Constructions of Almost Optimal Resilient Boolean Functions on Large Even Number of Variables

In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number of variables can be constructed. It is shown that given any $m$, one can construct infinitely many $n$-variable ($n$ even), $m$-resilient functions with nonlinearity $>2^{n-1}-2^{n/2}$. A large class of highly nonlinear resilient functions which were not known are obtained. Then one method to optimize the degree of the constructed functions is proposed. Last, an improved version of the main construction is given.Comment: 14 pages, 2 table

Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Systems with Time-Varying Delays

The stabilization of uncertain LTI/LPV time delay systems with time varying delays by state-feedback controllers is addressed. At the difference of other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exact-memory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow to check the stability of the closed-loop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, the $\mathcal{H}_\infty$ performance measure is considered. The interest of the approach is finally illustrated through several examples

New advances in H∞ control and filtering for nonlinear systems

The main objective of this special issue is to summarise recent advances in H∞ control and filtering for nonlinear systems, including time-delay, hybrid and stochastic systems. The published papers provide new ideas and approaches, clearly indicating the advances made in problem statements, methodologies or applications with respect to the existing results. The special issue also includes papers focusing on advanced and non-traditional methods and presenting considerable novelties in theoretical background or experimental setup. Some papers present applications to newly emerging fields, such as network-based control and estimation

High-Resilience Limits of Block-Shaped Order Books

We show that wealth processes in the block-shaped order book model of Obizhaeva/Wang converge to their counterparts in the reduced-form model proposed by Almgren/Chriss, as the resilience of the order book tends to infinity. As an application of this limit theorem, we explain how to reduce portfolio choice in highly-resilient Obizhaeva/Wang models to the corresponding problem in an Almgren/Chriss setup with small quadratic trading costs.Comment: 12 page

Modelling migration futures: development and testing of the rainfalls agent-based migration model – Tanzania

This paper describes the conceptual and practical development and testing of the Rainfalls Agent-Based Migration Model – Tanzania (RABMM-T). Drawing upon the literature on the process of developing and parameterizing a social simulation in the absence of spatio-temporal data, the paper outlines the translation of the conceptual framework into a working agent-based model. The possible impact of a change in local rainfall variability and mean upon household income, food production, and therefore the resilience and migration of members, is simulated to permit consideration of the possible impact of the artificial scenarios tested. In addition to the influence of changing rainfall, other non-rainfall scenarios are tested to explore the scale of the changes simulated. It is proposed that while a relatively clear impact of rainfall scenarios upon household resilience is simulated, the impact upon migration of household members is generally less clear. Furthermore, demographic and societal changes to the model are also seen to clearly contribute to the simulation outputs generated. The paper concludes that RABMM-T offers the first step in developing a potentially valuable resource for producing comparable migration forecasts that consider a range of contributory mechanisms. However, careful parameterisation is required to ensure the quality and value of model outputs

Bounds for Input- and State-to-Output Properties of Uncertain Linear Systems

We consider the effect of parametric uncertainty on properties of Linear Time Invariant systems. Traditional approaches to this problem determine the worst-case gains of the system over the uncertainty set. Whilst such approaches are computationally tractable, the upper bound obtained is not necessarily informative in terms of assessing the influence of the parameters on the system performance. We present theoretical results that lead to simple, convex algorithms producing parametric bounds on the $\mathcal{L}_2$-induced input-to-output and state-to-output gains as a function of the uncertain parameters. These bounds provide quantitative information about how the uncertainty affects the system.Comment: To appear in the proceedings of the 8th IFAC Symposium on Robust Control Design - ROCOND'1