- The paper presents a novel MPC scheme using Hankel matrices to predict system trajectories directly from past data, avoiding explicit system identification.
- It guarantees exponential stability and robust constraint satisfaction, as demonstrated through theoretical analysis and numerical tests on a four-tank system.
- The approach incorporates slack variables to manage noisy measurements, paving the way for reliable control in complex, uncertain environments.
Data-Driven Model Predictive Control with Stability and Robustness Guarantees
This paper introduces a robust data-driven Model Predictive Control (MPC) scheme for linear time-invariant (LTI) systems, emphasizing stability and robustness. Unlike traditional MPC, which depends on a priori system identification, this approach utilizes behavioral systems theory to predict future system trajectories directly from past input-output data. The key contribution lies in its theoretical guarantees on stability, constraint satisfaction, and detailed analysis of the closed-loop properties, a novel contribution in purely data-driven MPC schemes.
Methodology and Theoretical Results
The methodology removes the need for an explicit model by using the Hankel matrix of previously observed data to capture the system dynamics. This is based on the concept that a persistently exciting input sequence spans the trajectory space of an LTI system, as per Willems et al. (2005). The proposed MPC scheme includes terminal equality constraints ensuring that the predicted states align with the desired steady-state, a critical addition guaranteeing exponential stability under noise-free conditions.
The authors extend this to scenarios involving measurement noise by introducing a slack variable and regularizing it in the cost function. This approach accounts for noise both in the initial data and online measurements, providing robust stability guarantees for the closed loop. The theoretical analysis confirms practical exponential stability, meaning the closed loop converges to a neighborhood of the desired state, with the size of this neighborhood dependent on the noise level.
Numerical Results and Implications
Numerical simulations on a four-tank system, a benchmark control problem, demonstrate the method's effectiveness. The proposed MPC maintained stability and achieved desired setpoint tracking, even under noisy conditions, where traditional MPC without terminal constraints failed. This showcases the method's robustness and practical applicability in real-world scenarios.
Implications and Future Directions
The robust data-driven approach is particularly significant for control applications lacking explicit models or where system identification is complex or infeasible. It circumvents the challenges associated with model inaccuracies and parameter estimation. The findings provide a pathway for extending data-driven control strategies to nonlinear or time-varying systems, enhancing their resilience to uncertainties.
For future work, integrating adaptive or learning-based mechanisms to update the predictive model online would be an interesting direction. Further exploration into nonlinear system applications, leveraging the flexibility of data-driven methods, could broaden the scope of robust MPC schemes.
Overall, this research advances the field of data-driven control by formalizing MPC schemes with strong stability and robustness guarantees, presenting a viable solution for complex, uncertain environments.