Provably Safe and Robust Learning-Based Model Predictive Control (1107.2487v2)

Abstract: Controller design faces a trade-off between robustness and performance, and the reliability of linear controllers has caused many practitioners to focus on the former. However, there is renewed interest in improving system performance to deal with growing energy constraints. This paper describes a learning-based model predictive control (LBMPC) scheme that provides deterministic guarantees on robustness, while statistical identification tools are used to identify richer models of the system in order to improve performance; the benefits of this framework are that it handles state and input constraints, optimizes system performance with respect to a cost function, and can be designed to use a wide variety of parametric or nonparametric statistical tools. The main insight of LBMPC is that safety and performance can be decoupled under reasonable conditions in an optimization framework by maintaining two models of the system. The first is an approximate model with bounds on its uncertainty, and the second model is updated by statistical methods. LBMPC improves performance by choosing inputs that minimize a cost subject to the learned dynamics, and it ensures safety and robustness by checking whether these same inputs keep the approximate model stable when it is subject to uncertainty. Furthermore, we show that if the system is sufficiently excited, then the LBMPC control action probabilistically converges to that of an MPC computed using the true dynamics.

• The paper presents a dual-model framework that decouples safety and performance through an approximate robust model and a statistically learned dynamic model.
• It guarantees deterministic safety and robustness by verifying stability with bounded uncertainty and invariant set construction.
• Experimental results in HVAC systems, flight control, and jet engine simulations demonstrate improved performance over traditional MPC approaches.

Overview of "Provably Safe and Robust Learning-Based Model Predictive Control"

The paper presents a framework for learning-based model predictive control (LBMPC) that ensures both robustness and performance optimization in control systems. The primary contribution lies in the innovative decoupling of safety and performance, utilizing two models: an approximate model with uncertainty bounds and a statistical model updated through learned dynamics.

Key Insights and Methodology

LBMPC incorporates statistical identification tools to refine system models and improve control performance while maintaining safety and robustness through deterministic guarantees:

• Model Structure: The control framework maintains two system models. The first is an approximate model ensuring robustness, characterized by bounded uncertainty. The second model, which is refined using statistical learning, optimizes the cost function subject to the learned dynamics.
• Optimization Framework: The decoupling of safety and performance in LBMPC allows for optimization by minimizing a cost function subject to the dynamics of the learned model. Importantly, safety is ensured by verifying that the inputs stabilize the approximate model under uncertainty.
• Deterministic Guarantees: The paper provides theoretical proofs of safety, stability, and robustness through techniques like invariant set construction. This is achieved by ensuring that all system trajectories remain within pre-defined constraints even under bounded disturbances.
• Convergence: It is shown that under sufficient excitation, the LBMPC control actions converge probabilistically to the performance of a model predictive control (MPC) scheme that accurately models the true dynamics. This convergence is crucial as it highlights the potential for LBMPC to improve control performance over time as more information about the system is learned.

Experimental and Numerical Results

The authors have applied LBMPC in several experimental testbeds and simulations:

• Energy-Efficient Building Automation: LBMPC has been implemented in a building automation setting, achieving significant energy savings by optimally controlling HVAC systems based on learned models of thermal dynamics.
• High-Performance Flight Control: The framework was tested on quadrotor helicopters, where LBMPC was able to maintain robustness while improving flight performance and stability.
• Jet Engine Compression System Simulation: Numerical simulations on the Moore-Greitzer compression model demonstrated the efficacy of LBMPC in achieving higher performance than linear MPC, without compromising on safety and robustness.

Implications and Future Directions

The practical implications of this research are profound. LBMPC provides a robust framework for systems requiring both high performance and strict safety guarantees. This is particularly relevant in applications such as autonomous vehicles, robotic systems, and energy systems.

Future work could explore the design of even more effective learning methods within the LBMPC framework. The paper suggests that using globally-regularized nonparametric methods such as support vector regression could enhance learning capability while retaining theoretical guarantees needed for robust control.

In summary, the paper's contribution to control theory through the development of LBMPC offers a promising pathway for integrating advanced learning techniques with robust control frameworks. This could lead to significant improvements in the performance and safety of a wide range of dynamic systems.