this paper studies the generalized version of thezakharov-kuznetsov benjamin-bona-mahoney equation. the functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. there are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. the results of this pape...

We investigate control systems as variational equations in non-standard chains of rigged Hilbert spaces. Monotonicity properties of nonlinearities are introduced with respect to such riggings generated by Lyapunov operators and invariant cones. Sufficient frequency domain conditions for boundedness and the existence of Bohr and Stepanov almost periodic solutions are derived. As an example we co...

In this paper, we consider the one-phase Stefan problem with surface tension, set in a two-dimensional strip-like geometry, periodic boundary conditions respect to horizontal direction [Formula: see text]. We prove that system is locally null-controllable any positive time, by means of control supported within an arbitrary open and non-empty subset. proceed linear test duality, but quickly find...

Repetitive Control is a relatively new technique for controlling systems that contain periodic reference signals or periodic disturbances. The fundamental idea behind the method is to use the internal model of the periodic signal to guarantee asymptotic reference tracking or disturbance rejection. In this paper two recent Repetitive Control algorithms are applied to a simulation model of a damp...

In this report, a control method for the stabilization of periodic orbits for a class of discrete-time systems that are topologically conjugate to symbolic dynamics is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any perio...

In this report, we propose a periodic state feedback control law for a class of continuous-time linear periodic systems. The proposed control law generates a sufficiently high frequency sinusoidal in the coefficient of a closed loop system, then the closed loop system is shown to be exponentially stable based on the averaging method. It is also shown that a closed loop solution is approximated ...