Oscar Mauricio Agudelo

Flood Control with Model Predictive Control for River Systems with Water Reservoirs

Many control strategies can be found in the literature for controlling river systems. One of these methods is model predictive control (MPC), and it has already shown its efficiency for set-point control of reaches and irrigation channels. This paper shows that MPC can also be used for flood control of river systems. The proposed controllers use the buffer capacity of water reservoirs in an optimal way when there is a risk of flooding, and they recover the used buffer capacity as fast as possible. The performance of the controllers is tested on a river system consisting of multiple channels, gates, and a water reservoir. One controller is used in combination with a Kalman filter, which estimates all the states of the river system on the basis of a very limited number of measured water levels. It was observed that the influence of this estimator on the control performance was minimal. DOI: 10.1061/(ASCE)IR.1943-4774.0000577.

Positive Polynomial Constraints for POD-based Model Predictive Controllers

This paper presents an application of positive polynomials to the reduction of the number of temperature constraints of a proper orthogonal decomposition (POD)-based predictive controller for a non-isothermal tubular reactor. The objective of the controller is to maintain the reactor at a desired operating condition in spite of disturbances in the feed flow, while keeping the maximum temperature low enough to avoid the formation of undesired byproducts. The controller is based on a model derived by means of POD, which reduces the high dimensionality of the discretized system used to approximate the partial differential equations that model the reactor. However, POD does not lead to a reduction in the number of temperature constraints which is typically very large. If we use univariate polynomials to approximate part of the basis vectors derived with the POD technique, it is possible to apply the theory of positive polynomials to find good approximations of the temperature constraints by linear matrix inequalities and to get a reduction in their number. This is the approach that is followed in this paper. The simulation results show that the predictive controller presented a good behavior and that it dealt with the temperature constraints very well.

Incremental multi-class semi-supervised clustering regularized by Kalman filtering

This paper introduces an on-line semi-supervised learning algorithm formulated as a regularized kernel spectral clustering (KSC) approach. We consider the case where new data arrive sequentially but only a small fraction of it is labeled. The available labeled data act as prototypes and help to improve the performance of the algorithm to estimate the labels of the unlabeled data points. We adopt a recently proposed multi-class semi-supervised KSC based algorithm (MSS-KSC) and make it applicable for on-line data clustering. Given a few user-labeled data points the initial model is learned and then the class membership of the remaining data points in the current and subsequent time instants are estimated and propagated in an on-line fashion. The update of the memberships is carried out mainly using the out-of-sample extension property of the model. Initially the algorithm is tested on computer-generated data sets, then we show that video segmentation can be cast as a semi-supervised learning problem. Furthermore we show how the tracking capabilities of the Kalman filter can be used to provide the labels of objects in motion and thus regularizing the solution obtained by the MSS-KSC algorithm. In the experiments, we demonstrate the performance of the proposed method on synthetic data sets and real-life videos where the clusters evolve in a smooth fashion over time.

Modelling of a river system with multiple reaches

Abstract In this paper we present a new approach to model river systems. In general the dynamics of a single reach can be described with the Saint-Venant equations. These equations can be combined with nonlinear gate equations to fully characterize the behavior of river systems with multiple reaches. Simulating the dynamics of a river system while taking all these nonlinearities into account, can take a lot of time. The complete linearization of these equations can drastically decrease the computational burden on one hand, but on the other hand it can compromise the accuracy of the results. Therefore in this paper we propose to combine the linear version of the Saint-Venant equations with the nonlinear gate equations in order to reduce the computational load while generating accurate results. In addition, we show that the use of Proper Orthogonal Decomposition (POD) and Galerkin Projection can lead to an extra computational saving.

Assimilation of ozone measurements in the air quality model AURORA by using the Ensemble Kalman Filter

This paper presents the results of using the Ensemble Kalman Filter (EnKF) for improving the ozone estimations of the air quality model AURORA. The EnKF is built around a stochastic formulation of the model, where some of its parameters are assumed to be uncertain. These uncertainties turn out to be the main reason behind the differences between the model predictions and the real measurements. The filter estimates these parameters as well as the ozone concentration field by using ground-based measurements from the Airbase database. The assimilation experiments are carried out over a region that consists of Belgium, Luxembourg, and some small parts of Germany, France and the Netherlands. The simulations results show that the EnKF significantly reduces the error of the ozone estimations.

Hammerstein system identification through best linear approximation inversion and regularisation

ABSTRACT Hammerstein systems are composed by the cascading of a static nonlinearity and a linear system. In this paper, a methodology for identifying such systems using a combination of least squares support vector machines (LS-SVM) and best linear approximation (BLA) techniques is proposed. To do this, a novel method for estimating the intermediate variable is presented allowing a clear separation of the identification steps. First, an approximation to the linear block is obtained through the BLA of the system. Then, an approximation to the intermediate variable is obtained using the inversion of the estimated linear block and the known output. Afterwards, a nonlinear model is calculated through LS-SVM using the estimated intermediate variable and the known input. To do this, the regularisation capabilities of LS-SVM play a crucial role. Finally, a parametric re-estimation of the linear block is made. The method was tested in three examples, two of them with hard nonlinearities, and was compared with four other methods showing very good performance in all cases. The obtained results demonstrate that also in the presence of noise, the method can effectively identify Hammerstein systems. The relevance of these findings lies in the fact that it is shown how the regularisation allows to bypass the usual problems associated with the noise backpropagation when the inversion of the estimated linear block is used to compute the intermediate variable.

Impulse response constrained LS-SVM modelling for MIMO Hammerstein system identification

ABSTRACT In this paper, a new methodology for identifying multiple inputs multiple outputs Hammerstein systems is presented. The proposed method aims at incorporating the impulse response of the system into a least-squares support vector machine (LS-SVM) formulation and therefore the regularisation capabilities of LS-SVM are applied to the system as a whole. One of the main advantages of this method comes from the fact that it is flexible concerning the class of problems it can model and that no previous knowledge about the underlying non-linearities is required except for very mild assumptions. Also, it naturally adapts to handle different numbers of inputs/outputs and performs well in the presence of white Gaussian noise. Finally, the method incorporates information about the structure of the system but still the solution of the model follows from a linear system of equations. The performance of the proposed methodology is shown through three simulation examples and compared with other methods in the literature.

Hammerstein system identification using LS-SVM and steady state time response

In this paper a new system identification approach for Hammerstein systems is proposed. A straightforward estimation of the nonlinear block through the use of LS-SVM is done by making use of the behavior of Hammerstein systems in steady state. Using the estimated nonlinear block, the intermediate variable is calculated. Using the latter and the known output, the linear block can be estimated. The results indicate that the method can effectively identify Hammerstein systems also in the presence of a considerable amount of noise. The well-known capabilities of LS-SVM for the representation of nonlinear functions play an important role in the generalization capabilities of the method allowing to work with a wide range of model classes. The proposed methods main strength lies precisely in the identification of the nonlinear block of the Hammerstein system. The relevance of these findings resides in the fact that a very good estimation of the inner workings of a Hammerstein system can be achieved.

Model Predictive Control applied to a river system with two reaches

Many control strategies can be found in literature for controlling a river system. Most of these methods focus on set-point control such that the most upstream or downstream part of each reach tracks a certain reference trajectory while minimizing the effect of disturbances. However many of the control techniques suitable for set-point control cannot be used at the same time for preventing a river from flooding when large disturbances take place. In this paper we show that Model Predictive Control can be used for set-point control and flood control of a river system consisting of two reaches and one gate. For this we use a linearized version of the Saint-Venant equations with special attention to the gate dynamics.

Reduction of the computational burden of POD models with polynomial nonlinearities

This paper presents a technique for making the evaluation of POD models with polynomial nonlinearities less intensive. Regularly, Proper Orthogonal Decomposition (POD) and Galerkin projection have been employed to reduce the high-dimensionality of the discretized systems used to approximate Partial Differential Equations (PDEs). Although a large model-order reduction can be obtained with these techniques, the computational saving during simulation is small when we have to deal with nonlinear or Linear Time Variant (LTV) models. In this paper, we present a method that exploits the polynomial nature of POD models derived from input-affine high-dimensional systems with polynomial nonlinearities, for generating compact and efficient representations that can be evaluated much faster. Furthermore, we show how the use of the feature selection techniques can lead to a significant computational saving.