Related papers: Fourier-Gegenbauer Pseudospectral Method for Solvi…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…
The aim of this work is to give a broad panorama of the control properties of fractional diffusive models from a numerical analysis and simulation perspective. We do this by surveying several research results we obtained in the last years,…
Recent work has shown that stabilizing an affine control system to a desired state while optimizing a quadratic cost subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier…
The optimal power flow problem plays an important role in the market clearing and operation of electric power systems. However, with increasing uncertainty from renewable energy operation, the optimal operating point of the system changes…
A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is…
This paper develops a comprehensive framework for optimal control of systems governed by fractional backward stochastic evolution equations (FBSEEs) in Hilbert spaces. We first establish a stochastic maximum principle (SMP) as a necessary…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
We analyse an optimal control with the following features: the dynamical system is linear, and the dependence upon the control parameter is affine. More precisely we consider $\dot x_\alpha(t) = (G + \alpha(t) F)x_\alpha(t)$, where $G$ and…
We present an optimal control procedure for the non-adiabatic transport of ultracold neutral thermal atoms in optical tweezers arranged in a one-dimensional array, with focus on reaching minimal transfer time. The particle dynamics are…
We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann-Liouville…
The key idea of this contribution is the partial compensation of non-minimum phase zeros or unstable poles. Therefore the integer-order zero/pole is split into a product of fractional-order pseudo zeros/poles. The amplitude and phase…
In this article, we develop a simple mathematical GNU Octave/MATLAB code that is easy to modify for the simulation of mathematical models governed by fractional-order differential equations, and for the resolution of fractional-order…
There is a class of physical filtration processes where the input is adequately modeled by a continuous periodic function f (x) of bounded variation over its period, and the output depends only on certain harmonics of the Fourier expansion…
Quantum controls realize the unitary or nonunitary operations employed in quantum computers, quantum simulators, quantum communications, and other quantum information devices. They implement the desired quantum dynamics with the help of…
This paper introduces a novel fractional-order chemostat model (FOCM) incorporating Caputo fractional derivative with sliding memory (CFDS) to capture microbial memory effects in biological water treatment, addressing limitations of…
The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the…
We present a frequency domain based $H_\infty$-control strategy to solve boundary control problems for systems governed by parabolic or hyperbolic partial differential equation, where controllers are constrained to be physically…
We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity…
The first order optimality conditions of optimal control problems (OCPs) can be regarded as boundary value problems for Hamiltonian systems. Variational or symplectic discretisation methods are classically known for their excellent long…