arXiv subjects

Bhathiya Rathnayake

Publications and source records attributed to Bhathiya Rathnayake.

11 recordsLinked to original sources

arXiv2026

Cluster-Based Distributed Small-Signal Stability Certificates for Grid-Forming Inverter Networks

Large-scale power networks are often organized by geography, ownership, or control authority, making stability certificates that require a fully assembled global model challenging. This paper develops a time-domain small-signal stability certification framework for grid-forming inverter networks with selectable clustering resolution. The objective is to certify stability at the same scale at which the network is organized and operated: each cluster verifies conditions using intra-cluster and limited boundary information, and these checks collectively yield a network-level stability certificate without requiring a global eigenvalue computation. After linearization about a phase-cohesive synchronized operating point, a small-angle approximation decomposes the model into a voltage subsystem and an angle-frequency subsystem, where the latter is certified by an energy argument using the symmetric weighted-Laplacian network structure. For the voltage subsystem, node-to-node gains are introduced and a cyclic small-gain argument yields a family of sufficient exponential stability certificates ranging from fully decentralized to cluster-based and centralized. For an arbitrary network partition, each cluster verifies intra-cluster directed-cycle conditions and inter-cluster path conditions. The singleton- and single-cluster limits recover the decentralized and centralized certificates, respectively. The resulting stability indices provide diagnostic information beyond a pass/fail verdict by localizing the limiting margin to individual nodes, internal feedback loops, and inter-cluster channels.

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arXiv2026

Grid-Forming Control with Assignable Voltage Regulation Guarantees and Safety-Critical Current Limiting

This paper develops a nonlinear grid-forming (GFM) controller with provable voltage-formation guarantees, with over-current limiting enforced via a control-barrier-function (CBF)-based safety filter. The nominal controller follows a droop-based inner-outer architecture, in which voltage references and frequency are generated by droop laws, an outer-loop voltage controller produces current references using backstepping (BS), and an inner-loop current controller synthesizes the terminal voltage. The grid voltage is treated as an unknown bounded disturbance, without requiring knowledge of its bound, and the controller design does not rely on any network parameters beyond the point of common coupling (PCC). To robustify voltage formation against the grid voltage, a deadzone-adapted disturbance suppression (DADS) framework is incorporated, yielding practical voltage regulation characterized by asymptotic convergence of the PCC voltage errors to an assignably small and known residual set. Furthermore, the closed-loop system is proven to be globally well posed, with all physical and adaptive states bounded and voltage error transients (due to initial conditions) decaying exponentially at an assignable rate. On top of the nominal controller, hard over-current protection is achieved through a minimally invasive CBF-based safety filter that enforces strict current limits via a single-constraint quadratic program. The safety filter is compatible with any locally Lipschitz nominal controller. Rigorous analysis establishes forward invariance of the safe-current set and boundedness of all states under current limiting. Numerical results demonstrate improved transient performance and faster recovery during current-limiting events when the proposed DADS-BS controller is used as the nominal control law, compared with conventional PI-based GFM control.

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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

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

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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arXiv2023

Observer-based Event-triggered Boundary Control of the One-phase Stefan Problem

This paper provides an observer-based event-triggered boundary control strategy for the one-phase Stefan problem using the position and velocity measurements of the moving interface. The infinite-dimensional backstepping approach is used to design the underlying observer and controller. For the event-triggered implementation of the continuous-time observer-based controller, a dynamic event triggering condition is proposed. The triggering condition determines the times at which the control input needs to be updated. In between events, the control input is applied in a \textit{Zero-Order-Hold} fashion. It is shown that the dwell-time between two triggering instances is uniformly bounded below excluding \textit{Zeno behavior}. Under the proposed event-triggered boundary control approach, the well-posedness of the closed-loop system along with certain model validity conditions is provided. Further, using Lyapunov approach, the global exponential convergence of the closed-loop system to the setpoint is proved. A simulation example is provided to illustrate the theoretical results.

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arXiv2023

Event-triggered Boundary Control of a Class of Reaction-Diffusion PDEs with Time-dependent Reactivity

This paper presents an event-triggered boundary control strategy for a class of reaction-diffusion PDEs with time-varying reactivity under Robin actuation. The control approach consists of a backstepping full-state feedback boundary controller and a dynamic event-triggering condition, which determines the time instants when the control input needs to be updated. It is proved that under the proposed event-triggered boundary control approach, there is a uniform minimal dwell-time between two event times. Furthermore, the well-posedness and the global exponential convergence of the closed-loop system to zero in $L^2$-sense are established. A simulation is conducted to validate the theoretical developments.

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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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arXiv2021

Sampled-Data and Event-triggered Boundary Control of a Class of Reaction-Diffusion PDEs with Collocated Sensing and Actuation

This paper provides observer-based sampled-data and event-triggered boundary control strategies for a class of reaction-diffusion PDEs with collocated sensing and Robin actuation. Infinite-dimensional backstepping design is used as the underlying control approach. It is shown that the continuous-time output feedback boundary control applied in a sample-and-hold fashion ensures global closed-loop exponential stability, provided that the sampling period is sufficiently small. Further, robustness to perturbations of the sampling schedule is guaranteed. For the event-triggered implementation of the continuous-time controller, a dynamic triggering condition is utilized. The triggering condition determines the time instants at which the control input needs to be updated. Under the observer-based event-triggered boundary control, it is shown that there is a minimal dwell-time between two triggering instants independent of initial conditions. Further, the global exponential convergence of the closed-loop system to the equilibrium point is established. A simulation example is provided to validate the theoretical results.

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