Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system

The Computational Structure of Spike Trains

Neurons perform computations, and convey the results of those computations through the statistical structure of their output spike trains. Here we present a practical method, grounded in the information-theoretic analysis of prediction, for inferring a minimal representation of that structure and for characterizing its complexity. Starting from spike trains, our approach finds their causal state models (CSMs), the minimal hidden Markov models or stochastic automata capable of generating statistically identical time series. We then use these CSMs to objectively quantify both the generalizable structure and the idiosyncratic randomness of the spike train. Specifically, we show that the expected algorithmic information content (the information needed to describe the spike train exactly) can be split into three parts describing (1) the time-invariant structure (complexity) of the minimal spike-generating process, which describes the spike train statistically; (2) the randomness (internal entropy rate) of the minimal spike-generating process; and (3) a residual pure noise term not described by the minimal spike-generating process. We use CSMs to approximate each of these quantities. The CSMs are inferred nonparametrically from the data, making only mild regularity assumptions, via the causal state splitting reconstruction algorithm. The methods presented here complement more traditional spike train analyses by describing not only spiking probability and spike train entropy, but also the complexity of a spike train's structure. We demonstrate our approach using both simulated spike trains and experimental data recorded in rat barrel cortex during vibrissa stimulation.Comment: Somewhat different format from journal version but same conten

Techno-economic analysis of residential thermal flexibility for demand side management

The continuing rise in solar and wind production leads to an increasing demand of flexibility to stabilize the electricity grid. Furthermore, we can assume a gradual but intensive rise in the use of electrical heatpumps for household spatial heating, for different reasons. Therefore, this paper investigates the feasibility and viability of entering the flexibility market by aggregating residential thermal loads. For this research, a dataset of 200 dwellings in the Netherlands, equipped with a heatpump and smart metering infrastructure, is analysed. By means of a greybox modeling approach, a thermal model and control framework have been set up for every house, in order to identify the load shift potential and the accompanying cost of providing flexibility for the houses. We find that thermal flexibility is asymmetric: downwards flexibility is, apart from much more dependent on outdoor temperature than upwards flexibility, strictly lower than upwards flexibility. The cost for downwards flexibility is strictly negative in terms of the prosumer. Concerning upwards flexibility, the cost is most of the time positive. Moreover, it can be concluded that there is a potentially viable business case for the flexibility aggregator