Learning to Boost the Performance of Stable Nonlinear Systems

The growing scale and complexity of safety-critical control systems underscore the need to evolve current control architectures aiming for the unparalleled performances achievable through state-of-the-art optimization and machine learning algorithms. However, maintaining closed-loop stability while...

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Bibliographic Details
Published in:IEEE Open Journal of Control Systems 2024, Vol.3, p.342-357
Main Authors: Furieri, Luca, Galimberti, Clara Lucia, Ferrari-Trecate, Giancarlo
Format: Article
Language:English
Subjects:
Artificial neural networks
Closed-loop stability
Control systems
Cost function
Costs
distributed control
internal model control
learning for control
Numerical stability
optimal control
Stability criteria
uncertain systems
Vectors
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Summary:The growing scale and complexity of safety-critical control systems underscore the need to evolve current control architectures aiming for the unparalleled performances achievable through state-of-the-art optimization and machine learning algorithms. However, maintaining closed-loop stability while boosting the performance of nonlinear control systems using data-driven and deep-learning approaches stands as an important unsolved challenge. In this paper, we tackle the performance-boosting problem with closed-loop stability guarantees. Specifically, we establish a synergy between the Internal Model Control (IMC) principle for nonlinear systems and state-of-the-art unconstrained optimization approaches for learning stable dynamics. Our methods enable learning over specific classes of deep neural network performance-boosting controllers for stable nonlinear systems; crucially, we guarantee \mathcal {L}_{p} closed-loop stability even if optimization is halted prematurely. When the ground-truth dynamics are uncertain, we learn over robustly stabilizing control policies. Our robustness result is tight, in the sense that all stabilizing policies are recovered as the \mathcal {L}_{p} -gain of the model mismatch operator is reduced to zero. We discuss the implementation details of the proposed control schemes, including distributed ones, along with the corresponding optimization procedures, demonstrating the potential of freely shaping the cost functions through several numerical experiments.
ISSN:2694-085X
2694-085X
DOI:10.1109/OJCSYS.2024.3441768