Jairo Espinosa

Algorithmic procedures for Bayesian MEG/EEG source reconstruction in SPM

The MEG/EEG inverse problem is ill-posed, giving different source reconstructions depending on the initial assumption sets. Parametric Empirical Bayes allows one to implement most popular MEG/EEG inversion schemes (Minimum Norm, LORETA, etc.) within the same generic Bayesian framework. It also provides a cost-function in terms of the variational Free energy—an approximation to the marginal likelihood or evidence of the solution. In this manuscript, we revisit the algorithm for MEG/EEG source reconstruction with a view to providing a didactic and practical guide. The aim is to promote and help standardise the development and consolidation of other schemes within the same framework. We describe the implementation in the Statistical Parametric Mapping (SPM) software package, carefully explaining each of its stages with the help of a simple simulated data example. We focus on the Multiple Sparse Priors (MSP) model, which we compare with the well-known Minimum Norm and LORETA models, using the negative variational Free energy for model comparison. The manuscript is accompanied by Matlab scripts to allow the reader to test and explore the underlying algorithm.

A general Bayesian treatment for MEG source reconstruction incorporating lead field uncertainty

There is uncertainty introduced when a cortical surface based model derived from an anatomical MRI is used to reconstruct neural activity with MEG data. This is a specific case of a problem with uncertainty in parameters on which M/EEG lead fields depend non-linearly. Here we present a general mathematical treatment of any such problem with a particular focus on co-registration. We use a Metropolis search followed by Bayesian Model Averaging over multiple sparse prior source inversions with different headlocation/orientation parameters. Based on MEG data alone we can locate the cortex to within 4 mm at empirically realistic signal to noise ratios. We also show that this process gives improved posterior distributions on the estimated current distributions, and can be extended to make inference on the locations of local maxima by providing confidence intervals for each source.

Feasible-Cooperation Distributed Model Predictive Control Scheme Based on Game Theory

Abstract This work deals with the formulation of a distributed model predictive control scheme as a decision problem in which the decisions of each subsystem affect the decisions of the other subsystems and the performance of the whole system. This decision problem is formulated as a bargaining game. This formulation allows each subsystem to decide whether to cooperate or not depending on the benefits that the subsystem can gain from the cooperation. A solution based on game theory is proposed. The convexity and feasibility properties of the proposed solution are also presented. The proposed control scheme is tested on a case study with a chain of two continuous stirred tank reactors followed by a nonadiabatic flash separator.

A multiobjective-based switching topology for hierarchical model predictive control applied to a hydro-power valley

In a Hierarchical Model Predictive Control (H-MPC) framework, this paper explores suitable time-variant structures for the hierarchies of different local MPC controllers. The idea is to adapt to different operational conditions by changing the importance of the local controllers. This is done by defining the level of the hierarchy they belong to, and solving within each level the local MPC problem using the information provided by the higher levels at the current time step and the predicted information from the lower levels obtained in the previous time step. As selecting a hierarchy results in a combinatorial optimization problem, it is explicitly solved for a limited number of relevant topologies only and then the switching between topologies is defined with a multiobjective optimizer, so as to decide the best H-MPC scheme according to the expected performance. A comparison with fixed-topology H-MPC controllers is done, showing the effectiveness of the proposed approach for the power control of a hydro-power valley.

Robust Energy Management System Based on Interval Fuzzy Models

Energy management systems (EMSs) are used for operators to optimize, monitor, and control the performance of a power system. In microgrids, the EMS automatically coordinates the energy sources aiming to supply the demand. The coordination is carried out considering the operating costs, the available energy, and the generation and transmission capabilities of the grid. With this purpose, the available energy of the sources is predicted, and the operating costs are minimized. Thereby, an optimal operation of the microgrid is achieved. Often, the optimization procedure is executed throughout a receding horizon (model predictive control approach). Such approach provides some robustness to the microgrid operation. But, the high variability of the nonconventional energy sources makes the prediction task very complex. As a consequence, the reliable operation of the microgrid is compromised. In this paper, a scenario-based robust EMS is proposed. The scenarios are generated by means of fuzzy interval models. These models are used for solar power, wind power, and load forecasting. Since interval fuzzy models provide a range rather than a trajectory, upper and lower boundaries for these variables are obtained. Such boundaries are used to formulate the EMS as a robust optimization problem. In this sense, the solution obtained is robust against any realization of the uncertain variables inside the intervals defined by the fuzzy models. In addition, the original robust optimization problem is transformed into an equivalent second-order cone programming problem. Hence, desired mathematical properties such as the convexity of the optimization problem might be guaranteed. Therefore, efficient algorithms, based, e.g., on interior-point methods, could be applied to compute its solution. The proposed EMS is tested in the microgrid installed in Huatacondo, a settlement located at the north of Chile.

Cortical surface reconstruction based on MEG data and spherical harmonics

Estimates of coefficients of a spherical harmonic Fourier decomposition of the cortical surface can be obtained solely using MEG/EEG data and free energy as objective function. A stochastic methodology based on a Metropolis Search followed by a Bayesian Model Averaging is proposed to reconstruct cortical anatomy based functional information.

Non-Linear Model Predictive Control Based on Game Theory for Traffic Control on Highways

Abstract This paper presents a methodology for traffic control using a distributed model predictive control scheme based on game theory (GT-DMPC). Using the traffic model METANET as prediction model, the control objective is to minimize the total time spent by vehicles in the traffic network. The proposed control methodology is compared with a centralized model predictive control approach and a non-controlled-case. The simulations show that the GT-DMPC controller efficiently distributes the vehicles entering the highway, and presents a similar performance in comparison with centralized MPC.

Prediction of batch-end quality for an industrial polymerization process

In this paper, an inferential sensor for the final viscosity of an industrial batch polymerization reaction is developed using multivariate statistical methods. This inferential sensor tackles one of the main problems of chemical batch processes: the lack of reliable online quality estimates. In a data preprocessing step, all batches are brought to equal lengths and significant batch events are aligned via dynamic time warping. Next, the optimal input measurements and optimal model order of the inferential multiway partial least squares (MPLS) model are selected. Finally, a full batch model is trained and successfully validated. Additionally, intermediate models capable of predicting the final product quality after only 50% or 75% batch progress are developed. All models provide accurate estimates of the final polymer viscosity.

LQR control for speed and torque of internal combustion engines

Abstract This paper presents a robust automation model for internal combustion engines test beds. A Linear Quadratic Regulator (LQR) allows setting the desired engine speed and torque on both compression and spark ignition engines. With this methodology, the user can change the engine by another one of different characteristics with few adjustments on the controller parameters. The controller was implemented using a microcontroller in order to guarantee operation in real time. The LQR controller performance has been validated in a wide range of engine operating modes, from low to high speeds and variable loads showing a good response. The description of the model using first order transfer functions with delay has proven to be a good approximation, despite of the nonlinearities caused by the turbocharger and the electronic control unit (ECU) incorporated in the engines. This low cost automation system has been tested for the last three years in a test rig at a university laboratory showing a good performance.

An economic MPC approach for a microgrid energy management system

In this paper we address the problem of managing the energy production of a microgrid while satisfying a given demand. Emerging from the Smart Grid technologies, microgrids can be considered as subsections of the main grid with the capability to operate connected or isolated from the main network. An Economic Model Predictive Control (EMPC) scheme is proposed in order to achieve the optimal economic performance in the operational costs of the microgrid. The control scheme is tested in a simulated microgrid composed of a wind turbine, a set of PV panels, an energy storage device, and the connection to the main grid.