Related papers: Reachability and Controllability Problems for the …
The main purpose of this article is to prove a logarithmic convexity estimate for the solution of a linear heat equation subject to dynamic boundary conditions in a bounded convex domain. As an application, we prove the impulsive null…
This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method we show that the cost of driving the Stokes system to rest at time T is of order e^C/T when T -->0^+,i.e., the…
The problem of local null controllability for the control-affine nonlinear systems $\dot x(t)=f(x(t))+Bu(t)+w(t),$ $t\in[0,T]$ is considered in this paper. The principal requirements on the system are that the LTI pair $\left((\partial…
The goal of this paper is to analyze the pointwise controllability properties of a one-dimensional degenerate/singular equation. We prove the conditions that characterize approximate and null controllability. Besides, a numerical simulation…
We consider both the internal and boundary controllability problems for wave equations under non-negativity constraints on the controls. First, we prove the steady state controllability property with nonnegative controls for a general class…
We consider a linear nonlocal heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$ with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when…
This paper investigates a minimal time control problem for the heat equation with multiple impulse controls. We first establish the maximum principles for this problem and then prove the equivalence between the minimal time impulse control…
The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an…
In this paper, we study the concept of approximate controllability of retarded network systems of neutral type. On one hand, we reformulate such systems as free-delay boundary control systems on product spaces. On the other hand, we use the…
This paper is concerned with impulse approximate controllability for stochastic evolution equations with impulse controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The minimal norm…
We consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multi-dimensional heat equation with a periodic terminal state constraint. This problem has a unique…
In this article we study the internal controllability of 1D linear hyperbolic balance laws when the number of controls is equal to the number of state variables. The controls are supported in space in an arbitrary open subset. Our main…
We consider the null-controllability problem for the generalized Baouendi-Grushin equation $(\partial_t - \partial_x^2 - q(x)^2\partial_y^2)f = 1_\omega u$ on a rectangular domain. Sharp controllability results already exist when the…
This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…
Intercepting dynamic objects in uncertain environments involves a significant unresolved challenge in modern robotic systems. Current control approaches rely solely on estimated information, and results lack guarantees of robustness and…
This paper deals with the numerical computation of null controls for the linear heat equation. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a given positive time. In…
Under a regularity assumption we prove that reachability in fixed time for nonlinear control systems is robust under control sampling.
We consider linear one-dimensional parabolic equations with space dependent coefficients that are only measurable and that may be degenerate or singular.Considering generalized Robin-Neumann boundary conditions at both extremities, we prove…
It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to…
The null distributed controllability of the semilinear heat equation $y_t-\Delta y + g(y)=f \,1_{\omega}$, assuming that $g$ satisfies the growth condition $g(s)/(\vert s\vert \log^{3/2}(1+\vert s\vert))\rightarrow 0$ as $\vert s\vert…