Slide 0 In this talk, we address controllability and trajectory generation issues for a class of control systems we refer to as stratiied. The foundation of our work is exploiting the structure of a stratiied connguration space to obtain controllability results and to formulate trajectory generation algorithms. Outline Introduction and motivating examples. Mathematical preliminaries. Stratiied ...

This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semilinear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical resul...

The objective of the article is the numerical analysis of the absolute controllability of a parabolic system with delayed controls and non zero boundary conditions. Precisely the non zero Dirichlet conditions for the considered PDE are the main novelty of the article. As a result we gave the conditions of the controllability for the parabolic PDE with delayed controls. Key-Words: Controllabilit...

(Γ is relatively open in ∂Ω. The case Γ = ∂Ω is not excluded). The function f is a control which we use to steer the initial datum w0 ∈ L(Ω) to a target ξ ∈ L(Ω) at a certain time T . This kind of control problem has been studied by several authors and with different methods, since a system of the form (1) is important for the applications in viscoelasticity, thermodynamics of materials with me...

In this paper, we investigate the exact controllability properties of an advection-diffusion equation on a bounded domain, using timeand space-dependent velocity fields as the control parameters. This partial differential equation (PDE) is the Kolmogorov forward equation for a reflected diffusion process that models the spatiotemporal evolution of a swarm of agents. We prove that if a target pr...

This article is concerned with the analysis of semi-discrete-in-space and fully-discrete approximations of the null controllability (and controllability to the trajectories) for parabolic equations. We propose an abstract setting for space discretizations that potentially encompasses various numerical methods and we study how the controllability problems depend on the discretization parameters....

This paper is devoted to the analysis of the problem of controllability of fractional (in time) Ordinary and Partial Differential Equations (ODE/PDE). The fractional time derivative introduces some memory effects on the system that need to be taken into account when defining the notion of control. In fact, in contrast with the classical ODE and PDE control theory, when driving these systems to ...

Abstract. In this paper we prove a local exact controllability of the Navier–Stokes equations with the condition on the pressure on parts of the boundary. The local exact controllability is proved by using a global Carleman inequality and an estimate of an equation adjoint to a linearized Navier– Stokes equation with the nonstandard boundary condition. We also obtain the null controllability of...

It is well known that the controllability of a linear multidimensional control system depends on an algebraic property (namely, the torsion-freeness) of a certain module M associated with the system (Oberst, 1990; Pillai and Shankar, 1999; Pommaret and Quadrat, 1999a; 1999b). The recent survey (Wood, 2000) gives different equivalent formulations of controllability and, in particular, the equiva...

This paper deals with the approximate controllability of a functional differential equation with deviated argument and finite delay. Sufficient condition for approximate controllability is proved under the assumption that the linear control system is approximately controllable; thereby removing the need to assume the invertibility of a controllability operator which fails to exist in infinite d...