Exact controllability of non-Lipschitz semilinear systems

Exact Controllability of Semilinear Systems with Impulses

The purpose of this paper is to investigate the controllability of the impulsive semilinear system x′(t) = A(t)x(t) + f(t, x(t)) + B(t)u(t), t ≥ t0, t 6= tk, x(t+k ) = x(t − k ) + Ik(x(t − k )), k = 1, 2, 3, . . . . By making use of Schaefer’s fixed point theorem we obtain some results under which the system is completely controllable. Two examples are also given to illustrate the importance of...

Exact Global Controllability of Semilinear Thermoelastic Systems

Results of exact controllability will be reported for a semilinear thermoelastic system, with control placed in either the mechanical or thermal equation. The controlled partial differential equation (PDE) model will be considered in two cases: (i) rotational forces are present in the PDE, in which case, the underlying dynamics evince hyperbolic behavior; (ii) the rotational inertia parameter i...

Exact Controllability for Multidimensional Semilinear Hyperbolic Equations

In this paper, we obtain a global exact controllability result for a class of multidi-mensional semilinear hyperbolic equations with a superlinear nonlinearity and variable coefficients. For this purpose, we establish an observability estimate for the linear hyperbolic equation with an unbounded potential, in which the crucial observability constant is estimated explicitly by a function of the ...

Exact controllability of semilinear evolution equation and applications

where Z, U are Hilbert spaces, A : D(A) ⊂ Z −→ Z is the infinitesimal generator of strongly continuous semigroup {T (t)}t≥0 inZ, B ∈ L(U,Z), the control function u belongs to L(0, τ ;U) and F : [0, τ ]× Z × U −→ Z is a suitable function. First, we give a necessary and sufficient condition for the exact controllability of the linear system z′ = Az + Bu(t); Second, under some conditions on F , we...

On partial approximate controllability of semilinear systems