Global reconstruction of nonlinear systems from families of linear systems

This note concerns a fundamental issue in the modelling and realisation of nonlinear systems; namely, whether it is possible to uniquely reconstruct a nonlinear system from a suitable collection of transfer functions and, if so, under what conditions. It is established that a family of frozen-parameter linearisations may be associated with a class of nonlinear systems to provide an alternative realisation of such systems. Nevertheless, knowledge of only the inputoutput dynamics (transfer functions) of the frozen-parameter linearisations is insufficient to permit unique reconstruction of a nonlinear system. The difficulty with the transfer function family arises from the degree of freedom available in the choice of state-space realisation of each linearisation. Under mild structural conditions, it is shown that knowledge of a family of augmented transfer functions is sufficient to permit a large class of nonlinear systems to be uniquely reconstructed. Essentially, the augmented family embodies the information necessary to select state-space realisations for the linearisations which are compatible with one another and with the underlying nonlinear system. The results are constructive, with a state-space realisation of the nonlinear system associated with a transfer function family being obtained as the solution to a number of linear equations

Control of sideslip and yaw rate in 4-wheel steering car using partial decoupling and individual channel design

This paper presents a new steering control structure for cars equipped with 4-wheel steering. This control structure is based on a simplified linear model of the lateral dynamics of such cars and aims to decouple the control of sideslip from the control of yaw rate. The control design is based on a linear multivariable plant which incorporates the model of the lateral dynamics mentioned above and whose inputs are linear combinations of the front and rear steering angles. The plant also contains a cross-feedback element. The matrix transfer function of the resulting plant is upper-triangular (partially decoupled). The MIMO design problem can then be recast as two SISO design problems using channel decomposition according to the Individual Channel Design (ICD) paradigm. The proposed control structure has been applied to design sideslip and yaw rate controllers using a more accurate model of the lateral dynamics of 4-wheel steering cars. This model incorporates the tyre force dynamics and the steering actuators. Simulations are used to illustrate the performance and robustness of the designed controllers

Application of velocity-based gain-scheduling to lateral auto-pilot design for an agile missile

In this paper a modern gain-scheduling methodology is proposed which exploits recently developed velocity-based techniques to resolve many of the deficiencies of classical gain-scheduling approaches (restriction to near equilibrium operation, to slow rate of variation). This is achieved while maintaining continuity with linear methods and providing an open design framework (any linear synthesis approach may be used) which supports divide and conquer design strategies. The application of velocity-based gain-scheduling techniques is demonstrated in application to a demanding, highly nonlinear, missile control design task. Scheduling on instantaneous incidence (a rapidly varying quantity) is well-known to lead to considerable difficulties with classical gain-scheduling methods. It is shown that the methods proposed here can, however, be used to successfully design an effective and robust gain-scheduled controller

Fast, responsive decentralized graph coloring

Graph coloring problem arises in numerous networking applications. We solve it in a fully decentralized way (ı.e., with no message passing). We propose a novel algorithm that is automatically responsive to topology changes, and we prove that it converges to a proper coloring in O(NlogN) time with high probability for generic graphs, when the number of available colors is greater than Δ , the maximum degree of the graph, and in O(logN) time if Δ=O(1) . We believe the proof techniques used in this paper are of independent interest and provide new insight into the properties required to ensure fast convergence of decentralized algorithms

Updating Neighbour Cell List via Crowdsourced User Reports: A Framework for Measuring Time Performance

In modern wireless networks deployments, each serving node needs to keep its Neighbour Cell List (NCL) constantly up to date to keep track of network changes. The time needed by each serving node to update its NCL is an important parameter of the network’s reliability and performance. An adequate estimate of such parameter enables a significant improvement of self-configuration functionalities. This paper focuses on the update time of NCLs when an approach of crowdsourced user reports is adopted. In this setting, each user periodically reports to the serving node information about the set of nodes sensed by the user itself. We show that, by mapping the local topological structure of the network onto states of increasing knowledge, a crisp mathematical framework can be obtained, which allows in turn for the use of a variety of user mobility models. Further, using a simplified mobility model we show how to obtain useful upper bounds on the expected time for a serving node to gain Full Knowledge of its local neighbourhood

BLC: Private Matrix Factorization Recommenders via Automatic Group Learning

We propose a privacy-enhanced matrix factorization recommender that exploits the fact that users can often be grouped together by interest. This allows a form of “hiding in the crowd” privacy. We introduce a novel matrix factorization approach suited to making recommendations in a shared group (or “nym”) setting and the BLC algorithm for carrying out this matrix factorization in a privacy-enhanced manner. We demonstrate that the increased privacy does not come at the cost of reduced recommendation accuracy

Recommending access points to individual mobile users via automatic group learning

© 2017 IEEE. We consider user to cell association in a heterogeneous network with a mix of LTE/3G and WiFi cells. Individual user preferences are often neglected when a user to cell association decision is made. In this paper we propose use of a recommender system to inform the mapping of users to cells. We demonstrate the effectiveness of the proposed grouped-based user to cell associations for a set of synthetically generated user/cell ratings

Divide and conquer identification using Gaussian process priors

We investigate the reconstruction of nonlinear systems from locally identified linear models. It is well known that the equilibrium linearisations of a system do not uniquely specify the global dynamics. Information about the dynamics near to equilibrium provided by the equilibrium linearisations is therefore combined with other information about the dynamics away from equilibrium provided by suitable measured data. That is, a hybrid local/global modelling approach is considered. A non-parametric Gaussian process prior approach is proposed for combining in a consistent manner these two distinct types of data. This approach seems to provide a framework that is both elegant and powerful, and which is potentially in good accord with engineering practice

Divide and conquer identification using Gaussian process priors

We investigate the reconstruction of nonlinear systems from locally identified linear models. It is well known that the equilibrium linearisations of a system do not uniquely specify the global dynamics. Information about the dynamics near to equilibrium provided by the equilibrium linearisations is therefore combined with other information about the dynamics away from equilibrium provided by suitable measured data. That is, a hybrid local/global modelling approach is considered. A non-parametric Gaussian process prior approach is proposed for combining in a consistent manner these two distinct types of data. This approach seems to provide a framework that is both elegant and powerful, and which is potentially in good accord with engineering practice

OpenNym: privacy preserving recommending via pseudonymous group authentication

A user accessing an online recommender system typically has two choices: either agree to be uniquely identified and in return receive a personalized and rich experience, or try to use the service anonymously but receive a degraded non-personalized service. In this paper, we offer a third option to this “all or nothing” paradigm, namely use a web service with a public group identity, that we refer to as an OpenNym identity, which provides users with a degree of anonymity while still allowing useful personalization of the web service. Our approach can be implemented as a browser shim that is backward compatible with existing services and as an example, we demonstrate operation with the Movielens online service. We exploit the fact that users can often be clustered into groups having similar preferences and in this way, increased privacy need not come at the cost of degraded service. Indeed use of the OpenNym approach with Movielens improves personalization performance