Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints

This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost function in terms of expected values and higher moments of the states, and chance constraints that ensure probabilistic constraint satisfaction. The generalized polynomial chaos framework is used to propagate the time-invariant stochastic uncertainties through the nonlinear system dynamics, and to efficiently sample from the probability densities of the states to approximate the satisfaction probability of the chance constraints. To increase computational efficiency by avoiding excessive sampling, a statistical analysis is proposed to systematically determine a-priori the least conservative constraint tightening required at a given sample size to guarantee a desired feasibility probability of the sample-approximated chance constraint optimization problem. In addition, a method is presented for sample-based approximation of the analytic gradients of the chance constraints, which increases the optimization efficiency significantly. The proposed stochastic nonlinear model predictive control approach is applicable to a broad class of nonlinear systems with the sufficient condition that each term is analytic with respect to the states, and separable with respect to the inputs, states and parameters. The closed-loop performance of the proposed approach is evaluated using the Williams-Otto reactor with seven states, and ten uncertain parameters and initial conditions. The results demonstrate the efficiency of the approach for real-time stochastic model predictive control and its capability to systematically account for probabilistic uncertainties in contrast to a nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro

A Nonstationary Model of Newborn EEG

The detection of seizure in the newborn is a critical aspect of neurological research. Current automatic detection techniques are difficult to assess due to the problems associated with acquiring and labelling newborn electroencephalogram (EEG) data. A realistic model for newborn EEG would allow confident development, assessment and comparison of these detection techniques. This paper presents a model for newborn EEG that accounts for its self-similar and non-stationary nature. The model consists of background and seizure sub-models. The newborn EEG background model is based on the short-time power spectrum with a time-varying power law. The relationship between the fractal dimension and the power law of a power spectrum is utilized for accurate estimation of the short-time power law exponent. The newborn EEG seizure model is based on a well-known time-frequency signal model. This model addresses all significant time-frequency characteristics of newborn EEG seizure which include; multiple components or harmonics, piecewise linear instantaneous frequency laws and harmonic amplitude modulation. Estimates of the parameters of both models are shown to be random and are modelled using the data from a total of 500 background epochs and 204 seizure epochs. The newborn EEG background and seizure models are validated against real newborn EEG data using the correlation coefficient. The results show that the output of the proposed models has a higher correlation with real newborn EEG than currently accepted models (a 10% and 38% improvement for background and seizure models, respectively)

Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

Issued as Progress report, and Final report, Project no. E-21-67

Bubble size distribution measurement, modeling and control in a laboratory flotation column

Ce travail de recherche vise à mesurer et à contrôler la distribution du diamètre des bulles (DDB) dans une colonne de flottation. L'objectif se décompose en trois parties. La première phase vise à estimer correctement la taille des bulles grâce à des algorithmes de traitement d'images prises par une caméra. La DDB obtenue est ensuite modélisée par une distribution log-normale qui est définie par deux paramètres, la moyenne et l'écart type. Deuxièmement, grâce au nouveau système de mesure et à la représentation log-normale, un modèle dynamique à gains non linéaires (structure de Wiener) dont les sorties sont la moyenne et l'écart-type de la DDB est estimé. Une bonne concordance entre la réponse du système expérimental et celle du modèle identié est observée. Finalement, une stratégie de commande prédictive contrainte basée sur le modèle de Wiener est conçue afin de réguler la BSD. Les résultats de laboratoire obtenus sont très satisfaisants