Tracking control of uncertain systems

Deals with the problem of designing output tracking controllers for uncertain systems. The systems we consider may be non-minimum phase but are restricted to be linear. The problem is motivated by control applications where a desired output trajectory is specified, and the corresponding input to the system is to be found

Tracking control of uncertain systems

Deals with the problem of designing output tracking controllers for uncertain systems. The systems we consider may be non-minimum phase but are restricted to be linear. The problem is motivated by control applications where a desired output trajectory is specified, and the corresponding input to the system is to be found

Asymptotic equivalence of discretely observed diffusion processes and their Euler scheme: small variance case

This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models on the other side. The time horizon $T$ is kept fixed and both the cases of discrete and continuous observation of the path are treated. We allow non constant diffusion coefficient, bounded but possibly tending to zero. The asymptotic equivalences are established by constructing explicit equivalence mappings.Comment: 21 page

Optimal nonparametric estimation of the density of regression errors with finite support

Adaptation, Error depending on predictor, Heteroscedasticity, Minimax, Pinsker oracle,

Optimal Sequential Design in a Controlled Non-parametric Regression

In a non-parametric regression, the heteroscedasticity (dependence of the variance of the regression error on the predictor) can be a serious complication in estimation or visualization of an underlying regression function. If a controlled sampling is permitted, then the statistician can choose the design of predictors which attenuates the effect of heteroscedasticity. It is proposed to use a design which minimizes the mean integrated squared error of the regression function estimation. Then the corresponding optimal design density is proportional to the standard deviation of the regression error (the so-called scale function). Because in general the statistician does not know an underlying scale function, the natural question is as follows: is it possible to suggest a sequential design which performs as well as an oracle that knows the underlying scale function? The answer is 'yes', and a corresponding sequential procedure is developed. It is proved, for the first time in the literature, that a data-driven sequential design, together with an adaptive regression estimator, can mimic the oracle and be sharp minimax. Further, it is shown that the suggested method is feasible for small samples. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008.