction-diffusion PDE-ODE cascade systems, where the system and input matrices in the ODE as well as the spatially-varying reaction coefficient in the PDE are uncertain. A two-step backstepping transformation is constructed to derive the continuous-time control law. Then a novel dynamic event-triggered control strategy for the PDE-ODE cascade is proposed based on a switched event-triggering mechanism, ensuring global exponential stability of the closed-loop system in place of the exponential convergence commonly achieved with backstepping-based classical dynamic ETC, while inherently excluding Zeno behavior. To address the uncertainties in the PDE-ODE cascade, adaptive update laws are developed, leading to time-varying gain kernels that are adaptively scheduled through the event-triggered control mechanism. Furthermore,to facilitate efficient real-time implementation, deep neural operators (DeepONet) are employed to approximate the backstepping kernels as mappings from the estimated parameters to kernel functions, thereby eliminating the need to repeatedly solve kernel PDEs online. Through a Lyapunov analysis that incorporates the effects of the event-triggering mechanism, parameter adaptation, and kernel approximation errors, we prove the $L^2$ global asymptotic regulation of the resulting closed-loop system. In summary, the key contributions of the paper are threefold: (i) developing an adaptive DeepONet-based framework for reaction-diffusion PDE-ODE cascade systems; (ii) extending the existing adaptive event-triggered control design for reaction-diffusion PDEs to the case with more complex uncertainties; and (iii) generalizing switched dynamic ETC with global exponential stability to PDE-ODE cascades. The effectiveness of the proposed approach is demonstrated through numerical simulations.

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arXiv2026

Multi-layer Predictor Feedback Design for Nonlinear Integro-Differential Equations with State-dependent Input Delays

We develop a novel multi-layer predictor-feedback to achieve exact compensation of state-dependent input delay of general nonlinear integro-differential equations. The system of interest is an unconventional mixed Partial Differential Equation (PDE)-Ordinary Differential Equation (ODE) system, in which a nonlinear ODE is actuated through an inhomogeneous advection PDE. Moreover, the propagation speed of the PDE depends on a moving window integral of the ODE state. The two above features are not addressed yet in standard PDE backstepping-based predictor-feedback designs. Unlike the conventional Lyapunov-based approaches used in the field, our stability and well-posedness analysis rely on the characteristic method and a fixed-point argument. Both of our designs achieve global asymptotic stability (GAS) in the supremum norm of the PDE and ODE states under the mild assumption that the nonlinearity in the PDE governing equation is uniformly Lipschitz continuous. The transport speed, governed by the integral of the ODE state, models systems such as production or queuing processes in which the state of a finite buffer-namely, the inventory level-determines the production or service rate. Numerical simulations demonstrate the effectiveness of the proposed control design for buffer-regulated production lines and queuing systems, ensuring asymptotic stability under a locally safe softened bang-bang feedback law that preserves the positivity of both the system state and the actuation signal.

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arXiv2026

Observer-Based Performance-Barrier Event-Triggered Control of $2\times2$ Linear Hyperbolic PDEs

Performance-barrier event-triggered control (P-ETC) is a methodology implemented to increase the dwell-times between events while still preserving a prescribed performance of the system under event-triggered control (ETC). This is achieved by considering the performance residual of the system, which is a measure of the system performance with respect to the prescribed performance. This allows the Lyapunov function candidate to deviate from decreasing monotonically. In order to determine the performance residual, it is required to know the full-state information, leading to all work related to P-ETC to be under full-state feedback. In this article, we propose a novel dynamic performance-barrier under output feedback with an exponentially convergent observer. We consider event-triggered boundary control of a class of $2\times2$ linear hyperbolic PDEs with anti-collocated measurements with the control input. Under the proposed P-ETC mechanism, we prove the existence of a minimum dwell-time, and show the global exponential stability of the spatial $L^2$ norm of the solution of the system. Simulation results are presented to validate the theoretical claims.

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arXiv2026

Exponential Stabilization of Moving Shockwave in ARZ Traffic Model via Boundary Control: Explicit Gains and Arbitrary Decay Rate

This paper develops boundary feedback controls to stabilize traffic congestion toward a predefined shock equilibrium in the Aw-Rascle-Zhang (ARZ) traffic flow model. We transform the corresponding moving-boundary $2\times2$ hyperbolic system, covering free and congested flow regimes, respectively, into a shock-free $4\times4$ augmented system on a fixed domain via shock-location-based moving coordinates. By applying the modified Lyapunov functionals concerning shock perturbation, we show that the shock position and the state of the system in $H^2$-norm can be stabilized with an arbitrary exponential decay rate via the given feedback controls. Finally, the stabilization results are demonstrated by numerical simulations.

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arXiv2026

Stabilization of Predator-Prey Age-Structured Hyperbolic PDE when Harvesting both Species is Inevitable

Populations do not only interact over time but also age over time. It is therefore common to model them as age-structured PDEs, where age is the space variable. Since the models also involve integrals over age, both in the birth process and in the interaction among species, they are in fact integro-partial differential equations (IPDEs) with positive states. To regulate the population densities to desired profiles, harvesting is used as input. But non-discriminating harvesting, where wanting to repress one species will inevitably repress the other species as well, the positivity restriction on the input (no insertion of population), and the multiplicative nature of harvesting, makes control challenging even for ODE versions of such dynamics, let alone for their IPDE versions on an infinite-dimensional nonnegative state space. We introduce a design for a benchmark version of such a problem: a two-population predator-prey setup. The model is equivalent to two coupled ordinary differential equations (ODEs), actuated by harvesting which must not drop below zero, and strongly disturbed by two autonomous but exponentially stable integral delay equations (IDEs). We develop two control designs. With a modified Volterra-like control Lyapunov function, we design a simple feedback which employs possibly negative harvesting for global stabilization of the ODE model, while guaranteeing regional regulation with positive harvesting. With a more sophisticated, restrained controller we achieve regulation for the ODE model globally, with positive harvesting. For the full IPDE model, with the IDE dynamics acting as large disturbances, for both the simple and saturated feedback laws we provide explicit estimates of the regions of attraction. The paper charts a new pathway for control designs for infinite-dimensional multi-species dynamics and for nonlinear positive systems with positive controls.

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arXiv2025

Unbiased Extremum Seeking for MPPT in Photovoltaic Systems

This paper presents novel extremum seeking (ES) strategies for maximum power point tracking (MPPT) in photovoltaic (PV) systems that ensure unbiased convergence and prescribed-time performance. Conventional ES methods suffer from steady-state bias due to persistent dither signal. We introduce two novel ES algorithms: the exponential unbiased ES (uES), which guarantees exponential convergence to the maximum power point (MPP) without steady-state oscillation bias, and the unbiased prescribed-time ES (uPT-ES), which ensures convergence within a user-defined time horizon. Both methods leverage time-varying perturbation amplitudes and demodulation gains, with uPT-ES additionally utilizing chirp signals to enhance excitation over finite-time intervals. Experimental results on a hardware-in-the-loop testbed validate the proposed algorithms, demonstrating improved convergence speed and tracking accuracy compared to classical ES, under both static and time-varying environmental conditions.

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arXiv2025

Output Feedback Periodic Event-Triggered and Self-Triggered Boundary Control of Coupled $2\times 2$ Linear Hyperbolic PDEs

In this paper, we expand recently introduced observer-based periodic event-triggered control (PETC) and self-triggered control (STC) schemes for reaction-diffusion PDEs to boundary control of $2\times2$ coupled hyperbolic PDEs in canonical form and with anti-collocated measurement and actuation processes. The class of problem under study governs transport phenomena arising in water management systems, oil drilling, and traffic flow, to name a few. Relative to the state of the art in observer-based event-triggered control of hyperbolic PDEs, our contribution goes two steps further by proposing observer-based PETC and STC for the considered class of systems. These designs arise from a non-trivial redesign of an existing continuous-time event-triggered control (CETC) scheme. PETC and STC eliminate the need for constant monitoring of an event-triggering function as in CETC; PETC requires only periodic evaluations of the triggering function for event detection, whereas STC is a predictor-feedback that anticipates the next event time at the current event exploiting continuously accessible output measurements. The introduced resource-aware designs act as input holding mechanisms allowing for the update of the input signal only at events. Subject to the designed boundary output feedback PETC and STC control laws characterized by a set of event-trigger design parameters, the resulting closed-loop systems, which are inherently Zeno-free by design, achieve exponential convergence to zero in the spatial $L^2$ norm. We illustrate the feasibility of the approach by applying the control laws to the linearized Saint-Venant model, which describes the dynamics of shallow water waves in a canal and is used to design flow stabilizer feedback laws via gate actuation. The provided simulation results illustrate the proposed theory.

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arXiv2025

Constant-Sum High-Order Barrier Functions for Safety Between Parallel Boundaries

This paper takes a step towards addressing the difficulty of constructing Control Barrier Functions (CBFs) for parallel safety boundaries. A single CBF for both boundaries has been reported to be difficult to validate for safety, and we identify why this challenge is inherent. To overcome this, the proposed method constructs separate CBFs for each boundary. We begin by presenting results for the relative degree one case and then extend these to higher relative degrees using the CBF backstepping technique, establishing conditions that guarantee safety. Finally, we showcase our method by applying it to a unicycle system, deriving a simple, verifiable condition to validate the target CBFs for direct implementation of our results.

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arXiv2025

DeepONet of dynamic event-triggered backstepping boundary control for reaction-diffusion PDEs

We present an event-triggered boundary control scheme for a class of reaction-diffusion PDEs using operator learning and backstepping method. Our first-of-its-kind contribution aims at learning the backstepping kernels, which inherently induces the learning of the gains in the event trigger and the control law. The kernel functions in constructing the control law are approximated with neural operators (NOs) to improve the computational efficiency. Then, a dynamic event-triggering mechanism is designed, based on the plant and the continuous-in-time control law using kernels given by NOs,to determine the updating times of the actuation signal. In the resulting event-based closed-loop system, a strictly positive lower bound of the minimal dwell time is found, which is independent of initial conditions. As a result, the absence of a Zeno behavior is guaranteed. Besides, exponential convergence to zero of the L_2 norm of the reaction-diffusion PDE state and the dynamic variable in the event-triggering mechanism is proved via Lyapunov analysis. The effectiveness of the proposed method is illustrated by numerical simulation.

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arXiv2025

Performance-Barrier Event-Triggered PDE Control of Traffic Flow

For stabilizing stop-and-go oscillations in traffic flow by actuating a variable speed limit (VSL) at a downstream boundary of a freeway segment, we introduce event-triggered PDE backstepping designs employing the recent concept of performance-barrier event-triggered control (P-ETC). Our design is for linearized hyperbolic Aw-Rascle-Zhang (ARZ) PDEs governing traffic velocity and density. Compared to continuous feedback, ETC provides a piecewise-constant VSL commands-more likely to be obeyed by human drivers. Unlike the existing regular ETC (R-ETC), which enforces conservatively a strict decrease of a Lyapunov function, our performance-barrier (P-ETC) approach permits an increase, as long as the Lyapunov function remains below a performance barrier, resulting in fewer control updates than R-ETC. To relieve VSL from continuously monitoring the triggering function, we also develop periodic event-triggered (PETC) and self-triggered (STC) versions of both R-ETC and P-ETC. These are referred to as R/P-PETC and R/P-STC, respectively, and we show that they both guarantee Zeno-free behavior and exponential convergence in the spatial $L^2$ norm. With comparative simulations, we illustrate the benefits of the performance-barrier designs through traffic metrics (driver comfort, safety, travel time, fuel consumption). The proposed algorithms reduce discomfort nearly in half relative to driver behavior without VSL, while tripling the driver safety, measured by the average dwell time, relative to the R-ETC frequent-switching VSL schedule.

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arXiv2025

Observer-based Periodic Event-triggered and Self-triggered Boundary Control of a Class of Parabolic PDEs

This paper introduces the first observer-based periodic event-triggered control (PETC) and self-triggered control (STC) for boundary control of a class of parabolic PDEs using PDE backstepping control. We introduce techniques to convert a certain class of continuous-time event-triggered control into PETC and STC, eliminating the need for continuous monitoring of the event-triggering function. For the PETC, the event-triggering function requires only periodic evaluations to detect events, while the STC proactively computes the time of the next event right at the current event time using the system model and the continuously available measurements. For both strategies, the control input is updated exclusively at events and is maintained using a zero-order hold between events. We demonstrate that the closed-loop system is Zeno-free. We offer criteria for selecting an appropriate sampling period for the PETC and for determining the time until the next event under the STC. We prove the system's global exponential convergence to zero in the spatial $L^2$ norm for both anti-collocated and collocated sensing and actuation under the PETC. For the STC, local exponential convergence to zero in the spatial $L^2$ norm for collocated sensing and actuation is proven. Simulations are provided to illustrate the theoretical claims.

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arXiv2025

Performance-Barrier Event-Triggered Control of a Class of Reaction-Diffusion PDEs

We employ the recent performance-barrier event-triggered control (P-ETC) for achieving global exponential convergence of a class of reaction-diffusion PDEs via PDE backstepping control. Rather than insisting on a strictly monotonic decrease of the Lyapunov function for the closed-loop system, P-ETC allows the Lyapunov function to increase as long as it remains below an acceptable performance-barrier. This approach integrates a performance residual, the difference between the value of the performance-barrier and the Lyapunov function, into the triggering mechanism. The integration adds flexibility and results in fewer control updates than with regular ETC (R-ETC) that demands a monotonic decrease of the Lyapunov function. Our P-ETC PDE backstepping design ensures global exponential convergence of the closed-loop system in the spatial L^2 norm, without encountering Zeno phenomenon. To avoid continuous monitoring of the triggering function that generates events, we develop periodic event-triggered and self-triggered variants (P-PETC and P-STC, respectively) of the P-ETC. The P-PETC only requires periodic evaluation of the triggering function whereas the P-STC preemptively computes the time of the next event at the current event time using the system model and continuously available system states. The P-PETC and P-STC also ensure a Zeno-free behavior and deliver performance equivalent to that of the continuous-time P-ETC which requires continuous evaluation of the triggering function, in addition to the continuous sensing of the state. We provide numerical simulations to illustrate the proposed technique and to compare it with R-ETC associated with strictly decreasing Lyapunov functions.

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arXiv2024

Robust Control Barrier Function Design for High Relative Degree Systems: Application to Unknown Moving Obstacle Collision Avoidance

In safety-critical control, managing safety constraints with high relative degrees and uncertain obstacle dynamics pose significant challenges in guaranteeing safety performance. Robust Control Barrier Functions (RCBFs) offer a potential solution, but the non-smoothness of the standard RCBF definition can pose a challenge when dealing with multiple derivatives in high relative degree problems. As a result, the definition was extended to the marginally more conservative smooth Robust Control Barrier Functions (sRCBF). Then, by extending the sRCBF framework to the CBF backstepping method, this paper offers a novel approach to these problems. Treating obstacle dynamics as disturbances, our approach reduces the requirement for precise state estimations of the obstacle to an upper bound on the disturbance, which simplifies implementation and enhances the robustness and applicability of CBFs in dynamic and uncertain environments. Then, we validate our technique through an example problem in which an agent, modeled using a kinematic unicycle model, aims to avoid an unknown moving obstacle. The demonstration shows that the standard CBF backstepping method is not sufficient in the presence of a moving obstacle, especially with unknown dynamics. In contrast, the proposed method successfully prevents the agent from colliding with the obstacle, proving its effectiveness.

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arXiv2024

Setpoint Tracking and Disturbance Attenuation for Gas Pipeline Flow Subject to Uncertainties using Backstepping

In this paper, we consider the problem of regulating the outlet pressure of gas flowing through a pipeline subject to uncertain and variable outlet flow. Gas flow through a pipe is modeled using the coupled isothermal Euler equations, with the Darcy-Weisbach friction model used to account for the loss of gas flow momentum. The outlet flow variation is generated by a periodic linear dynamic system, which we use as a model of load fluctuations caused by varying consumer demands. We first linearize the nonlinear equations around the equilibrium point and obtain a 2-by-2 coupled hyperbolic partial differential equation (PDE) system expressed in canonical form. Using an observer-based PDE backstepping controller, we demonstrate that the inlet pressure can be manipulated to regulate the outlet pressure to a setpoint, thus compensating for fluctuations in the outlet flow. Furthermore, we extend the observer-based controller to the case when the outlet flow variation is uncertain within a bounded set. In this case, the controller is also capable of regulating the outlet pressure to a neighborhood of the setpoint by manipulating the inlet pressure, even in the presence of uncertain fluctuations in the outlet flow. We provide numerical simulations to demonstrate the performance of the controller.

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arXiv2024

Asymptotic, Exponential, and Prescribed-Time Unbiasing in Seeking of Time-Varying Extrema

Our recently developed "unbiased" extremum seeking (uES) algorithms ensure perfect convergence to the optimum at a user-assigned exponential rate or, more powerfully, within a user-prescribed time. Unlike classical approach, these algorithms use time-varying adaptation and controller gains, along with constant or time-varying probing frequencies (chirp signals). This paper advances our earlier uES designs from strongly convex maps with static optima to a broader class of convex cost functions with time-varying optima diverging at arbitrary rates, even in finite time. This advancement first motivates the use of Lie bracket averaging instead of classical averaging due to the average system system, which doesn't necessarily need to be exponentially convergent, and the existence of non-periodic time-varying parameters; second, it necessitates the formulation of non-trivial and key feasibility conditions for the choice of time-varying design parameters and their decay/growth rates in relation to the convexity of the map and the divergence rate of optima. These conditions indicate that, for constant-frequency probing, the user-defined asymptotic rate of unbiasing is limited by the convexity of the map. However, this rate can be made arbitrarily fast (including asymptotic, exponential, and prescribed time) using chirpy probing, which requires sufficiently rapid frequency and adaptation growth to enable tracking of faster-diverging optima. In addition to numerical simulations of the designs, we experimentally test the feasibility of exponential uES for tuning the angular velocity of a unicycle to seek a static light source.

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arXiv2024

Backstepping Neural Operators for $2\times 2$ Hyperbolic PDEs

Deep neural network approximation of nonlinear operators, commonly referred to as DeepONet, has proven capable of approximating PDE backstepping designs in which a single Goursat-form PDE governs a single feedback gain function. In boundary control of coupled PDEs, coupled Goursat-form PDEs govern two or more gain kernels-a PDE structure unaddressed thus far with DeepONet. In this paper, we explore the subject of approximating systems of gain kernel PDEs for hyperbolic PDE plants by considering a simple counter-convecting $2\times 2$ coupled system in whose control a $2\times 2$ kernel PDE system in Goursat form arises. Engineering applications include oil drilling, the Saint-Venant model of shallow water waves, and the Aw-Rascle-Zhang model of stop-and-go instability in congested traffic flow. We establish the continuity of the mapping from a total of five plant PDE functional coefficients to the kernel PDE solutions, prove the existence of an arbitrarily close DeepONet approximation to the kernel PDEs, and ensure that the DeepONet-approximated gains guarantee stabilization when replacing the exact backstepping gain kernels. Taking into account anti-collocated boundary actuation and sensing, our $L^2$-Globally-exponentially stabilizing (GES) approximate gain kernel-based output feedback design implies the deep learning of both the controller's and the observer's gains. Moreover, the encoding of the output-feedback law into DeepONet ensures semi-global practical exponential stability (SG-PES). The DeepONet operator speeds up the computation of the controller gains by multiple orders of magnitude. Its theoretically proven stabilizing capability is demonstrated through simulations.

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