In the article the problem of output setpoint tracking for affine non-linear system is considered. Presented approach combines state feedback linearization and homotopy numerical continuation in subspaces of phase space where feedback linearization fails. The method of numerical parameter continuation for solving systems of nonlinear equations is generalized to control affine non-linear dynamic...

In this paper we discuss the algebraic construction of the mKdV hierarchy in terms of an affine Lie algebra ŝl(2). An interesting novelty araises from the negative even grade sector of the affine algebra leading to nonlinear integro-differential equations admiting non-trivial vacuum configuration. These solitons solutions are constructed systematically from generalization of the dressing method...

We study the linear differential system associated with supersymmetric affine Toda field equations for Lie superalgebras, which has a purely odd simple root system. For an algebra, problem modified by conformal transformation leads to ordinary equation (ODE) that provides functional relations in integrable models. This is known as ODE/IM correspondence. superconformal are shown reduce couple of...

Fractional differential equations are a very important tool in modelling many phenomena of physics and, therefore, they deserve an independent study of their theories parallel to the well-known theory of differential equations, [10, 12, 15, 17]. On the other hand, a great number of papers about differential and integral equations with a modified argument have appeared in the literature recently...

We extend recent results on affine Volterra processes to the inhomogeneous case. This includes moment bounds of solutions equations driven by a Brownian motion with an kernel K(t,s) and drift diffusion coefficients b(s,Xs) σ(s,Xs). In case b σσT we show how conditional Fourier–Laplace functional can be represented solution Riccati–Volterra integral equation. For convolution type K(t,s)=K¯(t−s) ...