The ultimate goal, he says, is to exploit fully existing propulsion technologies in terms of fuel economy and pollutant emissions. His body of work on on the underlying the theory and algorithms for this this extends back several years to his 2008 doctoral thesis at the University of Michigan (subsequently published as a book: Real-time, self-learning identification and stochastic optimal control of advanced powertrain systems).

Malikopoulos has recently begun a DOE-funded project on developing autonomous intelligent plug-in hybrid electric vehicles (PHEVs); he presented an early update at the recent DOE 2012 Annual Merit Review meetings in Washington, DC. The objective of this project is to use the control algorithms to operate a PHEV at an instantaneous equilibrium operating point, assuring maximization of the efficiency of the PHEV at each instant of time.

Background. Current approaches to engine optimization and control generally establish static correlations between the variables and steady-state operating points or specific driving conditions (e.g., vehicle speed profiles for highway and city driving). These correlations are incorporated into the engine’s electronic control unit (ECU). However, notes Malikopoulos, this method seldom guarantees optimal engine operation for common driving habits such as stop-and-go driving, rapid acceleration, or rapid braking—i.e., transient operation.

Malikopoulos’ underlying hypothesis is that transient engine operation can be addressed by estimating the sequences of engine operating point transitions designated by the driver, and then deriving the values of the controllable variables for these sequences.

Malikopoulos treats the engine as a controlled stochastic system and the engine operation as a Markov decision process. The problem of engine calibration is thus reformulated as a sequential decision-making problem under uncertainty.

Engines are streamlined syntheses of complex physical processes determining a convoluted dynamic system. They are operated with reference to engine operating points and the values of various engine controllable variables. At each operating point, these values highly influence engine performance criteria, e.g., fuel economy, emissions, or acceleration. This influence becomes more important at engine operating point transitions designated partly by the driver’s driving style and partly by the engine controllable variables. Consequently, the engine is a system whose behavior is not completely foreseeable, and its future evolution (operating point transitions) depends on the driver’s driving style.

Transient operation constitutes the largest segment of engine operation over a driving cycle compared with the steady-state one...the optimal values of the controllable variables corresponding to steady-state operating points cannot capture efficiently the transient engine operation.

Engine operation is described in terms of its operating points, and the evaluation of performance indices is a function of various controllable variables. Here, the engine performance indices are treated as random functions, the engine is treated as a controlled stochastic system, and the engine operation is treated as a stochastic process. Engine calibration is thus reformulated as a sequential decision-making problem under uncertainty. The goal is to select values of the controllable variables for each engine operating point in real time that optimize the random functions (engine performance indices).

The Markov decision process (MDP) provides the mathematical framework for modeling sequential decision-making problems under uncertainty; it comprises (a) a decision maker (controller), (b) states (engine operating points), (c) control actions (engine controllable variables), (d) a transition probability matrix (driver), (e) a transition cost (or reward) matrix (engine performance criteria), and (f) an optimization criterion (e.g., maximizing fuel economy, minimizing pollutant emissions, and maximizing engine acceleration).

—Malikopoulos et al. (2010)

To validate the Predictive Optimal Decision-making (POD) computational learning model, Malikopoulos and his colleagues have modeled various case studies including:

• Gasoline engine with respect to spark ignition angle over aggressive acceleration profiles.

• Diesel engine with respect to injection timing over an acceleration and deceleration profile.

• Diesel engine with respect to injection timing and VGT over a segment of the FTP-75 driving cycle.

Resources

• Malikopoulos, Andreas A. Real-time, self-learning identification and stochastic optimal control of advanced powertrain systems; ProQuest, UMI Dissertation Publishing (September 2, 2011)

• Malikopoulos, Andreas A., Papalambros, Panos Y. and Assanis, Dennis N. (2010) Online Identification and Stochastic Control for Autonomous Internal Combustion Engines. J. Dyn. Sys., Meas., Control 132, 024504 doi: 10.1115/1.4000819

• Malikopoulos, A.A. (2012) Autonomous Intelligent Plug-In Hybrid Electric Vehicles (PHEVs) (DOE AMR VSS092)

• Malikopoulos, A.A., Charalambous, C.D. and Tzortzis, I., “Dual Constrained Optimization of Markov Chains Subject to Total Variation Distance Uncertainty,” Proceedings of the 51th IEEE Conference on Decision and Control and European Control Conference, Maui, Hawaii, December 10-13, 2012. (in review)