Fredy Ruiz

José Vuelvas, Fredy Ruiz

A rational behavior of a consumer is analyzed when the user participates in a Peak Time Rebate (PTR) mechanism, which is a demand response (DR) incentive program based on a baseline. A multi-stage stochastic programming is proposed from the demand side in order to understand the rational decisions. The consumer preferences are modeled as a risk-averse function under additive uncertainty. The user chooses the optimal consumption profile to maximize his economic benefits for each period. The stochastic optimization problem is solved backward in time. A particular situation is developed when the System Operator (SO) uses consumption of the previous interval as the household-specific baseline for the DR program. It is found that a rational consumer alters the baseline in order to increase the well-being when there is an economic incentive. As results, whether the incentive is lower than the retail price, the user shifts his load requirement to the baseline setting period. On the other hand, if the incentive is greater than the regular energy price, the optimal decision is that the user spends the maximum possible energy in the baseline setting period and reduces the consumption at the PTR time. This consumer behavior produces more energy consumption in total considering all periods. In addition, the user with high uncertainty level in his energy pattern should spend less energy than a predictable consumer when the incentive is lower than the retail price.

Sergio Vanegas, Lasse Lensu, Fredy Ruiz

Building black-box models for dynamical systems from data is a challenging problem in machine learning, especially when asymptotic stability guarantees are required. In this paper, we introduce a novel stability-ensuring and backpropagation-compatible projection scheme based on the Schur decomposition for the state matrix of linear discrete-time state-space layers, as well as an alternative pre-factorized formulation of the methodology. The proposed methods dynamically project the quasi-triangular factor of the state matrix's real Schur decomposition onto its nearest stable peer, ensuring stable dynamics with minimal overparameterization. Experiments on synthetic linear systems demonstrate that the method achieves accuracy and convergence rates comparable to those of state-of-the-art stable-system identification techniques, despite a marginal increase in computational complexity. Furthermore, the lower weight count facilitates convergence during training without sacrificing accuracy in stacked neural-network architectures with static nonlinearities targeting real-world datasets. These results suggest that the Schur-based projection provides a numerically robust framework for identifying complex dynamics on par with the State of the Art while satisfying strict asymptotic-stability requirements.