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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Robust Neural Networks: Analysis, Synthesis, and Control

Robust Neural Networks: Analysis, Synthesis, and Control

Pauli, Patricia

Paperback

Technology & EngineeringGeneral ComputersGeneral Mathematics

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ISBN10: 3832559868
ISBN13: 9783832559861
Publisher: Logos Verlag Berlin
Published: Aug 29 2025
Pages: 195
Weight: 0.44
Height: 0.51 Width: 5.61 Depth: 8.01
Language: English
Neural networks achieve remarkable performance across a wide range of applications, yet their lack of formal robustness and stability guarantees poses a major challenge for their use in safety-critical systems. This thesis develops system-theoretic methods for the analysis and design of neural networks with provable robustness and closed-loop stability properties. A central focus is the Lipschitz constant of the neural network, a key sensitivity measure to input perturbations. To estimate tight upper bounds, a scalable method based on semidefinite programming is proposed, leveraging the layer-wise structure of general feedforward architectures, which include convolutional and pooling layers. Beyond analysis, the thesis introduces training methods for neural networks with prescribed Lipschitz bounds by incorporating semidefinite constraints into the optimization problem. Efficient algorithms and network parameterizations are developed to ensure constraint satisfaction throughout training. Finally, robust control techniques are employed to certify closed-loop stability for systems with neural components. In particular, dynamic integral quadratic constraints are used to describe nonlinear activation functions, enabling a less conservative stability analysis than existing approaches. Overall, this work bridges the gap between control theory and deep learning by providing scalable tools for safely integrating neural networks into feedback control and safety-critical applications.

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