Related papers: Feedback theory extended for proving generation of…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
The theoretical analysis and numerical simulations of the magnetron operation with a feedback loop were performed assuming that the delay of the electromagnetic wave propagating in the loop is constant whereas the phase of the complex…
This work is devoted to the stabilization of parabolic systems with a finite-dimensional control subjected to a constant delay. Our main result shows that the Fattorini-Hautus criterion yields the existence of such a feedback control, as in…
These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of…
The focal point of this paper is to theoretically investigate and numerically validate the effect of time delay on the exponential stabilization of a class of coupled hyperbolic systems with delayed and non-delayed dampings. The class in…
We consider the standard thermodynamic processes with constraints, but with additional uncertainty about the control parameters. Motivated by inductive reasoning, we assign prior distribution that provides a rational guess about likely…
In this article a stabilizing feedback control is computed for a semilinear parabolic partial differential equation utilizing a nonlinear model predictive (NMPC) method. In each level of the NMPC algorithm the finite time horizon open loop…
Effective field theory provides a way of parameterizing strong-field deviations from General Relativity that might be observable in the gravitational waves emitted in a black hole merger. To perform numerical simulations of mergers in such…
This paper presents a new method for dynamic output feedback stabilizing controller design for decomposable systems with switching topology and delay. Our approach consists of two steps. In the first step, we model the decomposable systems…
We consider the problem of output feedback controller sparsification for systems with parametric uncertainties. We develop an optimization scheme that minimizes the performance deterioration caused by the sparsification process, while…
It is shown that a general two-component feedback loop can be viewed as a deformed Hamiltonian system. Some of the implications of using ideas from theoretical physics to study biological processes are discussed.
It is shown that an explicit oblique projection nonlinear feedback controller is able to stabilize semilinear parabolic equations, with time-dependent dynamics and with a polynomial nonlinearity. The actuators are typically modeled by a…
Time-delayed quantum feedback is a fast and efficient method to control and stabilize few and many-body quantum systems. However, a proper understanding of such systems stays opaque due to the non-Markovian nature of the feedback protocol.…
We present a well-posedness and stability result for a class of nondegenerate linear parabolic equations driven by rough paths. More precisely, we introduce a notion of weak solution that satisfies an intrinsic formulation of the equation…
This paper is dedicated to the investigation of the asymptotic behavior of a delayed wave equation without the presence of any position term. First, it is shown that the problem is well-posed in the sense of semigroups theory. Thereafter,…
We study a feedback stabilization problem for a first-order hyperbolic partial differential equation. The problem is inspired by the stabilization of equilibrium age profiles for an age-structured chemostat, using the dilution rate as the…
The damped nonlinear wave equation, also known as the nonlinear telegraph equation, is studied within the framework of semigroups and eigenfunction approximation. The linear semigroup assumes a central role: it is bounded on the domain of…
We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…
Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological,…
We present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by general, quasilinear, first-order hyperbolic PDEs. Since for such PDE-ODE cascades the speed of propagation depends on the PDE state…