Control Forward-Backward Consistency: Quantifying the Accuracy of Koopman Control Family Models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910102436446208 |
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| author | Haseli, Masih Cortés, Jorge Burdick, Joel W. |
| author_facet | Haseli, Masih Cortés, Jorge Burdick, Joel W. |
| contents | This paper extends the forward-backward consistency index, originally introduced in Koopman modeling of systems without input, to the setting of control systems, providing a closed-form computable measure of accuracy for data-driven models associated with the Koopman Control Family (KCF). Building on a forward-backward regression perspective, we introduce the control forward-backward consistency matrix and demonstrate that it possesses several favorable properties. Our main result establishes that the relative root-mean-square error of KCF function predictors is strictly bounded by the square root of the control consistency index, defined as the maximum eigenvalue of the consistency matrix. This provides a sharp, closed-form computable error bound for finite-dimensional KCF models. We further specialize this bound to the widely used lifted linear and bilinear models. We also discuss how the control consistency index can be incorporated into optimization-based modeling and illustrate the methodology via simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_27548 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Control Forward-Backward Consistency: Quantifying the Accuracy of Koopman Control Family Models Haseli, Masih Cortés, Jorge Burdick, Joel W. Optimization and Control Systems and Control This paper extends the forward-backward consistency index, originally introduced in Koopman modeling of systems without input, to the setting of control systems, providing a closed-form computable measure of accuracy for data-driven models associated with the Koopman Control Family (KCF). Building on a forward-backward regression perspective, we introduce the control forward-backward consistency matrix and demonstrate that it possesses several favorable properties. Our main result establishes that the relative root-mean-square error of KCF function predictors is strictly bounded by the square root of the control consistency index, defined as the maximum eigenvalue of the consistency matrix. This provides a sharp, closed-form computable error bound for finite-dimensional KCF models. We further specialize this bound to the widely used lifted linear and bilinear models. We also discuss how the control consistency index can be incorporated into optimization-based modeling and illustrate the methodology via simulations. |
| title | Control Forward-Backward Consistency: Quantifying the Accuracy of Koopman Control Family Models |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2603.27548 |