Stability Verification of Neural Network Controllers Using Mixed-Integer Programming

We propose a framework for the stability verification of Mixed-Integer Linear Programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be evaluated at a low computational cost, against a fixed baseline pol...

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Veröffentlicht in:IEEE transactions on automatic control Jg. 68; H. 12; S. 1 - 16
Hauptverfasser: Schwan, Roland, Jones, Colin N., Kuhn, Daniel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.12.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Approximation
Approximation error
Artificial neural networks
Closed loops
Computing costs
Integer programming
Linear programming
Mathematical analysis
Mixed integer
Neural networks
Numerical stability
Parameterization
Policies
Power converters
Power electronics
Predictive control
Programming
Quadratic programming
Stability analysis
Symmetric matrices
Verification
ISSN:0018-9286, 1558-2523
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Zusammenfassung:We propose a framework for the stability verification of Mixed-Integer Linear Programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be evaluated at a low computational cost, against a fixed baseline policy, which is known to be stable but expensive to evaluate. We provide sufficient conditions for the closed-loop stability of the candidate policy in terms of the worst-case approximation error with respect to the baseline policy, and we show that these conditions can be checked by solving a Mixed-Integer Quadratic Program (MIQP). Additionally, we demonstrate that an outer and inner approximation of the stability region of the candidate policy can be computed by solving an MILP. The proposed framework is sufficiently general to accommodate a broad range of candidate policies including ReLU Neural Networks (NNs), optimal solution maps of parametric quadratic programs, and Model Predictive Control (MPC) policies. We also present an open-source toolbox in Python based on the proposed framework, which allows for the easy verification of custom NN architectures and MPC formulations. We showcase the flexibility and reliability of our framework in the context of a DC-DC power converter case study and investigate its computational complexity.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3283213