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This paper investigates the mean square exponential stabilization problem for a class of coupled PDE-ODE systems with Markov jump parameters. The considered system consists of multiple coupled hyperbolic PDEs and a finite-dimensional ODE,…

Optimization and Control · Mathematics 2025-08-06 Kaijing Lyu , Umberto Biccari , Junmin Wang

This paper presents a control design for the one-phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's…

Optimization and Control · Mathematics 2019-01-29 Shumon Koga , Delphine Bresch-Pietri , Miroslav Krstic

Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…

Analysis of PDEs · Mathematics 2026-02-12 Buddhika Priyasad , Sérgio S. Rodrigues

We develop a feedback control framework for stabilizing the McKean-Vlasov PDE on the torus. Our goal is to steer the dynamics toward a prescribed stationary distribution or accelerate convergence to it using a time-dependent control…

Optimization and Control · Mathematics 2026-05-01 Dante Kalise , Lucas M. Moschen , Grigorios A. Pavliotis

This paper deals with the exponential input-to-state stabilization with respect to boundary disturbances of a class of diagonal infinite-dimensional systems via delay boundary control. The considered input delays are uncertain and…

Optimization and Control · Mathematics 2020-03-13 Hugo Lhachemi , Robert Shorten , Christophe Prieur

In this paper, we carry out numerical analysis to prove convergence of a novel sample-wise back-propagation method for training a class of stochastic neural networks (SNNs). The structure of the SNN is formulated as discretization of a…

Numerical Analysis · Mathematics 2022-12-20 Richard Archibald , Feng Bao , Yanzhao Cao , Hui Sun

Flow control occupies a special place in the fields of partial differential equations (PDEs) and control theory, where the complex behavior of solutions of nonlinear dynamics in very high dimension is not just to be understood but also to…

Optimization and Control · Mathematics 2023-06-21 Iasson Karafyllis , Miroslav Krstic

The paper is concerned with the strict-feedback form of hyperbolic distributed-parameter systems. Such a system structure is well known to be the basis for the recursive backstepping control design for nonlinear ODEs and is also reflected…

Systems and Control · Electrical Eng. & Systems 2026-03-16 Nicole Gehring

This paper considers the backstepping state feedback control of coupled linear parabolic PDEs with spatially varying coefficients and bilateral actuation. By making use of the folding technique, a system representation with unilateral…

Optimization and Control · Mathematics 2021-04-13 Simon Kerschbaum , Joachim Deutscher

We consider the problem of pointwise stabilization of a one-dimensional wave equation with an internal spatially varying anti-damping term. We design a feedback law based on the backstepping method and prove exponential stability of the…

Systems and Control · Computer Science 2018-12-31 Fathi Hassine

Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on…

Systems and Control · Computer Science 2017-10-11 Pedro Ascencio , Alessandro Astolfi , Thomas Parisini

In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow interacts across a…

Analysis of PDEs · Mathematics 2014-03-26 George Avalos , Francesca Bucci

Motivated by engineering applications of subsea installation by deepwater construction vessels in oil drilling, and of aid delivery by unmanned aerial vehicles in disaster relief, we develop output-feedback boundary control of…

Optimization and Control · Mathematics 2020-07-20 Ji Wang , Miroslav Krstic

This paper presents the design and analysis of an extremum seeking (ES) controller for scalar static maps in the context of infinite-dimensional dynamics governed by the 1D Euler-Bernoulli (EB) beam Partial Differential Equation (PDE). The…

Optimization and Control · Mathematics 2025-04-11 Paulo H. F. Biazetto , Gustavo A. de Andrade , Tiago Roux Oliveira , Miroslav Krstic

This paper studies the exponential stabilization of a Boussinesq system describing the two-way propagation of small amplitude gravity waves on the surface of an ideal fluid, the so-called Boussinesq system of the Korteweg-de Vries type. We…

Analysis of PDEs · Mathematics 2023-08-21 Roberto de A. Capistrano Filho , Eduardo Cerpa , Fernando A. Gallego

In this paper, we solve the problem of exponential stabilization for a class of cascade ODE-PDE system governed by a linear ordinary differential equation and a 1-d linearized Korteweg-de Vries equation (KdV) posed on a bounded interval.…

Analysis of PDEs · Mathematics 2018-01-04 Habib Ayadi

We solve the feedback stabilization problem for a tank, with friction, containing a liquid modeled by the viscous Saint-Venant system of Partial Differential Equations. A spill-free exponential stabilization is achieved, with robustness to…

Optimization and Control · Mathematics 2022-06-06 Iasson Karafyllis , Filippos Vokos , Miroslav Krstic

A novel adaptive control approach is proposed to solve the globally asymptotic state stabilization problem for uncertain pure-feedback nonlinear systems which can be transformed into the pseudo-affine form. The pseudo-affine pure-feedback…

Systems and Control · Computer Science 2016-09-29 Mingzhe Hou , Zongquan Deng , Guangren Duan

In this work we consider entropy stable discontinuous Galerkin methods applied to nonconservative hyperbolic systems. We introduce a new class of entropy conservative fluctuations that allow us to construct entropy conservative schemes…

Numerical Analysis · Mathematics 2026-01-15 Patrick Ersing , Andrew R. Winters

A new, improved split-step backward Euler (SSBE) method is introduced and analyzed for stochastic differential delay equations(SDDEs) with generic variable delay. The method is proved to be convergent in mean-square sense under conditions…

Numerical Analysis · Mathematics 2011-07-05 Xiaojie Wang , Siqing Gan