Article
Mathematics, Applied
Shuangxi Huang, Feng-Fei Jin
Summary: This paper discusses the problems of output tracking and disturbance rejection for a 1-D wave equation with in-domain feedback/recirculation of an intermediate point velocity. A disturbance estimator is designed using the active disturbance rejection control method to estimate the disturbance, and an observer is proposed and shown to exponentially converge to the original system. An output feedback controller is constructed based on the designed observer. The resulting closed-loop system is well-posed, with all internal signals bounded, and the output exponentially tracks the reference signal. Theoretical results are validated through numerical simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics
Baolin Ma, Yiyue Sun, Guojie Zheng
Summary: This paper investigates the stabilization of an unstable stochastic heat equation using the backstepping technique. It proposes a boundary feedback control scheme to stabilize the system and proves its robust stability against disturbances in the control channel under suitable conditions. Numerical simulations are provided to support the theoretical results.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Li Wang
Summary: This paper focuses on performance output tracking for a one-dimensional heat partial differential equation with unknown external disturbance and non-collocated configuration. The control input in this system is subject to a time delay. By representing the time delay as a first-order hyperbolic equation, the control system is modeled as a cascade construction, where the transport equation can be seen as the actuator dynamics of the heat partial differential system. The difficulties caused by the input delay are addressed by compensating for the actuator dynamics. A full state feedback law is constructed to achieve performance output tracking, and an error-based observer is successfully designed. The exponential stability of the closed-loop system and the well-posedness of the observer are proven.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Zhan-Dong Mei, Yi-Lin Mo
Summary: This paper focuses on performance output tracking for an Euler-Bernoulli beam equation with moment boundary control and shear boundary disturbance. The authors propose an infinite-dimensional disturbance estimator and an output feedback control law to compensate for the disturbance. It is proved that the performance output exponentially tracks the reference signal, and the closed-loop system remains bounded. The importance of this work lies in addressing the shear boundary term and presenting key steps to handle the problem.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Automation & Control Systems
Bao-Zhu Guo, Ren-Xi Zhao
Summary: This paper considers output regulation for a 1-d heat equation using an adaptive observer internal model approach to estimate unknown frequencies and achieve output regulation and disturbance rejection for this PDE.
Article
Mathematics, Applied
Maria Colombo, Silja Haffter
Summary: In this paper, we study the defocusing nonlinear wave equation in three dimensions. We prove the global well-posedness of the equation for any initial datum with a scaling-subcritical norm bounded by M0 at p = 5 + i, where i is from the interval (0, i0(M0)).
Article
Mathematics, Applied
Yongqiang Fu, Xiaoju Zhang
Summary: This paper investigates initial boundary value problems for the time-space fractional Rosenau equation, establishes decay estimates of weak solutions to corresponding linear equations, and proves the global existence and asymptotic behavior of weak solutions in time-weighted Sobolev spaces under small initial value conditions. Additionally, the regularity of weak solutions is discussed when initial value data are strengthened.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Yuxuan Gao, Ying Zhao, Yu Liu, Zhuo-Rui Pan, Rui Wang
Summary: A new output tracking control strategy is proposed for turbofan systems affected by multiple disturbances. The aim is to improve the output tracking performance while mitigating the effect of the disturbances. An observer is used to estimate the unmeasurable modeled disturbance and a corresponding controller is designed to optimize the output tracking performance and disturbance restraint. The developed control scheme is implemented on a hardware-in-loop simulation platform to enhance the output tracking performance of the turbofan system.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Weijiu Liu
Summary: This paper discusses the problem of exponential tracking and disturbance rejection for the nonlinear unstable gradient-dependent wave equation using boundary control. By splitting the tracking problem into a linear exponentially stable wave equation and a nonlinear dynamical regulator wave equation, an explicit boundary controller is constructed. The theoretical results are confirmed through a numerical example.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Seongyeon Kim, Yehyun Kwon, Ihyeok Seo
Summary: In this work, we obtain weighted L-2 estimates for the elastic wave equation perturbed by singular potentials, including the inverse-square potential. Additionally, we deduce Strichartz estimates under the sole ellipticity condition for the Lame operator -Delta*, improving upon previous results which required a stronger condition for ensuring self-adjointness of -Delta*. Furthermore, by establishing local energy estimates for the elastic wave equation, we also demonstrate that the solution possesses local regularity.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Computer Science, Interdisciplinary Applications
M. Vijayakumar, R. Sakthivel, F. Kong, S. Marshal Anthoni
Summary: In this article, the output tracking and disturbance rejection problem for a class of switched systems with state time-varying delay under asynchronous switching are discussed. Proportional-integral control law is implemented to achieve the required tracking performance, and an improved equivalent-input-disturbance estimator is used to estimate and suppress external disturbances. An average dwell time approach is employed to establish a set of conditions for the structure of linear matrix inequalities through setting a proper choice of multiple piecewise Lyapunov-Krasovskii functional. Two numerical examples and simulations of a DC motor driving model are presented to validate the efficiency and applicability of the proposed control synthesis.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
Paola Loreti, Daniela Sforza
Summary: We establish a hidden regularity result for weak solutions of time fractional diffusion-wave equations with a Caputo fractional derivative of order alpha in the range (1, 2) by analyzing the regularity properties of weak solutions in suitable interpolation spaces.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2021)
Article
Mathematics, Interdisciplinary Applications
Jinhong Jia
Summary: This study analyzes the well-posedness and regularity of a variably distributed-order time-fractional diffusion equation with a hidden-memory fractional derivative, which is a competitive approach for describing the anomalous transport of particles in heterogeneous media. It is proven that the solution of such an equation exhibits weak singularity at the initial time, dependent on the upper bound of the distributed order.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics
Frederik Broucke, Ljubica Oparnica
Summary: This paper focuses on the micro-local and qualitative analysis of the fractional Zener wave equation, including the determination of classical and Gevrey-type wave front sets of the fundamental solution, as well as addressing questions on dispersion, dissipation, wave propagation speed, and wave packet shape.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Yi Han
Summary: This article constructs unique martingale solutions to the damped stochastic wave equation and shows their applicability to a wider class of SPDEs. It also demonstrates the validity of the Smoluchowski-Kramers approximation.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Automation & Control Systems
Wenjie Cao, Fuke Wu, Minyu Wu
Summary: This paper focuses on the stability of stochastic hybrid systems with random delay driven by a singularly perturbed Markov chain. The limit system is obtained using weak convergence and the martingale method. By utilizing the limit system as a bridge, the moment exponential stability of the original system is established using Razumikhin-type techniques. An example is provided to illustrate the obtained result.
SYSTEMS & CONTROL LETTERS
(2024)
Article
Automation & Control Systems
Vincenzo Basco
Summary: This paper discusses distributed optimization techniques in multi-agent systems with time-varying communication networks and proposes a novel approach that leverages group actions and probabilistic selection of initial states to solve real-world optimization problems in decentralized environments.
SYSTEMS & CONTROL LETTERS
(2024)
Article
Automation & Control Systems
Jennifer Przybilla, Igor Pontes Duff, Peter Benner
Summary: This paper considers the problem of finding surrogate models for large-scale second-order linear time-invariant systems with inhomogeneous initial conditions. Two methodologies are proposed: reducing each component independently and extracting dominant subspaces from Gramians. The error bounds for the overall output approximation are also discussed.
SYSTEMS & CONTROL LETTERS
(2024)
Article
Automation & Control Systems
Shubham Singh, Anoop Jain
Summary: This paper proposes a distributed control design methodology to stabilize a desired formation shape in a multi-agent system while incorporating collision avoidance and connectivity preservation simultaneously. Time-varying constraints are applied to handle collision avoidance and connectivity preservation, and the concept of asymmetric time-varying barrier Lyapunov function is exploited to derive the stabilizing distributed control law.
SYSTEMS & CONTROL LETTERS
(2024)
Article
Automation & Control Systems
Han Zhang, Axel Ringh
Summary: Inverse Optimal Control (IOC) is a powerful framework for learning behavior from expert observations. In this study, we focused on identifying the cost and feedback law from observed trajectories. We proved that identifying the cost is generally an ill-posed problem, but we constructed an estimator for the cost function and showed that it provides a statistically consistent estimate for the true underlying control gain. The constructed estimator is based on convex optimization and exhibits statistical consistency in practice.
SYSTEMS & CONTROL LETTERS
(2024)
Article
Automation & Control Systems
Ky Quan Tran, Pham Huu Anh Ngoc
Summary: This paper investigates the exponential contraction in mean square of general functional differential equations with Markovian switching. Explicit criteria for such contraction are derived through a novel approach. An illustrative example is provided.
SYSTEMS & CONTROL LETTERS
(2024)
Article
Automation & Control Systems
Jiangyan Pu, Qi Zhang
Summary: This paper examines the continuous time intertemporal consumption and portfolio choice problems of an investor in a generalized stochastic differential utility preference of Epstein-Zin type with subjective beliefs and ambiguity. The paper provides closed-form optimal consumption and portfolio solutions with subjective beliefs and numerical solutions with ambiguity for the Heston model in an incomplete market.
SYSTEMS & CONTROL LETTERS
(2024)