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Learning Agent-based Model Predictive Control for Holistic Vehicle Performance
Jiaming Zhong, Reza Valiollahi Mehrizi, Mohammad Pirani, Chao Yu, Alireza Kasaiezadeh, Yash Vardhan Pant, Amir Khajepour
TL;DR
AMPC’s reliance on known contributions from all agents limits practical multi-agent vehicle control. The paper proposes LAMPC, combining GPR-based online learning, multi-step prediction, and stochastic MPC. Simulations and experiments show improved tracking in well-learned scenarios, constraint satisfaction in less-learned scenarios, real-time efficiency, and topology flexibility.
Problem
AMPC requires all agents or their contributions to be known, an assumption that is often too idealistic for practical implementation.
Method
LAMPC combines AMPC with GPR-based learning, online data management, multi-step prediction, and stochastic soft chance constraints.
Results
The yaw-rate MSE decreased from 18.2 deg/s2 to 5.9 deg/s2 when LAMPC controlled the RDT agent.
Takeaways & Limitations
LAMPC provides higher tracking performance when learning is reliable, guarantees constraint satisfaction, supports real-time implementation, and accommodates any kind or number of black-box agents.
Abstract
from arXiv · showhide
Agent-based model predictive control (AMPC) has recently been proposed as a distributed scheme that collaborates with all agents to achieve optimal holistic performance. However, its optimality highly depends on the prediction accuracy that requires all agents or their contributions to be known, which is too idealistic for actual implementation. This research proposes a novel practical hybrid control scheme - learning agent-based MPC (LAMPC), combining the model-based AMPC approach and data-based learning methods to improve the holistic vehicle performance for multi-agent systems. The Gaussian process regression (GPR) enhanced by an online data management strategy serves as the learning core to predict unknown contributions. A novel multi-step prediction mechanism leverages the GPR learning potential along the horizon. The predicted mean, representing the learned unknown contributions, completes the system model in the MPC for more accurate control. Meanwhile, a stochastic framework is formulated to guarantee control safety and feasibility using soft chance constraints based on the prediction variance. Both simulations and experiments show that, with the learning capability, LAMPC outperforms the traditional AMPC. LAMPC can achieve higher tracking performance in well-learned scenarios and always guarantee constraint satisfaction even in less-learned scenarios. Moreover, the proposed hybrid control scheme is efficient for real-time implementation and is flexible to any control agent topology.
I. INTRODUCTION
AMPC offers flexible distributed holistic vehicle control but assumes every agent and contribution is known, limiting practical deployment. LAMPC combines AMPC with learning, data management, and stochastic constraints to address accuracy, efficiency, safety, and feasibility challenges.
- AMPC models agents as locally tasked modules connected in a plug-and-play fashion while emulating centralized MPC performance.
- AMPC’s requirement that all agents be known is often unrealistic, and unknown third-party controllers can cause prediction errors and unexpected control results.
- LAMPC combines data-based learning with AMPC so the learning module predicts unknown information while MPC computes solutions within safety boundaries.
- LAMPC is proposed to improve tracking performance over AMPC while supporting arbitrary agent topologies.
- The proposed pipeline uses data management for efficient multi-step GPR prediction and soft chance constraints based on prediction variance for safety.
II. PRELIMINARIES
The preliminaries describe AMPC’s agent-based vehicle model and GPR as the learning tool for predicting unknown contributions. Standard GPR offers probabilistic predictions but incurs cubic time and quadratic memory complexity, motivating efficient implementation.
- AMPC separates vehicle behavior under net forces and moments from actuator dynamics, with actuators clustered into fully connected agent subsets.
- B. GP Regression: GPR models noisy input-output data with a Gaussian process and provides predictive mean and covariance for test inputs.
- B. GP Regression: Basic GPR has O(n^3) time and O(n^2) memory complexity because Gramian-matrix inversion is computationally expensive.
- B. GP Regression: The LAMPC formulation represents the unknown contribution over the horizon with GPR prediction means and variance.
C. Stochastic MPC
LAMPC uses GPR predictions to reconstruct the stochastic AMPC model: the mean estimates unknown contributions, while prediction variance informs soft chance constraints. Data preparation and management support online learning and computational efficiency.
- C. Stochastic MPC: Chance constraints permit constraint violations only below an admissible probability threshold, which is necessary for unbounded uncertainty.
- Online data management conditionally collects new paired data and selects subsets to reduce GPR inference cost.
- C. Stochastic MPC: The GPR prediction mean completes the MPC system model as an additive contribution, while variance propagates into soft chance constraints for safety and feasibility.
- LAMPC estimates unknown-agent contributions from vehicle dynamics using observations combining known and unknown agents.
- Model selection identifies relevant input-variable combinations using regression criteria and forward selection.
B. Data Management
LAMPC manages streaming data and GPR uncertainty to support efficient multi-step prediction and stochastic MPC. Its data-driven predictions complete the system model while softened chance constraints preserve feasibility.
- Data collection: Data management maintains continuous learning by controlling data density and selecting informative points during real-time operation.New points are added when distant, replace the farthest point when the dataset is full, or replace a nearby point when its output error is significant.
- Subset selection: Subset selection uses bounding boxes, bounding spheres, or K-nearest neighbors to sparsify data and reduce the Gramian dimension from O(n^3) toward a smaller subset size.All three methods use Euclidean distance.
- Multi-step prediction: The proposed multi-step GPR method predicts the entire horizon with one fixed input matrix, requiring Gram-matrix inversion only once per time step.The output vector is replaced by a matrix with one column per horizon step, enabling matrix-based mean prediction.
- Uncertainty propagation: GPR uncertainty propagates through the vehicle model and can grow with open-loop prediction, especially for long horizons or poorly learned scenarios.A linear-feedback assumption is introduced to limit error growth along the horizon.
- Soft stochastic LAMPC: Soft chance constraints use prediction variance and penalized slack polygons so the stochastic LAMPC optimization remains feasible while accounting for probabilistic safety.The unbounded GPR distribution is converted into a bounded uncertainty region using a chosen confidence level and admissible violation probability.
- Stability: Learning-based MPC stability is not fully established here because existing robust approaches assume bounded uncertainty, so stability is left for future work.The paper distinguishes nominal and robust stability and states that hybrid data/model-based stability guarantees will be studied later.
A. Agent Configuration
The vehicle example contains controllable, known uncontrollable, and unknown agents whose contributions are combined in a center-of-gravity vehicle model. The front differential torque agent supplies the black-box contribution that LAMPC must learn.
- Vehicle model: The system matrices describe vehicle stability dynamics using longitudinal and lateral speeds, yaw rate, net forces and moments, mass, and yaw inertia.These variables define the center-of-gravity vehicle model used to represent agent contributions.
- Agent roles: Four agents are modeled: RDT is controllable, STR and DT are known white-box agents, and FDT is an unknown black-box agent.The RDT controller is designed, while STR and DT control efforts are known but uncontrollable.
- Known agents: RDT, STR, and DT contributions are represented separately, with their mathematical models using actuator torques, tire forces, steering angle, and wheel geometry.The notation distinguishes the contribution of each known agent within the combined model.
- Unknown agent: The FDT ground-truth model combines PI feedback on yaw-rate error with feed-forward control proportional to the desired yaw rate.The simulated and experimental FDT contribution is manually specified for method verification.
B. LAMPC Controller
The LAMPC controller combines model selection, GPR uncertainty propagation, and soft chance constraints for vehicle stability control. It uses learned predictions while relaxing constraints with penalized slacks to preserve feasibility.
- Vehicle constraints: The controller enforces RDT actuator limits together with maximum rear-axle side slip and yaw-rate requirements.The constraints use wheel-motor torque bounds and stability limits derived from the vehicle model.
- Model selection and training: Model selection identifies the black-box FDT input variables using PMSE, adjusted R2, and AIC, while the squared exponential kernel models their relationship.The selected model has four input variables and six trained hyperparameters, including noise standard deviation.
- Stochastic formulation: LAMPC propagates GPR uncertainty through predicted states and controls, using Gaussian approximations and affine transformations to form constraint margins.The admissible violation probability determines the Gaussian quantile used for shrinking constraints.
- Soft constraints: Soft chance constraints introduce nonnegative slack variables for state and control limits, allowing constraint relaxation while penalizing violations.The nominal vehicle states and RDT inputs are used in the softened formulation.
V. REAL-TIME IMPLEMENTATION AND RESULTS
The study evaluates LAMPC through simulations and real-vehicle experiments, including less-learned and well-learned scenarios. The implementation uses a 20 Hz simulation controller and a 50 Hz vehicle controller.
- The simulation controller ran at 20 Hz using a calibrated high-fidelity Carsim vehicle model.The controller was developed in Matlab/Simulink with platform and controller settings reported in Table II.
- Real-vehicle experiments used a Chevrolet Equinox electric vehicle with LAMPC running at 50 Hz.
- LAMPC was evaluated in simulations and real-vehicle experiments across less-learned and well-learned scenarios.The less-learned tests examined safety, while well-learned tests examined performance improvement over conventional AMPC.
A. Less-learned Scenario: Safety Guarantee
In the less-learned double lane change scenario, insufficient GPR experience caused prediction uncertainty, exposing conventional controllers to constraint violations. LAMPC with soft chance constraints kept the vehicle within safety limits and maintained feasibility under propagated uncertainty.
- A. Less-learned Scenario: Safety Guarantee: The maximum absolute side slip angle reached 40 deg under the unsafe controllers in the less-learned scenario.
- A. Less-learned Scenario: Safety Guarantee: LAMPC with soft chance constraints kept rear slip angle and yaw rate within limits when AMPC and normal-constraint LAMPC violated them.AMPC and LAMPC with normal constraints produced constraint violations, whereas SCC maintained stable and safe vehicle behavior.
- A. Less-learned Scenario: Safety Guarantee: GPR failed to predict the black-box FDT contribution because similar experience was unavailable, producing large prediction errors and variances.The resulting RDT torque was substantially higher than required, explaining the unsafe behavior.
- A. Less-learned Scenario: Safety Guarantee: Uncertainty was propagated by shrinking state and control constraints from original limits to hard and then softened chance constraints along the prediction horizon.At T=5.75 the state trajectory was constrained, while at T=10.80 the control input was constrained; actual trajectories remained within the original constraints under εc.
B. Well-learned Scenario: Performance Improvement
In well-learned double lane change and real-vehicle sinewave tests, LAMPC improved tracking by learning unknown-agent contributions. Multi-step GPR produced more accurate predictions with only a small computational-time increase and maintained real-time efficiency.
- B. Well-learned Scenario: Performance Improvement: Multi-step GPR predicted compensated overall yaw rate more accurately than single-step GPR and improved tracking over AMPC and single-step variants.The advantage was especially evident when yaw rate changed rapidly.
- B. Well-learned Scenario: Performance Improvement: The proposed multi-step GPR only slightly increased computational time relative to single-step GPR and did not affect overall real-time efficiency.The total time consumption of all modules met real-time requirements.
- B. Well-learned Scenario: Performance Improvement: During repeated sinewave maneuvers, growing data collections reduced test-point distances and continually improved prediction accuracy.
- B. Well-learned Scenario: Performance Improvement: With the black-box FDT active, LAMPC produced measured yaw rates closer to the reference than traditional AMPC in real-vehicle sinewave maneuvers.Traditional AMPC improved tracking over driver-only control but still had significant error without black-box-agent information.
- B. Well-learned Scenario: Performance Improvement: LAMPC reduced yaw-rate MSE from 18.2 deg/s2 to 5.9 deg/s2 when controlling the RDT agent.The reduction was measured in the real-vehicle comparison shown in Fig. 10.
VI. CONCLUSION
The conclusion identifies LAMPC as a practical hybrid scheme that improves tracking, guarantees safety, supports real-time operation, and retains flexible agent configuration. These benefits are reported for systems containing black-box agents and arbitrary agent topologies.
- LAMPC significantly improves tracking performance in well-learned scenarios based on reliable learning results.
- Stochastic chance constraints, feedback uncertainty propagation, and soft constraints support safety and optimization feasibility.
- Data density control and subset selection support efficient GPR inference for real-time implementation.
- LAMPC preserves AMPC flexibility and can be applied to systems containing any kind or number of black-box agents.