The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given.

The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given.

A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal...

In this paper we review the concept of regional boundary observability, developed in (Michelitti, 1976), by means of sensor structures. This leads to the so-called boundary strategic sensors. A characterization of such sensors which guarantees regional boundary observability is given. The results obtained are applied to a two-dimensional system, and various cases of sensors are considered. We also describe an approach which leads to the estimation of the initial boundary state, which is illustrated...

The purpose of this paper is to study the problem of regional detection, to characterize internal or boundary regionally detectable sources and regionally spy sensors, and to establish a relationship between these sensors and regionally strategic sensors. It is shown how to reconstruct a regionally detectable internal or a boundary source from a given output, with an extension to the case when the output is affected by an observation error. Numerical results are given in the case of a diffusion...

The regularity of solutions of various dynamical equations (wave, Euler-Bernoulli, Kirchhoff, Schrödinger) in a bounded open domain $\mathrm{\Omega }$ in ${\mathbb{R}}^N$, subject to the action of a point control at some point of $\mathrm{\Omega }$, is studied. Detailed proofs of the results are contained in the references [8-10].

We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain $\Omega$ with control distributed in a subdomain $\omega \subset \Omega \subset {ℝ}^n,n\in \{2,3\}$. The result that we obtained in this paper is as follows. Suppose that $\widehat{v}(t,x)$ is a given solution of the Navier-Stokes equations. Let $v_0\left(x\right)$ be a given initial condition and $\parallel \widehat{v}(0,·)-v_0\parallel \<\epsilon$ where $\epsilon$ is small enough. Then there exists a locally distributed control $u,\text{supp}u\subset (0,T)\times \omega$ such that the solution $v(t,x)$ of the Navier-Stokes equations:$${\partial }_{t}v-\Delta v+(v,\nabla )v=\nabla p+u+f,\text{div}v=0,v{{|}_{\partial \Omega }=0,v|}_{t=0}=v_0$$coincides with...

We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain Ω with control distributed in a subdomain $\omega \subset \Omega \subset {ℝ}^n,n\in \{2,3\}$. The result that we obtained in this paper is as follows. Suppose that $\widehat{v}(t,x)$ is a given solution of the Navier-Stokes equations. Let $v_0\left(x\right)$ be a given initial condition and $\parallel \widehat{v}(0,·)-v_0\parallel <\epsilon$ where ε is small enough. Then there exists a locally distributed control $u,\text{supp}u\subset (0,T)\times \omega$ such that the solution v(t,x) of the Navier-Stokes equations: $${\partial }_{t}v-\Delta v+(v,\nabla )v=\nabla p+u+f,\text{div}v=0,v{{|}_{\partial \Omega }=0,v|}_{t=0}=v_0$$ coincides...

In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time T and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.