A Unified Framework for Online Data-Driven Predictive Control with Robust Safety Guarantees

A Unified Framework for Online Data-Driven Predictive Control with Robust Safety Guarantees

The paper "A Unified Framework for Online Data-Driven Predictive Control with Robust Safety Guarantees," authored by Amin Vahidi-Moghaddam, Kaian Chen, Kaixiang Zhang, Zhaojian Li, Yan Wang, and Kai Wu, presents an advanced, systematic approach to enhancing model predictive control (MPC) for nonlinear real-time systems. This unified framework integrates online data-driven methodologies to overcome the limitations posed by the need for accurate dynamical models and the high computational cost typically associated with traditional MPC.

Key Contributions

1. Discreet-Time STF-Based System Identification:

   • This paper introduces a concurrent learning scheme utilizing spatial temporal filters (STFs) to identify nonlinear system dynamics robustly. The use of STFs not only simplifies the model's interpretability but also ensures an efficient system identification process.
   • The proposed concurrent learning law is shown to relax the persistence of excitation (PE) condition commonly required in traditional methods, replacing it with a more practical rank condition. This improved condition is easier to monitor and implement, making the identification process more feasible for real-world applications.

2. Robust Control Barrier Function (RCBF)-Based Safety Guarantees:

   • To address model uncertainties, the authors developed a robust control barrier function (RCBF) approach that satisfies safety constraints despite the presence of unknown disturbances, control policy learning errors, and system identification errors. This method provides a safety guarantee by transforming the safety constraint into a robust form that is enforced through the optimization process.

3. Online Policy Correction Scheme:

   • The paper proposes an innovative online adaptation scheme incorporating Karush-Kuhn-Tucker (KKT) sensitivity analysis and an ancillary feedback controller. This method dynamically adjusts the control inputs to correct any deviations from the desired trajectory due to control learning errors and system disturbances. The adaptability ensures the performance loss is minimized while maintaining system safety.

Simulation Results and Practical Implications

The framework's efficacy is demonstrated through extensive simulations involving a cart-inverted pendulum system and an automotive powertrain control application. The results show that the proposed framework not only achieves a comparable performance to traditional MPC but does so with significantly reduced computational complexity.

1. Cart-Inverted Pendulum:

   • The simulations illustrate that the proposed control framework effectively stabilizes the pendulum and controls the cart position within the defined constraints, demonstrating the robustness of the concurrent learning scheme and the RCBF in handling nonlinear dynamics and unknown disturbances.

2. Automotive Powertrain Control:

   • In the context of automotive control, the proposed framework is deployed to manage a turbocharged internal combustion engine. The results highlight the framework's ability to optimize engine performance while adhering to safety constraints, showcasing the practical applicability of the framework in complex engineering systems.

Theoretical and Practical Implications

The theoretical advancements in this paper, particularly the development of the STF-based concurrent learning and the RCBF-based NMPC, provide a robust foundation for enhancing nonlinear control systems. These developments open new avenues for:

• Enhanced Safety: By incorporating RCBF, the framework ensures forward invariance of safety constraints, making it applicable to critical systems where safety guarantees are paramount.
• Reduced Computational Burden: The function approximator and online adaptation reduce the need for solving complex optimization problems at every time step, making the framework suitable for real-time applications with limited computational resources.
• Scalability: The framework's applicability to both simple mechanical systems and more complex automotive systems suggests its scalability, making it potentially beneficial across various domains in engineering and robotics.

Future Developments in AI

The incorporation of advanced data-driven methodologies in predictive control frameworks signals a promising direction for future developments in AI and control systems. Potential future research could focus on:

• Relaxing Model Assumptions: Extending the framework to handle systems with more relaxed assumptions on bounded disturbances and stronger guarantees on recursive feasibility.
• Real-World Applications: Deployment and validation of the framework in real-world scenarios, such as autonomous driving and industrial automation, to further demonstrate its practicality and adaptability.
• Integration with Other Learning Methods: Exploring the integration of this framework with other learning-based control approaches, such as reinforcement learning, to enhance its adaptability and performance in dynamic environments.

Conclusion

This paper offers a significant step forward in the field of predictive control by presenting a unified framework that effectively addresses the challenges of model accuracy and computational cost. The integration of the discrete-time STF-based concurrent learning, RCBF for safety guarantees, and an online policy correction scheme ensures robust and efficient control of nonlinear systems, paving the way for advanced real-time applications in various engineering domains.