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Online feedback optimization (OFO) enables optimal steady-state operations of a physical system by employing an iterative optimization algorithm as a dynamic feedback controller. When the plant consists of several interconnected…
In this work, we consider a diffuse interface model for tumour growth in the presence of a nutrient which is consumed by the tumour. The system of equations consists of a Cahn--Hilliard equation with source terms for the tumour cells and a…
A distributed optimal control problem for an extended model of phase field type for tumor growth is addressed. In this model, the chemotaxis effects are also taken into account. The control is realized by two control variables that design…
We establish a separation principle for the output feedback stabilisation of state-affine systems that are observable at the stabilization target. Relying on control templates (recently introduced in [4]), that allow to approximate a…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
We introduce a framework for analyzing ordinary differential equation (ODE) models of biological networks using statistical model checking (SMC). A key aspect of our work is the modeling of single-cell variability by assigning a probability…
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…
In this paper we present a continuation method which transforms spatially distributed ODE systems into continuous PDE. We show that this continuation can be performed both for linear and nonlinear systems, including multidimensional, space-…
Active matter swarms -- collectives of self-propelled particles that could self-assemble, ferry microscopic cargo, or endow materials with dynamic properties -- remain hard to steer. In crowded systems, tracking or controlling individual…
For population systems modeled by age-structured hyperbolic partial differential equations (PDEs), we redesign the existing feedback laws, designed under the assumption that the dilution input is directly actuated, to the more realistic…
This paper considers the backstepping state feedback and observer design for hyperbolic and parabolic PDEs, which are bidirectionally interconnected in a general coupling structure. Both PDE subsystems consist of coupled scalar PDEs with…
We consider a quasilinear degenerate diffusion-reaction system that describes biofilm formation. The model exhibits two non-linear effects: a power law degeneracy as one of the dependent variables vanishes and a super diffusion singularity…
The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…
A dynamic model of non-lineal time-dependent ordinary differential equations (ODE) has been applied to the interactions of a HIV infection with the immune system cells. This model has been simplified into two compartments: lymph node and…
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…
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…
In this paper, we design a controller for an interconnected system composed of a linear Stochastic Differential Equation (SDE) controlled through a linear hetero-directional hyperbolic Partial Differential Equation (PDE). Our objective is…
We propose a novel framework for analyzing the dynamics of distribution shift in real-world systems that captures the feedback loop between learning algorithms and the distributions on which they are deployed. Prior work largely models…
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…
This work presents a unified dissipaton-equation-of-motion (DEOM) theory and its evaluations on the Helmholtz free energy change due to the isotherm mixing of two isolated subsystems. One is a local impurity and another is a nonlocal…