Shortest path stochastic control for hybrid electric vehicles

Abstract

SUMMARYWhen a hybrid electric vehicle (HEV) is certified for emissions and fuel economy, its power management system must be charge sustaining over the drive cycle, meaning that the battery state of charge (SOC) must be at least as high at the end of the test as it was at the beginning of the test. During the test cycle, the power management system is free to vary the battery SOC so as to minimize a weighted combination of fuel consumption and exhaust emissions. This paper argues that shortest path stochastic dynamic programming (SP-SDP) offers a more natural formulation of the optimal control problem associated with the design of the power management system because it allows deviations of battery SOC from a desired setpoint to be penalized only at key off. This method is illustrated on a parallel hybrid electric truck model that had previously been analyzed using infinite-horizon stochastic dynamic programming with discounted future cost. Both formulations of the optimization problem yield a time-invariant causal state-feedback controller that can be directly implemented on the vehicle. The advantages of the shortest path formulation include that a single tuning parameter is needed to trade off fuel economy and emissions versus battery SOC deviation, as compared with two parameters in the discounted, infinite-horizon case, and for the same level of complexity as a discounted future-cost controller, the shortest-path controller demonstrates better fuel and emission minimization while also achieving better SOC control when the vehicle is turned off. Linear programming is used to solve both stochastic dynamic programs.

Comparative Study of Dynamic Programming and Pontryagin’s Minimum Principle on Energy Management for a Parallel Hybrid Electric Vehicle

“…Hence, the controller based on DP is effective only for the specific driving cycle that is used for the rule extraction. To remedy this problem, the stochastic dynamic programming (SDP) method [9][10][11] and the driving pattern detection within multiple driving cycles [12] had been suggested as the possible solutions. As a general case of the Euler-Lagrange equation, Pontryagin's minimum principle (PMP) was also introduced to obtain optimal control solution for hybrid vehicles [13][14][15][16], where the Hamiltonian is considered as an analytical function.…”

Performance comparison of hybrid vehicle energy management controllers on real-world drive cycle data

“…The controller design method studied here is Shortest Path Stochastic Dynamic Programming (SPSDP), which has been used in this application several times before [4], [6], [14]. Recent results [10] have developed this method so that realworld constraints on drivability and powertrain behavior can be incorporated.…”

“…To determine the optimal control strategy for this vehicle, the Shortest Path Stochastic Dynamic Programming (SPSDP) algorithm is used [6], [14]. This method directly generates a causal controller; characteristics of the future driving behavior are specified via a Markov chain rather than exact future knowledge.…”

“…The probability of each outcome a k+1 is estimated based on its frequency of occurrence during the design cycle. See [14] for more detail. In addition to fuel economy, it is desirable to study the drivability characteristics of the vehicle.…”

Convex Optimization for the Energy Management of Hybrid Electric Vehicles Considering Engine Start and Gearshift Costs

“…The control of the power flows among these devices is commonly referred to as the energy management or supervisory control [1]. There are many approaches [2] to design an energy management strategy, covering heuristic approaches [3][4][5][6] as well as optimization-based approaches, such as deterministic dynamic programming (DP) [7][8][9][10][11][12][13], Pontryagin's minimum principle (PMP) [14][15][16][17][18][19][20][21] and stochastic dynamic programming (SDP) [22][23][24][25][26]. Recently, convex optimization [27] has attracted attention in the research field of energy management for HEVs.…”