In the present short communication, we revisit nonlinearity management of the timeperiodic nonlinear Schrödinger equation and the related averaging procedure. By means of rigorous estimates, we show that the averaged nonlinear Schrödinger equation does not blow up in the higher dimensional case so long as the corresponding solution remains smooth. In particular, we show that the H norm remains ...

This paper develops a computational method for designing a feedback control system where the plant is an uncertain linear time-invariant convolution subsystem with a static memoryless input nonlinearity. The main design objective is to determine a controller ensuring that the error and the controller output are always within respective bounds for all uncertainties and for all inputs having boun...

We present numerical simulations of the defocusing nonlinear Schrödinger (NLS) equation with an energy supercritical nonlinearity. These computations were motivated by recent works of Kenig-Merle and Kilip-Visan who considered some energy supercritical wave equations and proved that if the solution is a priori bounded in the critical Sobolev space (i.e. the space whose homogeneous norm is invar...

This paper extends the idea of switching T-S fuzzy systems with linear consequent parts to nonlinear ones. Each nonlinear subsystem is exactly represented by a T-S fuzzy system with Lure’ type consequent parts, which allows to model and control wider classes of switching systems and also reduce the computation burden of control synthesis. With the use of a switching fuzzy Lyapunov function, the...

In this paper, an adaptive controller is investigated for a class of uncertain single-input-single-output nonlinear systems preceded by an unknown backlash-type hysteresis nonlinearity, which is modeled by a differential equation. Backstepping design procedure is employed to construct the control input and adaptation laws. A new algorithm is designed to reduce the computational burden compared ...

chaotic systems are nonlinear dynamic systems, the main feature of which is high sensitivity to initial conditions. to initiate a design process in fuzzy model, chaotic systems must first be represented by t-s fuzzy models. in this paper, a new fuzzy modeling method based on sector nonlinearity approach has been recommended for chaotic systems relating to initial condition variations using the ...

In this article, we consider a stochastic PDE of parabolic type, driven by a space-time white-noise, and its numerical discretization in time with a semi-implicit Euler scheme. When the nonlinearity is assumed to be bounded, then a dissipativity assumption is satisfied, which ensures that the SDPE admits a unique invariant probability measure, which is ergodic and strongly mixing with exponenti...

We consider bounded solutions of the semilinear heat equation ut = uxx+f(u) on R, where f is of a bistable type. We show that there always exist bounded solutions whose ω-limit set with respect to the locally uniform convergence contains functions which are not steady states. For balanced bistable nonlinearities, there are examples of such solutions with initial values u(x, 0) converging to 0 a...

This letter focuses on safety-critical control with sector-bounded uncertainties at the plant input. The can represent nonlinear and/or time-varying components. We propose a new robust barrier function (RCBF) approach to enforce safety requirements in presence of these uncertainties. primary objective is minimally alter given baseline command guarantee modeled uncertainty. resulting min-norm op...