Making future vehicles intelligent with improved fuel economy and satisfactory emissions are the main drivers for current vehicle research and development. The connected and autonomous vehicles still need years or decades to be widely used in practice. However, some advanced technologies have been developed and deployed for the conventional vehicles to improve the vehicle performance and safety, such as adaptive cruise control (ACC), automatic parking, automatic lane keeping, active safety, super cruise, and so on. On the other hand, the vehicle propulsion system technologies, such as clean and high efficiency combustion, hybrid electric vehicle (HEV), and electric vehicle, are continuously advancing to improve fuel economy with satisfactory emissions for traditional internal combustion engine powered and hybrid electric vehicles or to increase cruise range for electric vehicles.

## Article

Making future vehicles intelligent with improved fuel economy and satisfactory emissions are the main drivers for current vehicle research and development. Connected and autonomous vehicles still need years or decades to be widely used in practice. However, some advanced technologies have been developed and deployed for conventional vehicles to improve vehicle performance and safety, such as adaptive cruise control (ACC), automatic parking, automatic lane keeping, active safety, super cruise, and so on [1], [2], [3]. On the other hand, vehicle propulsion system technologies, such as clean and high efficiency combustion, hybrid electric vehicle (HEV), and electric vehicle, are continuously advancing to improve fuel economy with satisfactory emissions for traditional internal combustion engine powered and hybrid electric vehicles [4], [5] or to increase cruise range for electric vehicles [6], [7].

For connected and autonomous vehicle technology, the commercialized ACC technology is able to automatically control the vehicle to maintain a safe distance to the front vehicle while holding a desired speed if possible. With the development of connected vehicle technology, some extended ACC systems have been explored, e.g., cooperative ACC (CACC) and eco-ACC [8], [9], [10]. These extended ACC systems are able to improve fuel economy by reducing aerodynamic drag and waiting time for traffic signals (stop signs and traffic lights). However, under the ACC mode, the vehicle tracks either the driver-desired speed or current traffic flow speed, not the economic speed. Also, these ACC systems focus only on the vehicle speed control while the lane and route selection is controlled by the driver. In practice, there is more than one feasible route from the current vehicle position to the destination, and for each feasible route the fuel consumption could be quite different. Therefore, there is room for improving the vehicle fuel economy by combining the speed and route optimization with the existing ACC technology.

There are many studies in the area of speed and route optimization, however most of them focus on either route or speed. The route optimization, also called vehicle route planning (VRP) problem, has been widely used in our daily life through various navigation tools. However, few of them provide the economic route, and the commonly available shortest and fastest routes do not always minimize the fuel consumption [11]. Fuel economy related VRP research got started in the past decades, such as eco-routing navigation, green and pollution vehicle routing problems [12], [13], [14]. These research results show that the economic route is able to reduce both fuel consumption and emissions [11],[12]. The speed optimization is widely formed as a multi-objective fuel economy optimization problem with constraints on travel time, safety, comfort, and so on. A. Franceschetti, et al. [13] and M. Barth, et al. [14] studied the vehicle speed optimization problem with the known route and given trip time limit, and showed that vehicle speed optimization is able to decrease fuel consumption for a known route with given trip time limit. It also indicates that vehicle fuel economy could be further improved by combining route planning and speed optimization into a co-optimization problem.

For a traditional vehicle propulsion system, powered by an internal combustion (IC) engine, there is considerable room for improving fuel economy using the vehicle route and speed co-optimization [16]. Also, the HEV, propelled by both IC engine and electric motor(s), is able to improve fuel economy utilizing regenerative power and effective power management [11], [12] under a given operational condition. Furthermore, there is plenty of room for improving the HEV vehicle fuel economy by combining the vehicle route and speed co-optimization with the hybrid powertrain control system, which is the center of this article. Much research has been conducted in real-time HEV powertrain control and optimization. These strategies can be classified into rule-based strategies, such as fuzzy rule, state machine, power follower, and so on, and optimization-based ones [17], [18], [19], [20], such as dynamic programming (DP), stochastic dynamic programming, genetic algorithm (GA), robust control, model predictive control (MPC), etc. The MPC (model predictive control) drew more and more attention in recent years. It is achieved by optimizing over a finite time horizon with the predicted future states at each time step but only implementing the current control step. This process is called receding horizon control [19], [20]. Although this approach is suboptimal, it provides very good practical results.

Therefore, an optimal hybrid electric vehicle powertrain control problem based on route and speed optimization is formed in this article to improve the vehicle fuel economy for a given origin-destination (OD) pair with the given expected trip time *(T _{E}).* The proposed real-time optimal control scheme is shown in

**Figure 1**. The optimal control strategy contains two coupled optimization problems: vehicle route/speed cooptimization and hybrid powertrain control optimization for improving fuel economy. During the real-time optimization, speed profile (

*V*

^{*}) and the economic route (

*r*

^{*}) are optimized simultaneously using the vehicle macroscopic motion planning (VMMP) [21] method based on traffic data, powertrain configuration, and the proposed global power distribution (GPD) strategy, where the VMMP and GPD are coupled and optimized one at a time. The second GPD is used to generate feedforward control (u

_{ref}) and tracking reference state vector

*(x*based on the reference speed (

_{ref})*V*

^{*}). The real-time hybrid powertrain control input (u

^{*}) consists of the feedback ($u\u02dc*$) and feedforward control (u

_{ref}) for the optimized speed and route. The powertrain feedback module uses the receding horizon linear quadratic tracking (LQT) control, where the inputs are the state tracking errors ($x\u02dc$) and road coefficient variation ($w\u02dc$).

The remainder of this article describes the proposed optimal hybrid powertrain control strategy based on the route and speed co-optimization for improved fuel economy, and its associated real-time co-optimization process based on GA and receding horizon LQT to obtain the optimal vehicle route, speed profile, and hybrid powertrain control.

## Global Power Distribution (GPD) Strategy for HEV

## Power split hybrid electric vehicle system

Different from the traditional internal combustion engine vehicle, the HEV has several energy sources and its longitudinal dynamics are more complex.

**Figure 2** shows a simplified powertrain topology of a power split HEV. A forward dynamic model is built for control strategy development and validation. Note that the driver is simulated by two proportional-integralderivative (PID) controllers.

In **Figure 2**, SOC is the battery state of charge; *U _{oc}* is the open-circuit voltage;

*P*is the battery power;

_{bat}*U*and

*I*are voltage and current; J,

*T,*and

*ω*are the inertia, torque, and speed, respectively; subscripts

*e, A,*and

*B*represent the engine, generator-motor A (GMA) and B (GMB), respectively;

*v*and v*are actual and reference vehicle speeds, respectively; and

*a*is the pedal signal.

The HEV longitudinal dynamics model can be simplified as

where *M* is the vehicle mass; *R* is the wheel radius; *i _{0}* is the final ratio;

*C*is the drag coefficient;

_{d}*ρ*is the air density;

*A*is the frontal area;

*F*is the brake force;

_{b}*ß*=

*ζ*cosθ + sinθ is the road coefficient combining the rolling resistance coefficient (ζ) and road grade (θ);

*T*is the tractive torque;

_{t}*T*

_{C},

*T*

_{R}, and

*T*are the torque of carrier, ring, and sun gears, respectively. The speed and torque equations for the power splitter are

_{S}where *ω*_{C}, *ω _{R},* and

*ω*are the speed of carrier, ring and sun gears, respectively;

_{S}*K*is the coefficient of the planetary gear equal to the ratio from the sun to ring gear.

The SOC is defined as the amount of electrical charge stored in the battery relative to the total charge capacity [20], [22]. The commonly used model is described by

where *R _{0}* and

*Q*are the battery internal resistance and capacity, respectively; and

_{nom}*P*is the battery power. Note that positive

_{bat}*P*means discharging and negative

_{bat}*P*means charging.

_{bat}*is defined as*

^{P}batwhere *η _{A}* and

*η*are the efficiencies of GMA and GMB based on generator-motor A (B) map.

_{B}## Global power distribution strategy

The rule-based global power distribution (GPD) strategy is used to optimize the power among engine, GMA, and GMB to minimize the fuel consumption for a given speed profile. The key ideas of GPD are summarized as follows: a) conserve the electric energy over the entire speed profile so that the terminal SOC is close to the initial value; and b) operate the engine at its high efficiency area.

From (1), the power balance equation is obtained as

where $Pein=Jew\u02d9e\omega e$ is the inertia power (positive for acceleration and negative for deceleration); the same for *P _{Ain}* and

*P*; and

_{Bin}*P*is the tractive power at wheels:

_{t}Note that ideally the brake force should be zero for the best fuel economy. In case of braking, the GMB is able to provide the required torque for decelerating and convert the mechanical energy back to electricity. For the dynamic process with *υ* b o , the values of *P*_{ein}, *P _{Ain},* and

*P*are much smaller than

_{Bin}*P*so that

_{t}where *P _{d}* is the driving power demand.

The highlight of the GPD strategy is provided below.

**Step 1:** Calculate the driving power demand using (5) and (6) for the speed vector provided by VMMP (see details in the next section);

**Step 2:** For the power regeneration phase, find the negative *P _{d}* and calculate the total recycled electric energy

*W*

_{r}.**Step 3:** For the high driving power demand phase, find *P _{d}* associated with high power demand and calculate the total required electric energy

*W*Note that in this phase the driving power is provided by both engine and battery simultaneously.

_{h}.**Step 4:** For the low-speed phase, identify the low-speed region. Note that in this phase, the required engine power is zero *(P _{e}* = 0) and the remaining

*W*is used for low-speed driving.

_{r}**Step 5:** For the power balance phase, sort the remaining power *P _{d}* from low to high. Then use the ordered

*P*to find the operational mode among the three modes: electrical, hybrid, and mechanical. The associated engine power is 0,

_{d}*P*

_{low}, and

*P*

_{d}, respectively, where

*P*is selected based on the engine fuel efficiency map for the best fuel economy.

_{low}## Ga Co-Optimization of Vehicle Route and Speed

The proposed VMMP is a global optimization problem to find the optimal route (*r*^{*}) and speed vector (*V*^{*}) that minimize the cost function (*J*) for the given origin-destination pair and the expected trip time. Note that the optimized route and speed of the VMMP problem correspond to the given expected trip time

where *R* is the set of feasible routes for the given OD pair; *V _{r}* is the set speed at each observer location along route r;

*M*is the total number of observer locations along the route r; Δs(k) is the speed sensor distance; and

_{r}*f*(

*ß*(

*k*),

*v*(k)) is the fuel rate, subject to the system described by (1) and (2). The feasible route (

*r*) is an ordered sequence of some edges (branches) [21].

The vehicle route and speed profile are a pair of coupled binary vector and positive real array, respectively. The dimension and boundary of the speed vector depend on the corresponding route. The optimal speed profile is effective for its corresponding route and has no physical meaning for any other routes. So a GA (generic algorithm)-based method is proposed to co-optimize vehicle route and speed profile simultaneously in real-time; see **Figure 3**

**Figure 3** is self-explanatory and two GA iteration processes are embedded together. Note that *i* and *j* are the iteration indices for speed and route, respectively. The outer iteration loop is used for route optimization and the inner one is for speed optimization. The inputs to the speed optimization are provided by selected route individuals (see speed population initialization in **Figure 3**), and the fuel consumption *(J _{v}*) of the optimal speed profile is used as input to the route optimization (see route evaluation in

**Figure 3**). The route fuel consumption (

*J*

_{r}) is used to determine if the iteration is converged or not. More detailed discussion can be found in reference [21].

## Receding Horizon Lqt Feedback Control

After the economic route and speed profile are optimized, an optimal hybrid powertrain control strategy combining feedforward and feedback control is used to track the reference profile and minimize the fuel consumption. The feedforward module uses GPD outputs from before. The feedback module is a receding horizon LQT (linear quadratic tracking) controller, an application of MPC.

Note that the hybrid propulsion system described by (1) and (2) is nonlinear and a nonlinear state-space model was developed. The developed nonlinear state-space model was linearized at the current operational condition using the Taylor expansion at the current operational condition [23] and discretized with a sample period of 10 ms, resulting in the following linear discrete-time state-space realization:

The LQT optimization problem is try to find the optimal control that minimizes the fuel consumption and tracking errors. The LQT cost function *J _{LQT}* is expressed as

where *z* is the reference tracking signals based on the linearization points and reference trajectories from GPD (see **Figure 1**); *F* and *Q* are symmetric and positive semidefinite; and *R* is symmetric and positive definite.

Where

The terminal condition is given by

Therefore, the optimal control strategy combining the GPD feedforward and receding horizon LQT feedback controller is summarized in **Figure 4**. Note that *k _{f}* is the discrete-time finite horizon for the LQT control and only the first step of

*u*over the entire optimization horizon is used. The larger

^{*}*k*that is selected, the better the performance (fuel consumption and tracking error) of the LQT controller is, but the larger the deviation between the linear and nonlinear models becomes. Therefore,

_{f}*k*cannot be too small nor too large and is set to be 100 in this study.

_{f}## Simulation Validation and Discussions

A co-simulation model combining the traffic and powertrain models is developed to validate the proposed methods. The optimization models and controllers are compiled into Matlab m-code; the traffic model is built using SUMO [21]; and the forward powertrain model is established in Simulink. The connection between SUMO and Matlab/Simulink models is realized by the TraCI4Matlab, an API (application programming interface) developed in Matlab. It allows controlling the SUMO objects such as vehicles, traffic lights, junctions, etc. The simulation steps of the traffic and powertrain models should be the same and are set to be 0.01 second in this study. Details for the modeling process can be found in [22].

## Simulation study on receding horizon LQT controller

A simulation study based on HWFET (highway fuel economy test) driving cycle is designed to validate the proposed LQT controller. The simulation step is 10 ms and the receding horizon is 1.0 second. That is, there are 100 steps in each LQT optimization cycle. The simulation results are shown in **Figure 5**. The reference profiles are from GPD strategy and the tracking profiles from the proposed receding horizon LQT feedback controller.

From **Figure****5**, it can be seen that the LQT controller tracks the reference trajectories well, especially the engine speed *(ω _{e}* ), motor B speed (ω

_{B}), and the fuel rate. From the powertrain model in

**Figure**

**2**, we have

*V=Rω*Therefore, the tracking performance of

_{B}/i_{0}.*v*is also good based on the results of

*ω*The other signals (SOC,

_{B}.*T*and

_{A},*T*) do have some errors between their references and actual values. However, the tracking profiles are much smoother than the reference ones. More important, the terminal and initial SOCs are very close. This indicates that the derivations of SOC,

_{B}*T*and

_{A},*T*have less influence on the fuel economy and vehicle speed.

_{B}## Co-simulation validation for optimal control strategy

The developed traffic model (between Novi, MI and Southfield, MI) in SUMO is shown in **Figure****6**. The origin-destination is set to be “O” and “D” on the map and the given expected trip time (*T _{E}*) is larger than the fastest time to have a feasible solution. The “RF” and “RS” represent the fastest and shortest routes, respectively.

**Figure 7** shows the simulation results with different expected trip times. Three studies are conducted in simulations: a) the fixed route “RS” with different *T*_{E} between *t _{so}* and

*t*and the associated results are shown as “Route RS”; b) route “RF” with

_{n},*T*

_{E}between

*t*and

_{Fo}*t*and the associated results are shown as “Route RF”; and c) different routes and expected time; see the optimal results in

_{n},**Figure 7**. Note that

*t*and

_{so}*t*are the minimum trip times from “O” to “D” for routes “RS” and “RF,” respectively.

_{Fo}From **Figure 7**, it can be seen that for the fixed route studies, the fuel consumption decreases as *T _{E}* increases during time period

*t*and

_{So}~t_{Sl}*t*

_{Fo}~t_{Fl}, and then keeps the minimum values when the

*T*is larger than

_{E}*t*and

_{Sl}*t*

_{Fl}, respectively. For speed optimization studies a) and b), the vehicle fuel economy can be improved by up to 7.27% and 6.52% for routes ”RF” and ”RS”, respectively. For study c), the economic route is ”RF” if the given

*T*is located within

_{E}*t*and route ”RS” if the given

_{Fo}~t_{So}*T*is larger than

_{E}*t*With the co-optimization of vehicle route and speed, the vehicle fuel economy can be further improved by up to 14.2% compared with the fastest route without optimization. Note that, in

_{So}.**Figure 7**the controllers for studies a), b), and c) are the same as the proposed receding horizon LQT controller. Comparing with the power follower on the fastest route, the vehicle fuel economy can be improved by 31.7%.

## Conclusions

An optimal powertrain controller combining feedforward and feedback modules is developed based on route and speed co-optimization for improved fuel economy of hybrid electric vehicles. The vehicle route and speed is optimized for the given origin-destination with expected trip time by a genetic algorithm-based co-optimization method using the real-time traffic data and vehicle characteristics. The feedforward module is based on a global power distribution strategy and the feedback module is a receding horizon linear quadratic tracking control. A co-simulation model, combining a traffic model based on SUMO with the Simulink hybrid powertrain model, is developed and used for validating the proposed optimal control strategy. Co-simulation results indicate that the proposed control strategy is able to decrease the fuel consumption by up to 31.7% compared with the power follower hybrid strategy adopting the fastest route. Note that even with the same powertrain controller, the economic route and speed can also improve the fuel economy by 14.2% compared with the fastest route without optimization.

The future work will focus on the multi-variable global optimization problem with one cost function and three coupled optimization variables: vehicle route, speed, and powertrain control.

**About the Authors**

**Chengsheng Miao** received the B.S. and PhD degrees in mechanical engineering from Beijing Institute of Technology, Beijing, China, in 2012 and 2018, and studied as a joint Ph.D. student in the Energy and Automotive Research Lab of Mechanical Engineering Department, Michigan State University, East Lansing, MI, USA, between September 16,2015 and September 27,2017.

He is currently a research engineer of GAC Group, Guangzhou, China. His current research interests include vehicle connectivity, vehicle route planning, vehicle speed optimization, control of automated manual transmission and hybrid powertrain.

**Guoming G. Zhu** received the B.S. and M.S. degrees in mechanical and electrical Engineering, respectively, from Beijing University of Aeronautics and Astronautics (now called Beihang University), Beijing, China, in 1982 and 1984, respectively, and the Ph.D. degree in aerospace engineering from Purdue University, West Lafayette, IN, USA, in 1992.

He is currently a Professor with the Department of Mechanical Engineering (ME) and the Department of Electrical and Computer Engineering (ECE) at the Michigan State University, East Lansing, MI, USA. He has authored or coauthored two books and more than 220 refereed technical papers and received more than 40 U.S. patents. His current research interests include vehicle connectivity, closed-loop combustion control of internal combustion engines, engine and vehicle system modeling, hybrid powertrain control and optimization, linear parameter-varying system control with applications to aerospace and automotive systems, etc. Dr. Zhu is a Fellow of the Society of Automotive Engineers (SAE) and the American Society of Mechanical Engineers (AMSE). He was an Associate Editor of the ASME Journal of Dynamic Systems, Measurement, and Control. He is currently an associate editor of the ASME Dynamic Systems and Control Magazine and a member of the editorial board of the International Journal of Powertrains.