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In distributed model predictive control (DMPC), where a centralized optimization problem is solved in distributed fashion using dual decomposition, it is important to keep the number of iterations in the solution algorithm, i.e. the amount…
The aim article is to contribute to the definition of a versatile language for metastability in the context of partial differential equations of evolutive type. A general framework suited for parabolic equations in one dimensional bounded…
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…
We examine the evolution of a bistable reaction in a one-dimensional stretching flow, as a model for chaotic advection. We derive two reduced systems of ordinary differential equations (ODE's) for the dynamics of the governing…
Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
The paper addresses the boundary control of a class of hyperbolic PDEs, based on an equivalent representation in terms of an integral-difference equation. The situation is considered where direct compensation of reflection terms induces a…
We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…
In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
This paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients. Thereby, the coupling in the PDE is in-domain and at the…
This paper presents the design and analysis of the extremum seeking for static maps with input passed through a partial differential equation (PDE) of the diffusion type defined on a time-varying spatial domain whose boundary position is…
This paper deals with the gradient-based extremum seeking control (ESC) with actuation dynamics governed by distributed wave partial differential equations (PDEs). To achieve the control objective of real-time optimization for this class of…
A new explicit stabilized scheme of weak order one for stiff and ergodic stochastic differential equations (SDEs) is introduced. In the absence of noise, the new method coincides with the classical deterministic stabilized scheme (or…
Although the stabilization of underactuated systems remains a challenging problem, the total energy shaping approach provides a general framework for addressing this objective. However, the practical implementation of this method is…
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
A sliding-mode-based adaptive boundary control law is proposed for a class of uncertain thermal reaction-diffusion processes subject to matched disturbances. The disturbances are assumed to be bounded, but the corresponding bounds are…
Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…