On a switching control scheme for nonlinear systems with ill-defined relative degree

This paper discusses the applicability of a switching control scheme for a nonlinear system with ill-defined relative degree. The control scheme switches between exact and approximate input-output linearisation control laws. Unlike a linear system under a switching control scheme, the equilibria of a nonlinear system may change with the switching. It is pointed out that this is not sufficient to cause instability. When the region of the approximate linearisation control law is attractive to the exact zero dynamics, it is possible that the closed-loop system under the switching control scheme is still stable. The results in this paper shows that the switching control scheme proposed in Tonlin and Sastry (Systems & Control Letters 35(3)(1998) 145-154) is applicable for a wider class of nonlinear systems

On input/output maps for nonlinear systems via continuity in a locally convex topology

In this paper we show that the output of a nonlinear system with inputs in () whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via the study of the continuity of the solution in a locally convex topology generated by seminorms of Hilbert-Schmidt operators in Hilbert space. The result reveals an entirely new structure related to nonlinear systems which can lead to useful approximation results

Overparameterised controllers can reduce non-singular costs

By means of two examples we show that non-singular costs can been reduced for adaptive controllers by overparameterising the estimators. The examples are for scalar and second order systems respectively. In the second example the tuning function design and the overparameterised adaptive backstepping design are compared. In both cases a system is constructed for which the overparameterised design is superior w.r.t. a non-singular measure of transient performance

Recursive exact H-infinity identification from impulse-response measurements

We study the H∞-partial realization problem from a behavioral point of view; we give necessary and sufficient conditions for solvability, and a characterization of all solutions. Instrumental in such analysis is the notion of time- and space-symmetrization of the data, which allows to transform the realization problem with metric- and stability constraints into an unconstrained behavioral modeling one

A two-variable approach to solve the polynomial Lyapunov equation

A two-variable polynomial approach to solve the one-variable polynomial Lyapunov equation is proposed. Lifting the problem from the one-variable to the two-variable context allows to use Faddeev-type recursions in order to solve the polynomial Lyapunov equation in an iterative fashion. The method is especially suitable for applications requiring exact or symbolic computation

Parameter estimation in stochastic systems: some recent results and applications

Some recent work on the characterization of almost sure limit sets for maximum likelihood estimates for stochastic systems is reviewed. Applications to allied topics such as input selection for identification, model selection, self-tuning etc. are briefly discussed