CHING'S MARKOV CHAIN MODELS
HYBRID ELECTRIC VEHICLE ENERGY MANAGEMENT CONTROL
E. Mion (2017). Hybrid Electric Vehicle Energy Management Control Based on Stochastic Dynamic Programming, Master Thesis, University of Padova .
http://tesi.cab.unipd.it/54597/
In Mion (2017), the author considered the problem of optimization of fuel consumption in hybrid electric vehicle. He provided a real time optimal control strategy which allows to optimize fuel consumption of a hybrid electric vehicle thus reduces fuel consumption and pollutant emissions.
In order to compute the optimal control policy of torque and power energy management, the speed of the vehicle has to be estimated. Since the future driver power request under diverse driving conditions is uncertain, so Markov chain theory is exploited. For the cases that available profiles are more than one, the parsimonious multivariate Markov chain model in Ching et al. (2006) along with the parameter estimation method in Ching et al. (2006, 2008) is used.
The speed of the vehicle is modeled as a stochastic process so that it can be described by a Markov chain with finitely many states. Together with other available Markov chain like the combination of throttle and brake, the speed chain is analyzed by the parsimonious multivariate Markov Chain model in Ching et al. (2006) along with the parameter estimation method in Ching et al. (2006, 2008) to predict the next possible speed state. Following the model and parameter estimation method, the vehicle speed can be predicted efficiently by solving a linear programming problem. Thus, it becomes possible to be estimated by real-time analysis.
The author in Mion (2017) employed the parsimonious multivariate Markov chain model and algorithm to compute the prediction by taking into account the contribution of another sequence of data, as, in this case, the combination of throttle and brake. Comparing the original data set and the predicted one, the parsimonious multivariate Markov chain procedure fits almost everywhere the original behavior, see the figure below.
Taken from “Comparison between original data of Indian Driving cycle (blue), one step prediction (red),
two steps (green), and three steps predictions (cyan) computed with Markov Chain Algorithm, considering
only speed data”. Hybrid Electric Vehicle Energy Management Control Based on Stochastic Dynamic
Programming (2017) Mion, Enrico.’’ http://tesi.cab.unipd.it/54597/
W. Ching, E. Fung, and M. Ng (2008) Higher-order Multivariate Markov Chains and Their Applications,” Linear Algebra and its Applications, 15, 492--507.
https://www.sciencedirect.com/science/article/pii/S0024379507002169
W. Ching and M. Ng (2006). Markov Chains: Models, Algorithms and Applications. Springer.
