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Off-line supervised learning from data of robustly-stabilizing nonlinear explicit model predictive controllers (EMPC) is dealt with in this letter. The learning procedure relies on the construction of a suitably large set of specifically chosen sampling points of the state space in which the values of the optimal EMPC control function have to be computed. When bounding the magnitude of approximation errors is important for stability or performance specifications, regular gridding techniques are not feasible due to the curse of dimensionality arising from the structural exponential growth of the number of points with the state dimension. In this note, we consider non-regular sampling techniques - namely, i.i.d. sampling with uniform distribution, low-discrepancy sequences and lattice point sets - that offer a good covering of the state space without suffering from an unfeasible growth of the number of points, while preserving at the same time the method guarantees in terms of robustness and stability. Some theoretical properties of the proposed sampling schemes are briefly discussed, and their successful application is showcased in a practically-relevant optimal heating problem involving a 21-dimensional state space that rules out the use of regular gridding techniques.

An approximation algorithm for high-dimensional, continuous-state stochastic dynamic programming was first presented based on an orthogonal array (OA) state space discretization and a Multivariate Adaptive Regression Splines (MARS) value function approximation. Given the popularity of Number Theoretic Methods (NTM), this paper compares OA-based experimental designs and NTMs for state space discretization using a ninedimensional inventory forecasting problem. The statistical model employed for future value function approximation is Artificial Neural Networks (ANN).

A novel measurement approach for power-flow analysis in medium-voltage (MV) networks, based on load power measurements at low-voltage level in each secondary substation (SS) and only one voltage measurement at the MV level at primary substation busbars, was proposed by the authors in previous works. In this paper, the method is improved to cover the case of temporary unavailability of load power measurements in some SSs. In particular, a new load power estimation method based on artificial neural networks (ANNs) is proposed. The method uses historical data to train the ANNs and the real-time available measurements to obtain the load estimations. The load-flow algorithm is applied with the estimated load powers, and the MV network state variables are obtained. The proposed method is validated for the real MV distribution network of the island of Ustica. The loads of selected SSs are estimated for two full days of different seasons. In comparison with previous works, satisfactory results are obtained in terms of uncertainty in the calculated power flows, thus suggesting the applicability of the proposed method for real-time monitoring of MV distribution networks.