Finite Time Research Articles

Stochastic disturbance with finite-time chaos stabilization and synchronization for a fractional-order nonautonomous hybrid nonlinear complex system via a sliding mode control

This paper provides a novel approach to studying the chaos control and synchronization of fractional-order hybrid Darcy–Brinkman systems (FOHDBs). We use the truncated Galerkin method to transform the system of partial differential equations (PDEs) into ordinary differential equations (ODEs) based on Fourier modes in a nonlinear low-dimensional Brinkman model. In the nonlinear complex system, hybrid nanoparticles and fluid flow physical characteristics are considered to be external disturbances. As a result, the implications of model uncertainty and external disruptions are fully absorbed into the problem, further complicating it and resulting in highly complex and unpredictable behaviors. In addition, To assure the occurrence of the sliding motion in a finite amount of time, an appropriate robust fractional sliding mode technique is proposed. Sliding motion is shown to occur in finite time using the fractional Lyapunov stability. Following that, we discussed control techniques for achieving infinitesimally close to an equilibrium of chaotic states and tracking errors. It is important to note that FOHDBs and external stochastic disturbances can be controlled using the proposed fractional nonsingular terminal sliding mode control technique. Finally, the effectiveness and applicability of the suggested finite-time control technique are graphically illustrated by the analytical and numerical simulations.

Robust attitude tracking control for a variable‐pitch quadrotor with uncertainties

SummaryVariable‐pitch quadrotors have demonstrated their capability to enhance control performance and overcome limitations compared to conventional fixed‐pitch quadrotors, while still facing challenges such as nonlinearity, couplings, uncertainties and so on. This article aims to address the robust attitude control problem of variable‐pitch quadrotors afflicted with parametric uncertainties and unpredictable external disturbances. Initially, a practical actuator allocation strategy for the motor‐propeller is proposed, followed by the development of a nonlinear robust attitude tracking controller capable of addressing all uncertainties. The effectiveness of the proposed controller in ensuring exponential stability of the closed‐loop system, thereby driving the attitude tracking error to a small range within a finite time, has been substantiated. To evaluate the control performance, a hardware‐in‐the‐loop testbed is constructed to conduct real‐time experiments. The experimental results from attitude control case, comparative case, and position control case demonstrate that the designed motor‐propeller allocation method and robust controller are effective in achieving a fast response and excellent control performance.

Ultra-fast and compact optical Galois field adder based on the LPhC structure and phase shift keying.

In this study, we propose a novel, to the best of our knowledge, all-optical Galois field (AOGF) adder that utilizes logic all-optical XOR gates. The design is founded on optical beams' constructive and destructive interference phenomenon and incorporates the phase shift keying technique within a two-dimensional linear photonic crystal (2D-LPhC) structure. The suggested AOGF adder comprises eight input ports and four output ports. We employ the finite difference time domain (FDTD) procedure to obtain the electric field distribution in this structure. The FDTD simulation results of the proposed AOGF adder demonstrate that the minimum and maximum values of the normalized power at ON and OFF states (P 1,min, P 0,max) for the output ports are 95% and 1.7%, respectively. Additionally, we obtain different functional parameters, including the ON-OFF contrast ratio, rise time, fall time, and total footprint, which are measured at 17.47dB, 0.1ps, 0.05ps, and 147µm 2, respectively.

Finite-step alternating approximately bi-similar symbolic model for Markov jump systems

Establishing a bi-similar abstraction (symbolic model) of control systems has been demonstrated as a viable approach for implementing temporal logic tasks on control systems. Previous research primarily focused on logic tasks over an infinite time horizon. However, practical scenarios often involve control tasks defined within finite time intervals. Hence, this paper addresses the finite-time bi-similar problem specifically for a significant class of stochastic switched systems known as Markov jump systems (MJSs). To achieve this, two novel concepts are introduced: finite-time stochastic incremental stability (FSIS) and finite-step alternating approximate bi-simulation relation. A sufficient condition is firstly established for FSIS of MJSs by leveraging the incremental weak infinitesimal operator. Subsequently, a symbolic model is developed for MJSs by employing gridding techniques. Furthermore, a sufficient condition is derived to ensure that the developed symbolic model exhibits finite-step alternating approximate bi-similarity with the original MJSs. Finally, two numerical examples illustrate the application of the proposed results.

Learning to Order for Inventory Systems with Lost Sales and Uncertain Supplies

We consider a stochastic lost-sales inventory control system with lead time L over a planning horizon T. Supply is uncertain, and it is a function of the order quantity (because of random yield/capacity, etc.). We aim to minimize the T-period cost, a problem that is known to be computationally intractable even under known distributions of demand and supply. In this paper, we assume that both the demand and supply distributions are unknown and develop a computationally efficient online learning algorithm. We show that our algorithm achieves a regret (i.e., the performance gap between the cost of our algorithm and that of an optimal policy over T periods) of [Formula: see text] when [Formula: see text]. We do so by (1) showing that our algorithm’s cost is higher by at most [Formula: see text] for any [Formula: see text] compared with an optimal constant-order policy under complete information (a widely used algorithm) and (2) leveraging the latter’s known performance guarantee from the existing literature. To the best of our knowledge, a finite sample [Formula: see text] (and polynomial in L) regret bound when benchmarked against an optimal policy is not known before in the online inventory control literature. A key challenge in this learning problem is that both demand and supply data can be censored; hence, only truncated values are observable. We circumvent this challenge by showing that the data generated under an order quantity q2 allow us to simulate the performance of not only q2 but also, q1 for all [Formula: see text], a key observation to obtain sufficient information even under data censoring. By establishing a high-probability coupling argument, we are able to evaluate and compare the performance of different order policies at their steady state within a finite time horizon. Because the problem lacks convexity, commonly used learning algorithms, such as stochastic gradient decent and bisection, cannot be applied, and instead, we develop an active elimination method that adaptively rules out suboptimal solutions. This paper was accepted by Victor Martínez-de-Albéniz, operations management. Funding: This work is supported by the National Science Foundation [Grant CCF-2312205]. Z. Zhou also acknowledges the New York University’s 2024 Center for Global Economy and Business [Faculty Research Grant] and New York University [Research Catalyst Prize]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.02476 .

Practical Finite-Time Event-Triggered Control of Underactuated Surface Vessels in Presence of False Data Injection Attacks

Abstract The results of studies on a trajectory-tracking problem affected by false data injection attacks (FDIAs) and internal and external uncertainties are presented in this paper. In view of the FDIAs experienced by the system, we compensate for the serious navigation deviation caused by malicious attacks by designing an online approximator. Next, we study the internal and external uncertainties introduced by environmental factors, system parameter fluctuations, or sensor errors, and we design adaptive laws for these uncertainties to approximate their upper bounds. To further enhance the response velocity and stability of the system, we introduce finite-time technology to ensure that the unmanned underactuated surface vessels (USVs) reach the predetermined trajectory-tracking target within finite time. To further reduce the update frequency of the controller, we introduced event-triggered control (ETC) technology. This saves the system’s communication resources and optimizes the system. Through Lyapunov stability theory, a strict and complete stability analysis is provided for the control scheme. Finally, the effectiveness of the control scheme is verified using two sets of simulations.

On the optimal control for the wave equation in heterogeneous materials

This article deals with the wave equation in heterogeneous materials. Under this premise, we obtain a result for the following optimal interior control problem: reach optimally (in finite time T) any point on a given trajectory (called the reference trajectory) determined by the solution of the wave equation in a homogeneous medium. In this article, we explicitly build an optimal control function using the decomposition into eigenmodes (or eigenfunctions) of the associated Laplacian operator, emphasizing that our approach is more advantageous than the classical numerical techniques when we need to control only some eigenmodes of the wave equation while ignoring others. As a main result, we obtain a useful expression for the optimal control solution based on the calculation of effective wave coefficients. This expression is given as a linear combination of control terms, each of them controlling an eigenmode associated to the heterogeneous system.

Dynamic control of the Bose–Einstein-like condensation transition in scalar active matter

The dynamics of a generic class of scalar active matter exhibiting a diffusivity edge is studied in a confining potential where the amplitude is governed by a time-dependent protocol. For such non-equilibrium systems, the diffusion coefficient vanishes when the single-particle density field reaches a critical threshold, inducing a condensation transition that is formally akin to Bose–Einstein condensation. We show that this transition arises even for systems that do not reach a steady state, leading to condensation in finite time. Since the transition can be induced for a fixed effective temperature by evolving the system, we effectively show that the temporal coordinate constitutes an alternative control parameter to tune the transition characteristics. For a constant-amplitude protocol, our generalised thermodynamics reduces in the steady-state limit to earlier results. Lastly, we show numerically that for periodic modulation of the potential amplitude, the condensation transition is reentrant.

Trajectory Tracking Control of Human Support Robots via Adaptive Sliding-Mode Approach.

In this article, the tracking problem of the adaptive sliding-mode control (SMC) design for human support robots based on a disturbance observer is investigated. First, a finite-time controller using nonsingular fast terminal SMC is proposed. Then, a robust disturbance observer is developed to estimate system uncertainties and disturbances. Simultaneously, to deal with the unknown bounded disturbance observer error, an adaptive control technology is developed. Furthermore, the proposed controller is synthesized to ensure that the tracking errors can be stabilized in finite time. Finally, simulations are performed to demonstrate that human support robots employing the proposed controller can converge to the desired trajectory.

Consensus-Based Merging and Spacing Method for Aircraft Self-Separation at Intersections

Within the context of delegating separation related tasks from an air traffic controller to the flight deck, this paper analyzes the merging and spacing problem for autonomous aircraft operations at busy airway intersections. A consensus-based control protocol is developed to achieve an ordered and safe traffic flow at a given intersection waypoint. Two primary implementation steps are covered in the protocol. In the first step, consensus on the target merging flow is achieved, where the merging stream is modeled as a straight line with the minimum total converging distance. In the second step, multiple aircraft with double-integrator dynamics and time-varying communication topologies are guided to merge into the target flow while maintaining appropriate interaircraft spacing. A state control law is designed, and the Lyapunov analysis method is leveraged to derive sufficient conditions on the communication topology and the control parameter for merging agents to reach consensus in finite time. Performance of the proposed method is evaluated through experimental simulations under different hypothetical scenarios in the two-dimensional plane.

Perturbed Unicycle Mobile Robots: A Second-Order Sliding-Mode Trajectory Tracking Control

This paper contributes to the design of a second–order sliding–mode controller for the trajectory tracking problem in perturbed unicycle mobile robots. The proposed strategy takes into account the design of two particular sliding variables, which ensure the convergence of the tracking error to the origin in a finite time despite the effect of some external perturbations. The straightforward structure of the controller is simple to tune and implement. The global, uniform and finite–time stability of the closed–loop tracking error dynamics is demonstrated by means of Lyapunov functions. Furthermore, the performance of the proposed approach is validated through some experiments using a QBot2 unicycle mobile robot.

Non-homogeneous fully nonlinear contracting flows of convex hypersurfaces

Abstract We consider a general class of non-homogeneous contracting flows of convex hypersurfaces in R n + 1 ${\mathbb{R}}^{n+1}$ , and prove the existence and regularity of the flow before extincting to a point in finite time.

A synthetic diagnostics platform for microwave imaging diagnostics in tokamaks

Interpreting experimental diagnostics data in tokamaks, while considering non-ideal effects, is challenging due to the complexity of plasmas. To address this challenge, a general synthetic diagnostics (GSD) platform has been established that facilitates microwave imaging reflectometry and electron cyclotron emission imaging. This platform utilizes plasma profiles as input and incorporates the finite-difference time domain, ray tracing and the radiative transfer equation to calculate the propagation of plasma spontaneous radiation and the external electromagnetic field in plasmas. Benchmark tests for classical cases have been conducted to verify the accuracy of every core module in the GSD platform. Finally, 2D imaging of a typical electron temperature distribution is reproduced by this platform and the results are consistent with the given real experimental data. This platform also has the potential to be extended to 3D electromagnetic field simulations and other microwave diagnostics such as cross-polarization scattering.

Smart city compatible thin film solar cell based on extraordinary transmission and metallic patch nanoantenna

An effective performance enhancement model for the thin film solar cell conjointly based on extraordinary transmission and nanoantenna is proposed and investigated. The absorber layer of the extraordinary transmission based solar cell contains a metallic thin film with periodic holes. Maximum extraordinary transmission is accomplished as the metallic film has the same refractive index on both sides. Increased light transmission causes the absorber layer to absorb more light, which increases short circuit current density and subsequently the efficiency of the thin film solar cell. The presented analysis demonstrates that adding a square nano patch on the top surface of the absorber layer can further boost the extraordinary transmission. The extraordinary transmission is increased because of the formation of cavity nanoantenna. Cavity nanoantenna increases the coupling of light into the hole due to the excitation of surface plasmons polaritons. The proposed design of solar cell exhibits around 98% absorption and the short circuit current density is increased by a factor of 3.23. The study has been carried out using finite difference time domain (FDTD) method.

Dynamic Event-Triggered-Based Adaptive Finite-Time Neural Control for Active Suspension Systems With Displacement Constraint.

In this article, we give an event-based control algorithm for nonlinear active suspension systems (ASSs) with the vertical displacement constraint. For in-vehicle communication networks, the controller area network (CAN) is a widely used standard for interconnecting electronic control units (ECUs). The main task in this work is, thus, to reduce the communication burden on the CAN. To this end, we develop a dynamic event-triggered communication mechanism in ASSs. Meanwhile, in practice, the vehicle safety is degraded when the body vibration exceeds the allowable maximum. Thus, the vertical displacement of ASSs should be constrained within a reliable range. For this purpose, we present a novel finite-time integral barrier Lyapunov function (FTIBLF), which not only guarantees that the vertical displacement constraint bounds are not violated, but also enables the position of the suspension to be stabilized in the neighborhood of a desired position in finite settling time. Furthermore, neural networks (NNs) are utilized to identify the unknown nonlinear characteristics in ASSs subjected to the modeling error and unknown mass. As a result, we propose an adaptive neural control technique based on the dynamic event-triggered condition, which helps to improve the ride comfort while ensuring the driving safety and handling stability. Finally, simulation results are provided to verify the validity of the presented methodology.

Trade-offs in concentration sensing in dynamic environments

When cells measure concentrations of chemical signals, they may average multiple measurements over time in order to reduce noise in their measurements. However, when cells are in an environment that changes over time, past measurements may not reflect current conditions—creating a new source of error that trades off against noise in chemical sensing. What statistics in the cell’s environment control this trade-off? What properties of the environment make it variable enough that this trade-off is relevant? We model a single eukaryotic cell sensing a chemical secreted from bacteria (e.g., folic acid). In this case, the environment changes because the bacteria swim—leading to changes in the true concentration at the cell. We develop analytical calculations and stochastic simulations of sensing in this environment. We find that cells can have a huge variety of optimal sensing strategies ranging from not time averaging at all to averaging over an arbitrarily long time or having a finite optimal averaging time. The factors that primarily control the ideal averaging are the ratio of sensing noise to environmental variation and the ratio of timescales of sensing to the timescale of environmental variation. Sensing noise depends on the receptor-ligand kinetics, while environmental variation depends on the density of bacteria and the degradation and diffusion properties of the secreted chemoattractant. Our results suggest that fluctuating environmental concentrations may be a relevant source of noise even in a relatively static environment.

Effect of correlation time of combustion noise on early warning indicators of thermoacoustic instability.

In this paper, we analyze the effects of finite correlation time (noise color) of combustion noise on noise-induced coherence and early warning indicators (EWIs) via numerical and experimental studies. We consider the Rijke tube as a prototypical combustion system and model combustion noise as an additive Ornstein-Uhlenbeck process while varying noise intensity and correlation time. We numerically investigate corresponding effects on coherence resonance and multi-fractal properties of pressure fluctuations. Subsequently, we experimentally validate results and elucidate the influence of noise color and intensity on trends in coherence resonance and multi-fractal measures that can be expected in a practical scenario using an electroacoustic simulator. We find that the coherence factor, which quantifies the relative contribution of coherent oscillations in a noisy signal, increases as the system approaches the thermoacoustic instability-irrespective of the correlation time. It works at most levels of combustion noise (except for too low and too high noise levels). The Hurst exponent reduces as the system approaches thermoacoustic instability only when the correlation time is small. These results have implications on the prediction and monitoring of thermoacoustic instability in practical combustors.

975 nm multimode semiconductor lasers with high-order Bragg diffraction gratings

The 975 nm multimode diode lasers with high-order surface Bragg diffraction gratings have been simulated and calculated using the 2D finite difference time domain (FDTD) algorithm and the scattering matrix method (SMM). The periods and etch depth of the grating parameters have been optimized. A board area laser diode (BA-LD) with high-order diffraction gratings has been designed and fabricated. At output powers up to 10.5 W, the measured spectral width of full width at half maximum (FWHM) is less than 0.5 nm. The results demonstrate that the designed high-order surface gratings can effectively narrow the spectral width of multimode semiconductor lasers at high output power.

Optimal maintenance over a finite time horizon for a system under imperfect inspection and dynamic working environment

Inspections play a crucial role in determining the state of a system and informing timely maintenance decisions. However, due to the limitations of adopted inspection technologies, inspection errors are often inevitable. More importantly, the likelihood of such errors is often influenced by the system's working environment that varies over time and space. Despite this, most studies on imperfect inspections largely overlook the effects of such dynamic working environments on inspection errors. To address this gap, this paper proposes a maintenance policy accounting for imperfect inspections for a degrading system with hidden failures under a dynamic working environment. We develop two models based on a recursive method. The first model examines a case where the working environment affects only inspection errors, whereas the second one accounts for its impact on both inspection errors and the system's degradation process. Our focus is to determine the optimal interval and number of inspections that minimize the expected maintenance cost over a finite time horizon. Numerical examples are provided to illustrate the proposed method to ensure the effectiveness of maintenance actions. The optimization outcomes not only offer a valuable tool for engineers seeking to reduce maintenance costs but also shed light on broader managerial implications.

An optimal selective maintenance policy for multi-state series production systems by considering environment impact

Series production systems are prevalent in the manufacturing industry. The productivity of these systems is influenced by various factors, including system conditions, on-site environment, maintenance planning, and others. Efforts to develop an effective maintenance plan that considers the on-site environment are crucial for maximizing net revenue over the system’s lifetime, which has practical significance. Against this backdrop, a selective maintenance model is constructed for a multi-state series production system over a finite time horizon. This model describes the operation and maintenance processes at any decision period and analyzes the impact of the on-site environment on system productivity. Subsequently, an optimal maintenance strategy is formulated with the goal of maximizing net revenue throughout the system’s lifetime. To efficiently solve this optimal strategy, a hybrid solution approach is developed by integrating a deterministic method with a heuristic method. Finally, a numerical example involving a real chip mounter system is presented to verify the developed maintenance strategy. This is followed by a comparative experiment to validate the performance of the hybrid solution approach. Additionally, sensitivity analysis is conducted to test the strategy’s robustness. The results from the numerical example, comparative experiment, and sensitivity analysis demonstrate that the developed strategy is effective and robust, and the hybrid approach is efficient.