Continuous Time Modelling Based on an Exact Discrete Time Representation

This chapter provides a survey of methods of continuous time modelling based on an exact discrete time representation. It begins by highlighting the techniques involved with the derivation of an exact discrete time representation of an underlying continuous time model,providing specificc details for a second-order linear system of stochastic differential equations. Issues of parameter identification, Granger causality, nonstationarity, and mixed frequency data are addressed, all being important considerations in applications in economics and other disciplines. Although the focus is on Gaussian estimation of the exact discrete time model, alternative time domain (state space) and frequency domain approaches are also discussed. Computational issues are explored and two new empirical applications are included along with a discussion of applications in the field of macroeconometric modelling

System Identification, State Estimation, And Control Approaches to Gestational Weight Gain Interventions

abstract: Excessive weight gain during pregnancy is a significant public health concern and has been the recent focus of novel, control systems-based interventions. Healthy Mom Zone (HMZ) is an intervention study that aims to develop and validate an individually tailored and intensively adaptive intervention to manage weight gain for overweight or obese pregnant women using control engineering approaches. Motivated by the needs of the HMZ, this dissertation presents how to use system identification and state estimation techniques to assist in dynamical systems modeling and further enhance the performance of the closed-loop control system for interventions. Underreporting of energy intake (EI) has been found to be an important consideration that interferes with accurate weight control assessment and the effective use of energy balance (EB) models in an intervention setting. To better understand underreporting, a variety of estimation approaches are developed; these include back-calculating energy intake from a closed-form of the EB model, a Kalman-filter based algorithm for recursive estimation from randomly intermittent measurements in real time, and two semi-physical identification approaches that can parameterize the extent of systematic underreporting with global/local modeling techniques. Each approach is analyzed with intervention participant data and demonstrates potential of promoting the success of weight control. In addition, substantial efforts have been devoted to develop participant-validated models and incorporate into the Hybrid Model Predictive Control (HMPC) framework for closed-loop interventions. System identification analyses from Phase I led to modifications of the measurement protocols for Phase II, from which longer and more informative data sets were collected. Participant-validated models obtained from Phase II data significantly increase predictive ability for individual behaviors and provide reliable open-loop dynamic information for HMPC implementation. The HMPC algorithm that assigns optimized dosages in response to participant real time intervention outcomes relies on a Mixed Logical Dynamical framework which can address the categorical nature of dosage components, and translates sequential decision rules and other clinical considerations into mixed-integer linear constraints. The performance of the HMPC decision algorithm was tested with participant-validated models, with the results indicating that HMPC is superior to "IF-THEN" decision rules.Dissertation/ThesisDoctoral Dissertation Chemical Engineering 201

Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

Parametric Macromodels of Differential Drivers and Receivers

This paper addresses the modeling of differential drivers and receivers for the analog simulation of high-speed interconnection systems. The proposed models are based on mathematical expressions, whose parameters can be estimated from the transient responses of the modeled devices. The advantages of this macromodeling approach are: improved accuracy with respect to models based on simplified equivalent circuits of devices; improved numerical efficiency with respect to detailed transistor-level models of devices; hiding of the internal structure of devices; straightforward circuit interpretation; or implementations in analog mixed-signal simulators. The proposed methodology is demonstrated on example devices and is applied to the prediction of transient waveforms and eye diagrams of a typical low-voltage differential signaling (LVDS) data link

A hybrid systems model for supervisory cognitive state identification and estimation in neural prosthetics

This paper presents a method to identify a class of hybrid system models that arise in cognitive neural prosthetic medical devices that aim to help the severely handicapped. In such systems a “supervisory decoder” is required to classify the activity of multi-unit extracellular neural recordings into a discrete set of modes that model the evolution of the brain’s planning process. We introduce a Gibbs sampling method to identify the key parameters of a GLHMM, a hybrid dynamical system that combines a set of generalized linear models (GLM) for dynamics of neuronal signals with a hidden Markov model (HMM) that describes the discrete transitions between the brain’s cognitive or planning states. Multiple neural signals of mixed type, including local field potentials and spike arrival times, are integrated into the model using the GLM framework. The identified model can then be used as the basis for the supervisory decoding (or estimation) of the current cognitive or planning state. The identification algorithm is applied to extracellular neural recordings obtained from set of electrodes acutely implanted in the posterior parietal cortex of a rhesus monkey. The results demonstrate the ability to accurately decode changes in behavioral or cognitive state during reaching tasks, even when the model parameters are identified from small data sets. The GLHMM models and the associated identification methods are generally applicable beyond the neural application domain