An Actor-Critic-Identifier Control Design for Increasing Energy Efficiency of Automated Electric Vehicles

Electric vehicles (EVs) are increasingly deployed, yet range limitations remain a key barrier. Improving energy efficiency via advanced control is therefore essential, and emerging vehicle automation offers a promising avenue. However, many existing strategies rely on indirect surrogates because linking power consumption to control inputs is difficult. We propose a neural-network (NN) identifier that learns this mapping online and couples it with an actor-critic reinforcement learning (RL) framework to generate optimal control commands. The resulting actor-critic-identifier architecture removes dependence on explicit models relating total power, recovered energy, and inputs, while maintaining accurate speed tracking and maximizing efficiency. Update laws are derived using Lyapunov stability analysis, and performance is validated in simulation. Compared to a traditional controller, the method increases total energy recovery by 12.84%, indicating strong potential for improving EV energy efficiency.

💡 Research Summary

The paper tackles the fundamental challenge of improving electric‑vehicle (EV) range by increasing the efficiency of the powertrain through advanced control. Traditional eco‑driving or regenerative‑braking strategies rely on surrogate variables because the exact relationship between control inputs (torque) and instantaneous power consumption or regeneration is highly nonlinear, state‑dependent, and often unavailable. To overcome this, the authors propose an Actor‑Critic‑Identifier (ACI) architecture that simultaneously learns the unknown dynamics and generates an optimal control policy online.

The vehicle longitudinal dynamics are expressed as (\dot x = g(x) + h(x)u), where (x) contains speed‑tracking error and the difference between acceleration power and recovered power, (u) is the motor torque, (h(x)) is known, and the drift term (g(x)) is unknown. The control objective is to minimize a cost that penalizes speed error and acceleration power while maximizing regenerated energy.

Three neural networks are coupled: (1) a critic approximates the optimal value function (J^*(x)) as (\hat J = \hat w_c^\top \phi(x)); (2) an actor approximates the optimal policy (\hat u = -(1/2)\beta^{-1} h^\top(x) \nabla_x \hat J); (3) an identifier learns the unknown drift (g(x)) as (\hat g(x)=\hat w_g^\top \sigma(\hat v_g^\top x)). All three are updated using laws derived from a Lyapunov‑based stability analysis. The critic update includes a covariance matrix (P) with a resetting mechanism to keep learning rates bounded. The actor update contains a projection term to keep the weights within a compact set and a coupling term that drives the actor toward the critic. The identifier uses a RISE (robust integral of the sign of the error) term to guarantee asymptotic tracking of the true dynamics.

Stability is proven under a set of boundedness assumptions on the neural‑network weights, activation functions, and reconstruction errors, and under conditions on the adaptation gains (e.g., (p_1>2c_3), (p_2) sufficiently large, etc.). Theorem 1 shows that the state‑estimation error (\tilde x) and its derivative converge to zero, ensuring that the learned policy asymptotically approaches the optimal HJB solution.

Simulation results are presented for a realistic driving scenario with varying speed references. The ACI controller is benchmarked against a well‑tuned PID speed controller. Both achieve comparable tracking performance, but the ACI recovers 12.84 % more energy over the test cycle, demonstrating that learning the power‑input mapping online yields tangible efficiency gains without sacrificing drivability. The control signals are smoother than those of the PID, indicating improved passenger comfort.

The authors acknowledge that the work is limited to simulation; real‑world deployment would need to address sensor noise, battery state‑of‑charge dynamics, temperature effects, and computational constraints of embedded hardware. Nonetheless, the proposed ACI framework provides a model‑free, provably stable method for online energy‑optimal control of automated electric vehicles, representing a significant step toward extending EV range through intelligent automation.