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We consider systems satisfying a matching condition which are functionally known up to weighted L2 and Loo measures of uncertainty. A modified LQ measure of control and state transient performance is given, and the performance of a class of approximate model based adaptive controllers is studied. An upper performance bound is derived in terms of the(More)
This paper is concerned with the gap metric approach to controller discretisation problems for continuous-time nonlinear systems with disturbances in both input and output channels. The principal idea is to construct a discrete controller based on a given stabilizing continuous time controller via a fast sampling and hold procedure and to calculate the gap(More)
Robust and adaptive backstepping designs for an uncertain strict feedback system are compared with respect to a cost functional which is based on an instantaneous quadratic penalty measuring both the output transient and the control effort. It is shown that the adaptive design outperforms the robust design when the actual uncertainty level is sufficiently(More)
We consider the adaptive tracking problem for a chain of integrators, where the uncertainty is static and functional. The uncertainty is speci ed by L2=L1 or weighted L2=L1 norm bounds. We analyse a standard Lyapunov based adaptive design which utilizes a function approximator to induce a parametric uncertainty, on which the adaptive design is completed.(More)
We consider the construction of adaptive controllers for minimum phase linear systems which achieve non-zero robustness margins in the sense of the gap metric. The gap perturbation margin may be more constrained for larger disturbances and for larger parametric uncertainties. Working in an L2 setting, and within the framework of the nonlinear gap metric,(More)
The performance of function approximator based adaptive control designs may scale badly with approximator dimension. For a simple system class, both projection based designs and multiresolution approximation based designs have been shown to have good scaling properties with respect to to linear quadratic (LQ) costs. Here we show that by considering a cost(More)
Graph topologies for nonlinear operators which admit coprime factorisations are defined w.r.t. a gain function notion of stability in a general normed signal space setting. Several metrics are also defined and their relationship to the graph topologies are examined. In particular, relationships between nonlinear generalisations of the gap and graph metrics,(More)
The main result establishes that if a controller C (comprising of a linear feedback of the output and its derivatives) globally stabilizes a (nonlinear) plant P , then global stabilization of P can also be achieved by an output feedback controller C[h] where the output derivatives in C are replaced by an Euler approximation with sufficiently small delay h >(More)