We study a linear stochastic approximation algorithm that arises in the context of reinforcement learning. The algorithm employs a decreasing step-size, and is driven by Markov noise with time-varying statistics. We show that under suitable conditions, the algorithm can track the changes in the statistics of the Markov noise, as long as these changes are slower than the rate at which the step-s...

A Popov criterion is derived for systems with slowly timevarying parameters. The parameters and their time derivatives are assumed to take values in convex polytopes.

A double sequence x = {xk,l} of points in R is slowly oscillating if for any given ε > 0, there exist α = α(ε) > 0, δ = δ(ε) > 0, and N = N(ε) such that |xk,l−xs,t| < ε whenever k, l ≥ N(ε) and k ≤ s ≤ (1 + α)k, l ≤ t ≤ (1 + δ)l. We study continuity type properties of factorable double functions defined on a double subset A × A of R into R, and obtain interesting results related to uniform cont...

In this study we investigate temporal slowness as a learning principle for receptive fields using slow feature analysis, a new algorithm to determine functions that extract slowly varying signals from the input data. We find a good qualitative and quantitative match between the set of learned functions trained on image sequences and the population of complex cells in the primary visual cortex (...

The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback....

The optimal worst-case uncertainty that can be achieved by identification depends on the observation time. In the first part of the paper, this dependence is evaluated for selected linear time invariant systems in the 2’ and H” norms and shown to be derivable from a monotonicity principle. The minimal time required is shown to depend on the metric complexity of the a priori information set. Two...

This report forms, in two parts, deliverable D2.14 of the TurboNoiseCFD project. It describes the recommended innovative “triple plane pressure” in-duct matching strategy (TPP) at inlet and bypass duct side, and it describes in detail the newly developed and favourably tested CAA code for the propagation and radiation problem at the exhaust side. Due to the presence of the jet, this solution is...

The paper deals with an approximate analysis of non-linear oscillation problems with slowly varying system parameters. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by using the generalized averaging method of Sinha and Srinivasan based on ultraspherical polynomial expansions. The Bogoliubov-Mitro...

Performance analysis for slowly varying spatiotemporal systems is presented in the case when the controller design is based on frozen spatially and temporally invariant descriptions of the plant. This approach generalizes the results developed for the standard case for slowly time-varying systems. We show that the l∞ to l∞ performance of such systems cannot be much worse than that of the frozen...