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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.06832 |
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| _version_ | 1866918410171973632 |
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| author | Ravasio, Daniele Saccani, Danilo Farina, Marcello Ferrari-Trecate, Giancarlo |
| author_facet | Ravasio, Daniele Saccani, Danilo Farina, Marcello Ferrari-Trecate, Giancarlo |
| contents | This work proposes a two-layered control scheme for constrained nonlinear systems represented by a class of recurrent neural networks and affected by additive disturbances. In particular, a base controller ensures global or regional closed-loop l_p-stability of the error in tracking a desired equilibrium and the satisfaction of input and output constraints within a robustly positive invariant set. An additional control contribution, derived by combining the internal model control principle with a stable operator, is introduced to improve system performance. This operator, implemented as a stable neural network, can be trained via unconstrained optimisation on a chosen performance metric, without compromising closed-loop equilibrium tracking or constraint satisfaction, even if the optimisation is stopped prematurely. In addition, we characterise the class of closed-loop stable behaviours that can be achieved with the proposed architecture. Simulation results on a pH-neutralisation benchmark demonstrate the effectiveness of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning stabilising policies for constrained nonlinear systems Ravasio, Daniele Saccani, Danilo Farina, Marcello Ferrari-Trecate, Giancarlo Systems and Control This work proposes a two-layered control scheme for constrained nonlinear systems represented by a class of recurrent neural networks and affected by additive disturbances. In particular, a base controller ensures global or regional closed-loop l_p-stability of the error in tracking a desired equilibrium and the satisfaction of input and output constraints within a robustly positive invariant set. An additional control contribution, derived by combining the internal model control principle with a stable operator, is introduced to improve system performance. This operator, implemented as a stable neural network, can be trained via unconstrained optimisation on a chosen performance metric, without compromising closed-loop equilibrium tracking or constraint satisfaction, even if the optimisation is stopped prematurely. In addition, we characterise the class of closed-loop stable behaviours that can be achieved with the proposed architecture. Simulation results on a pH-neutralisation benchmark demonstrate the effectiveness of the proposed approach. |
| title | Learning stabilising policies for constrained nonlinear systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2511.06832 |