Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by mainly redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone

Error-constrained filtering for a class of nonlinear time-varying delay systems with non-gaussian noises

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this technical note, the quadratic error-constrained filtering problem is formulated and investigated for discrete time-varying nonlinear systems with state delays and non-Gaussian noises. Both the Lipschitz-like and ellipsoid-bounded nonlinearities are considered. The non-Gaussian noises are assumed to be unknown, bounded, and confined to specified ellipsoidal sets. The aim of the addressed filtering problem is to develop a recursive algorithm based on the semi-definite programme method such that, for the admissible time-delays, nonlinear parameters and external bounded noise disturbances, the quadratic estimation error is not more than a certain optimized upper bound at every time step. The filter parameters are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Leverhulme Trust of the U.K., the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and Grant 61074016, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany. Recommended by Associate Editor E. Fabre

A Survey of the Probability Density Function Control for Stochastic Dynamic Systems

Probability density function (PDF) control strategy investigates the controller design approaches in order to to realise a desirable distributions shape control of the random variables for the stochastic processes. Different from the existing stochastic optimisation and control methods, the most important problem of PDF control is to establish the evolution of the PDF expressions of the system variables. Once the relationship between the control input and the output PDF is formulated, the control objective can be described as obtaining the control input signals which would adjust the system output PDFs to follow the pre-specified target PDFs. This paper summarises the recent research results of the PDF control while the controller design approaches can be categorised into three groups: 1) system model-based direct evolution PDF control; 2) model-based distribution-transformation PDF control methods and 3) databased PDF control. In addition, minimum entropy control, PDF-based filter design, fault diagnosis and probabilistic decoupling design are also introduced briefly as extended applications in theory sense

Robust Probabilistic Prediction for Stochastic Dynamical Systems

It is critical and challenging to design robust predictors for stochastic dynamical systems (SDSs) with uncertainty quantification (UQ) in the prediction. Specifically, robustness guarantees the worst-case performance when the predictor's information set of the system is inadequate, and UQ characterizes how confident the predictor is about the predictions. However, it is difficult for traditional robust predictors to provide robust UQ because they were designed to robustify the performance of point predictions. In this paper, we investigate how to robustify the probabilistic prediction for SDS, which can inherently provide robust distributional UQ. To characterize the performance of probabilistic predictors, we generalize the concept of likelihood function to likelihood functional, and prove that this metric is a proper scoring rule. Based on this metric, we propose a framework to quantify when the predictor is robust and analyze how the information set affects the robustness. Our framework makes it possible to design robust probabilistic predictors by solving functional optimization problems concerning different information sets. In particular, we design a class of moment-based optimal robust probabilistic predictors and provide a practical Kalman-filter-based algorithm for implementation. Extensive numerical simulations are provided to elaborate on our results

An EKF-Based Performance Enhancement Scheme for Stochastic Nonlinear Systems by Dynamic Set-Point Adjustment

YesIn this paper, a performance enhancement scheme has been investigated for a class of stochastic nonlinear systems via set-point adjustment. Considering the practical industrial processes, the multi-layer systematic structure has been adopted to achieve the control design requirements subjected to random noise. The basic loop control is given by PID design while the parameters have been fixed after the design phase. Alternatively, we can consider that there exists an unadjustable loop control. Then, the additional loop is designed for performance enhancement in terms of the tracking accuracy. In particular, a novel approach has been presented to dynamically adjust the set-points using the estimated states of the systems through extended Kalman filter (EKF). Minimising the entropy criterion, the parameters of the set-point adjustment controller can be optimised which will enhance the performance of the entire closed-loop systems. Based upon the presented scheme, the stochastic stability analysis has been given to demonstrate that the closed-loop tracking errors are bounded in probability one. To indicate the effectiveness of the presented control scheme, the numerical examples have been given and the simulation results imply that the designed systems are bounded and the tracking performance can be enhanced simultaneously. In summary, a new framework for system performance enhancement has been presented even if the loop control is unadjustable which forms the main contribution of this paper