Boundary Control Research Articles

Fault tolerant vibration control of constrained flexible beam systems with uncertain parameters and actuator failures

This work presents an adaptive fault-tolerant boundary control algorithm for a flexible beam system with actuator failures, external disturbances, and uncertain system parameters. Firstly, partial differential equations with boundary conditions are employed to model the system, and an adaptive compensation method is introduced to solve the issue that the overall number of faults can be infinite, encompassing complete and partial faults. By constructing the barrier Lyapunov function, a fault-tolerant boundary controller is designed to dampen beam vibrations and ensure that all states of flexible beam systems remain within the constraint domain. Simultaneously, the uniformly bounded stability of the flexible beam system is proved by Lyapunov's direct approach. Lastly, the validity of the presented algorithm is demonstrated through simulation results.

Boundary event-triggered FTC of uncertain Euler–Bernoulli beam systems with actuator failures

This work presents an event-triggered fault-tolerant boundary control approach for Euler–Bernoulli beam systems with actuator failures, uncertain system parameters, and external disturbances. Firstly, partial differential equations with boundary conditions are employed to model the system, and an adaptive compensation method is introduced to solve the issue of infinite times actuator faults, encompassing complete and partial faults. By using the relative threshold strategy, the event-triggered fault-tolerant boundary controller is developed to dampen vibration and reduce communication load between actuators and controllers. Simultaneously, the uniformly bounded stability and well-posedness of flexible beam systems are proved by Lyapunov's direct approach and semigroup theory, respectively. Lastly, the validity of the presented algorithm is demonstrated through simulation results.

Robust adaptive vibration control of a gantry crane system with flexible cable

SummaryIn this paper, a robust adaptive vibration control method for gantry crane system is proposed considering unknown parameters brought by unknown payload, cable length and tension. The control objective is to transport the cargo to the desired position while suppressing the vibration of the cable in the presence of unknown parameters. For this purpose, a boundary controller is designed with an adaptive law to compensate the parameter uncertainty of the system. The well‐posedness of the closed‐loop system is proved by means of operator semigroup theory and the asymptotic stability of the closed‐loop system is analyzed. Finally, the effectiveness of the proposed control approach is demonstrated through both numerical simulation comparisons and physical experiments.

Virtual Element Method for Control Constrained Dirichlet Boundary Control Problem Governed by the Diffusion Problem

Virtual Element Method for Control Constrained Dirichlet Boundary Control Problem Governed by the Diffusion Problem

Enhancing Vibration Control in Cable–Tip–Mass Systems Using Asymmetric Peak Detector Boundary Control

In this study, a boundary controller based on a peak detector system has been designed to reduce vibrations in the cable–tip–mass system. The control procedure is built upon a recent modification of the controller, incorporating a non-symmetric peak detector mechanism to enhance the robustness of the control design. The crucial element lies in the identification of peaks within the boundary input signal, which are then utilized to formulate the control law. Its mathematical representation relies on just two tunable parameters. Numerical experiments have been conducted to assess the performance of this novel approach, demonstrating superior efficacy compared to the boundary damper control, which has been included for comparative purposes.

Internal boundary control in lane-free automated vehicle traffic: Comparison of approaches via microscopic simulation

The recently introduced TrafficFluid concept proposes that automated vehicles drive lane-free, thus enabling capacity sharing between the two opposite road directions via real-time Internal Boundary Control (IBC). This novel traffic control measure was demonstrated, using macroscopic traffic flow models, to deliver unprecedented improvements of traffic flow efficiency. The present study completes and validates the IBC concept in a much more realistic way via microscopic simulation and active internal boundary moving, using the SUMO-based TrafficFluid-Sim simulation tool. To effectuate IBC, a Linear Quadratic Regulator (LQR), which is a feedback control scheme, is employed. In addition, to enhance the performance of the LQR controller, a feedforward term, accounting for external disturbances, i.e. entering flow and on-ramp flows, is also designed, leading to an augmented LQR-FF control scheme. The LQR and LQR-FF controllers are tested and compared in the created realistic environment, demonstrating how IBC may operate in practice to combat traffic congestion on highways.

Modular Architecture of Advanced Driver Assistance Systems for Effective Traffic Sign Recognition

Analysis of modern approaches to the implementation of driver assistance systems, as well as the implementation of the architecture of the driver assistance system, aimed at recognizing traffic signs at the maximum distance from it under difficult weather conditions, for early feedback to the driver. The paper considers the main signals used in the implementation and operation of the driver assistance system: data from the car's CAN bus, information from a GPS receiver, video fragments from a digital camera. The presented modular architecture uses the listed data sources for estimating the traffic situation, as well as neural network methods for recognizing traffic signs. The modular architecture of the driver assistance system is presented, which allows notifying the driver about traffic signs. The system is equipped with lane boundary control to alert the driver to signs related to the adjacent carriageway when turning. It has been experimentally proven that the modular architecture of the driver assistance system presented in the paper is not inferior in speed and accuracy to alternative systems, acting as a comprehensive autonomous solution.

Well-posedness and properties of the flow for semilinear evolution equations

We derive conditions for well-posedness of semilinear evolution equations with unbounded input operators. Based on this, we provide sufficient conditions for such properties of the flow map as Lipschitz continuity, bounded-implies-continuation property, boundedness of reachability sets, etc. These properties represent a basic toolbox for stability and robustness analysis of semilinear boundary control systems. We cover systems governed by general C0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0$$\\end{document}-semigroups, and analytic semigroups that may have both boundary and distributed disturbances. We illustrate our findings on an example of a Burgers’ equation with nonlinear local dynamics and both distributed and boundary disturbances.

K-Surfaces: Bézier-Splines Interpolating at Gaussian Curvature Extrema

K-surfaces are an interactive modeling technique for Bézier-spline surfaces. Inspired by k -curves by [Yan et al. 2017], each patch provides a single control point that is being interpolated at a local extremum of Gaussian curvature. The challenge is to solve the inverse problem of finding the center control point of a Bézier patch given the boundary control points and the handle. Unlike the situation in 2D, bi-quadratic Bézier patches may exhibit none, one, or several extrema, and finding them is non-trivial. We solve the difficult inverse problem, including the possible selection among several extrema, by learning the desired function from samples, generated by computing Gaussian curvature of random patches. This approximation provides a stable solution to the ill-defined inverse problem and is much more efficient than direct numerical optimization, facilitating the interactive modeling framework. The local solution is used in an iterative optimization incorporating continuity constraints across patches. We demonstrate that the surface varies smoothly with the handle location and that the resulting modeling system provides local and generally intuitive control. The idea of learning the inverse mapping from handles to patches may be applicable to other parametric surfaces.

Boundary control associated with a parabolic equation

Boundary control associated with a parabolic equation

Existence of unattainable states for Schrödinger type flows on the half-line

Abstract We prove that the solutions of the Schrödinger and biharmonic Schrödinger equations do not have the exact boundary controllability property on the half-line by showing that the associated adjoint models lack observability. We consider the framework of $L^2$ boundary controls with data spaces $H^{-1}(\mathbb{R}_+)$ and $H^{-2}(\mathbb{R}_+)$ for the classical and biharmonic Schrödinger equations, respectively. The lack of controllability on the half-line contrasts with the corresponding dynamics on a finite interval for a similar regularity setting. Our proof is based on an argument that uses the sharp fractional time trace estimates for solutions of the adjoint models. We also make several remarks on the connection of controllability and temporal regularity of spatial traces.

On Magnetic Boundary Control for Metric Graphs

On Magnetic Boundary Control for Metric Graphs

Boundary Controllability of a Simplified Stabilized Kuramoto-Sivashinsky System

Boundary Controllability of a Simplified Stabilized Kuramoto-Sivashinsky System

Power Boundary Controlled Single-Stage LLC Power Factor Correction Converter and Its Optimal Parameter Design

The time-domain analysis on single-stage LLC power factor correction (PFC) converter is performed in this paper, which reveals that PON mode may occur around the peak point of instantaneous input power and cause instability issue. In order avoid PON mode, the power boundary between PO and PON mode is calculated. For the common design methods of LLC PFC converter with average mode control strategy, the power boundary requires to be higher than the instantaneous input power at its worst point. However, higher power boundary brings higher RMS value of resonant current, and causes higher reactive power loss. Therefore, it is a wasteful designing methodology, as the other points of instantaneous input power don't need such high power boundary. In order to improve the efficiency, a power boundary control strategy is proposed in this paper. By controlling the input current to make the instantaneous input power follow the power boundary, PON mode is eliminated. Consequently, the required power boundary is overall reduced, and the minimal RMS current of resonant tank can be achieved. Furthermore, the optimal parameter design is also presented. A 90∼240VAC input and 250W/48V output experimental prototype has been built to verify the analysis results.

Boundary Controllability of Semilinear Impulsive Sobolev-type Neutral Integrodifferential System with Timevarying Delays in Banach Space

Boundary Controllability of Semilinear Impulsive Sobolev-type Neutral Integrodifferential System with Timevarying Delays in Banach Space

Input-to-state stability analysis of heat equation with boundary finite-time control

This paper addresses the problem of input-to-state stabilization for heat equation with external input via boundary control strategy. Following Polyakov et al., 2017, based on the backstepping approach, a switching boundary control law depending on the system state is designed. By estimating the upper bound of kernel functions, switching levels are determined and commutation law is further constructed. For the chosen switched control, the well-posedness property is verified. It is proved that the resulting system is input-to-state stable, and the solutions of the system will not exceed the highest admissible level dependent on the disturbance amplitude. Meanwhile, a stronger result is also obtained, that is the finite-time stability for the disturbance-free system. The numerical example is provided to support the derived result.

Determination of black holes by boundary measurements

For a wave equation with time-independent Lorentzian metric consider an initial-boundary value problem in [Formula: see text], where [Formula: see text] is the time variable and [Formula: see text] is a bounded domain in [Formula: see text]. Let [Formula: see text] be a subdomain of [Formula: see text]. We say that the boundary measurements are given on [Formula: see text] if we know the Dirichlet and Neumann data on [Formula: see text]. The inverse boundary value problem consists of recovery of the metric from the boundary measurements. In the author’s previous works a localized variant of the boundary control method was developed that allows the recovery of the metric locally in a neighborhood of any point of [Formula: see text] where the spatial part of the wave operator is elliptic. This allows the recovery of the metric in the exterior of the ergoregion. The goal of this survey paper is to recover the black holes. In some cases the ergoregion coincides with the black hole. In the case of two space dimensions we recover the black hole inside the ergoregion assuming that the ergosphere, i.e. the boundary of the ergoregion, is not characteristic at any point of the ergosphere.

Adaptive Backstepping Boundary Control for a Class of Modified Burgers’ Equation

Adaptive Backstepping Boundary Control for a Class of Modified Burgers’ Equation

Stability for an Interface Transmission Problem of Wave-Plate Equations with Dynamical Boundary Controls

Stability for an Interface Transmission Problem of Wave-Plate Equations with Dynamical Boundary Controls

Adaptive constrained tracking control for dynamical actuator driven linear 2 × 2 hyperbolic PDE systems with nonlinear uncertainties

The paper develops an adaptive constrained tracking control technique for a class of 2 × 2 hyperbolic partial differential equation (PDE) systems with boundary actuator dynamics, which are described by a set of ordinary differential equations (ODEs) in the presence of unknown parametric nonlinearities. Since the control input only appears in the uncertain ODE subsystem rather than directly on the boundary of PDE subsystem, the control task becomes quite difficult and the existing direct boundary control approaches are ineffective. Moreover, in this paper, a more challenging problem is considered such that the controlled output and the states of ODE actuators are constrained. To this end, by utilizing finite and infinite dimensional backstepping techniques, barrier Lyapunov functions (BLFs) and adaptive methods, a novel adaptive tracking control approach is proposed. It is the first time that such a constrained tracking control problem is addressed for the PDE-ODE coupled systems considered in this paper. On the basis of the presented method, the rigorous theoretical proof is provided to show that the PDE controlled output and all the states of the ODE actuator stay within the predefined compact sets. Finally, the results are illustrated via a comparative numerical simulation.