Regional gradient controllability of sub-diffusion processes

Gradient Controllability for Hyperbolic Systems

This paper deals with the problem of regional gradient controllability of hyperbolic systems. We show how one can reach a desired state gradient given only on a part of the system evolution domain. Also we explore a numerical approach using Hilbert Uniqueness Method (HUM) that leads to an explicit formula of the optimal control. The obtained results are successfully tested through computer simu...

An inverse inequality for some transport-diffusion equation. Application to the regional approximate controllability

In this paper we prove an inverse inequality for the parabolic equation ut − ε∆u+M · ∇u = f1ω with Dirichlet boundary conditions. With the motivation of finding an estimate of f in terms on the trace of the solution in O × (0, T ) for ε small, our approach consists in studying the convergence of the solutions of this equation to the solutions of some transport equation when ε→ 0, and then recov...

Approximate controllability of a reaction-diffusion system

An open-loop control for a system coupling a reaction-diffusion system and an ordinary differential equation is proposed in this study. We use a flatness-like property, indeed, the solution can be expressed in terms of an infinite series depending on a flat output, its derivatives and its integrals. This series is shown to be convergent if the flat output is Gevrey of order 1 < a ≤ 2. Approxima...

On the null-controllability of diffusion equations

Stability and Controllability of Batch Processes

Im proving the perform ance ofbatch processes requires tools that are tailored to the specificities of batch operations.These include a m athem atical representation thatexplicitly showsthe two independenttim e variables(the run tim e t and therun index k)aswellasthetwo typesofoutputs(therun-tim eand run-end outputs).Furtherm ore,corrective action can be taken via both on-line and run-to-run co...