Boundary control of nonlinear parabolic PDEs is an open problem with applications that include fluids, thermal, chemically-reacting, and plasma systems. In this paper we present stabilizing control designs for a broad class of nonlinear parabolic PDEs in 1-D. Our approach is a direct infinite dimensional extension of the finite-dimensional feedback linearization/backstepping approaches and empl...

Recently, a nonlinear transformation of autocorrelation coefficients named Phase AutoCorrelation (PAC) coefficients has been considered for feature extraction [1]. PAC based features show improved robustness to additive noise as a result of two operations, performed during the computation of PAC, namely energy normalization and inverse cosine transformation. In spite of the improved robustness ...

A nonlinear heat diffusion problem is considered when the thermal conductivity and heat capacity are nonlinear functions of the temperature. At one of the boundaries a highly nonlinear condition is imposed involving both the flux and the temperature. We apply equivalence transformation which allows to reformulate the problem as an equation with linear diffusion for the transformed function. Thi...

In this paper, the problems of control and stabilization of switched nonlinear cascade systems is investigated. The so called simultaneous domination limitation (SDL) is introduced in previous works to assure the existence of a common quadratic Lyapunov function (CQLF) for switched nonlinear cascade systems. According to this idea, if all subsystems of a switched system satisfy the SDL, a CQLF ...

Abstract: This paper presents a case study how to apply the recently proposed TP model transformation technique, that has been introduced for nonlinear statefeedback control design, to nonlinear observer design. The study is conducted through an example. This example treats the question of observer design to the prototypical aeroelastic wing section with structural nonlinearity. This type of mo...

This paper presents the use of the generalized classical method (GCM) for solving linear and nonlinear differential equations. This method is based on the differential transformation (DT) technique. In the GCM, the solution of the nonlinear transient regimes in the physical processes can be written as a functional series with unknown coefficients. The series can be chosen to satisfy the initial...

A class of discrete-time nonlinear systems is studied which is described by a standard linear state-equation except that each state-component is subject to an identical odd 1-Lipschitz nonlinearity. This may represent a class of recurrent neural networks. The emphasis is on the development of an approach that makes the best use of the fact that the nonlinearity on each state-component is the sa...

This paper studies the design of feedback controllers for trajectory tracking in single-inputlsingle-output nonlinear systems X = f (x ) + g(x) u, y = h(x). A nonlinear transformation of the form z, = K ( X ) + X(x) u that transforms this nonlinear input/output system into a linear system is first constructed. On the basis of this transformation, an approach for designing control laws for traje...