The problem of expressing a given nonlinear statespace system as the cascade connection of a lossless system and a stable, minimum-phase system (inner-outer factorization) is solved for the case of a stable system having state-space equations affine in the inputs. The solution is given in terms of the stabilizing solution of a certain Hamilton-Jacobi equation. The stable, minimum-phase factor i...

It is well understood that an open-loop Lyapunov stable nonaffine-in-control nonlinear system can be asymptotically stabilized through feedback. But stabilizing an open-loop unstable nonaffine system remains an open research question. This paper derives the necessary conditions required to render a general open-loop unstable nonlinear system passive through static feedback. It is shown that thi...

This paper considers a gradient type of iterative algorithm applied to the open loop control for nonlinear affine systems. The convergence of the algorithm relies on the control signal in each iteration be nonsingular. We present an algorithm for computing the singular control for a general class of nonlinear affine systems. Various nonlinear mechanical systems, including nonholonomic systems, ...

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, robust control design is presented for a general class of uncertain non-affine nonlinear systems. The design employs feedback linearization, coupled with two high-gain observers— the first to estimate the feedback linearization error based on the full state information; the second to estimate the unmeasured states of the system when only the system output is available for feedbac...

A new discretization method for calculating a sampled-data representation of a nonlinear continuous-time system is proposed. The proposed method is based on the wellknown Taylor series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure, a sampled-data representation of a nonlinear system with a ...

the work deals with universal control formula which provides output global asymptotic stability for affine in control nonlinear system. Development of this result to input-to-output stability (IOS) is also considered. Copyright © 2002 IFAC

We review the correspondence between symmetric affine theories and the nonlinear Einstein-Proca system that was found by Einstein and Schrödinger. With the use of this correspondence, we investigate static spherically symmetric solutions in symmetric affine theory with no matter fields. Use of the correspondence leads to a significant simplification of the calculation. A special instance of “no...

The paper presents a methodology for the construction of an explicit nonlinear control law via approximation of the nonlinear constrained finitetime optimal control (CFTOC). This is achieved through an approximate mapping of a general nonlinear system in a set of linear piecewise affine (PWA) systems. The key advantages of this methodology are two-fold: firstly, the construction of an analytic ...

The sigma model approach to the closed bosonic string on the affine-metric manifold is considered. The two-loop metric counterterms for the nonlinear twodimensional sigma model with affine-metric target manifold are calculated. The correlation of the metric and affine connection is considered as the result of the conformal invariance condition for the nonlinear sigma model. The examples of the ...