相关论文: Stabilization of Age-Structured Chemostat Hyperbol…

This paper addresses the stabilization of a chain system consisting of three hyperbolic Partial Differential Equations (PDEs). The system is reformulated into a pure transport system of equations via an invertible backstepping…

The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…

Active nematics are out-of-equilibrium systems in which energy injection at the microscale drives emergent collective behaviors, from spontaneous flows to active turbulence. While the dynamics of these systems have been extensively studied,…

Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical…

This paper presents a boundary control scheme for prescribed-time (PT) stable of flexible string systems via backstepping method, and the dynamics of such systems modeled by Hamilton's principle is described as second-order hyperbolic…

We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs).…

We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on…

We build upon the recent steady-state Penna model solution, Phys.Rev.Lett. 89, 288103 (2002), to study the population dynamics within the Penna model. We show, that any perturbation to the population can be broken into a collection of modes…

This paper presents a delay-adaptive boundary control scheme for a $2\times 2$ coupled linear hyperbolic PDE-ODE cascade system with an unknown and arbitrarily long input delay. To construct a nominal delay-compensated control law, assuming…

This paper examines aspirational requirements for software addressing mixed-integer optimization problems constrained by the nonlinear Shallow Water partial differential equations (PDEs), motivated by applications such as river-flow…

Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this…

We study the properties of linear and non-linear determining functionals for dissipative dynamical systems generated by PDEs. The main attention is payed to the lower bounds for the number of such functionals. In contradiction to the common…

Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…

The dynamic partial differential equation (PDE) model governing longitudinal oscillations in magnetizable piezoelectric beams exhibits exponentially stable solutions when subjected to two boundary state feedback controllers. An analytically…

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…

Solving partial differential equations (PDEs) using neural networks has become a central focus in scientific machine learning. Training neural networks for singularly perturbed problems is particularly challenging due to certain parameters…

This paper presents a safe output regulation control strategy for a class of systems modeled by a coupled $2\times 2$ hyperbolic PDE-ODE structure, subject to fully distributed disturbances throughout the system. A state-feedback controller…

In this work, we consider the problem of boundary stabilization for a quasilinear 2X2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves H^2…

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…

A boundary feedback stabilisation problem of non-uniform linear hyperbolic systems of balance laws with additive disturbance is discussed. A continuous and a corresponding discrete Lyapunov function is defined. Using an…