Learning Discrete-Time Uncertain Nonlinear Systems With Probabilistic Safety and Stability Constraints
This paper presents a discrete-time dynamical system model learning method from demonstration while providing probabilistic guarantees on the safety and stability of the learned model. The controlled dynamic model of a discrete-time system with a zero-mean Gaussian process noise is approximated usin...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Open Journal of Control Systems |
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| Online Access: | https://ieeexplore.ieee.org/document/9926168/ |
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| author | Iman Salehi Tyler Taplin Ashwin P. Dani |
| author_facet | Iman Salehi Tyler Taplin Ashwin P. Dani |
| author_sort | Iman Salehi |
| collection | DOAJ |
| description | This paper presents a discrete-time dynamical system model learning method from demonstration while providing probabilistic guarantees on the safety and stability of the learned model. The controlled dynamic model of a discrete-time system with a zero-mean Gaussian process noise is approximated using an Extreme Learning Machine (ELM) whose parameters are learned subject to chance constraints derived using a discrete-time control barrier function and discrete-time control Lyapunov function in the presence of the ELM reconstruction error. To estimate the ELM parameters a quadratically constrained quadratic program (QCQP) is developed subject to the constraints that are only required to be evaluated at sampled points. Simulations validate that the system model learned using the proposed method can reproduce the demonstrations inside a prescribed safe set while converging to the desired goal location starting from various different initial conditions inside the safe set. Furthermore, it is shown that the learned model can adapt to changes in goal location during reproductions without violating the stability and safety constraints. |
| format | Article |
| id | doaj-art-ba149e1408bc44e49916fbfdd52582e4 |
| institution | Kabale University |
| issn | 2694-085X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Control Systems |
| spelling | doaj-art-ba149e1408bc44e49916fbfdd52582e42025-01-16T00:02:34ZengIEEEIEEE Open Journal of Control Systems2694-085X2022-01-01135436510.1109/OJCSYS.2022.32165459926168Learning Discrete-Time Uncertain Nonlinear Systems With Probabilistic Safety and Stability ConstraintsIman Salehi0https://orcid.org/0000-0002-9144-3573Tyler Taplin1https://orcid.org/0000-0002-9246-4122Ashwin P. Dani2https://orcid.org/0000-0002-7091-5607Department of Electrical and Computer Engineering at University of Connecticut, Storrs, CT, USADepartment of Electrical and Computer Engineering at University of Connecticut, Storrs, CT, USADepartment of Electrical and Computer Engineering at University of Connecticut, Storrs, CT, USAThis paper presents a discrete-time dynamical system model learning method from demonstration while providing probabilistic guarantees on the safety and stability of the learned model. The controlled dynamic model of a discrete-time system with a zero-mean Gaussian process noise is approximated using an Extreme Learning Machine (ELM) whose parameters are learned subject to chance constraints derived using a discrete-time control barrier function and discrete-time control Lyapunov function in the presence of the ELM reconstruction error. To estimate the ELM parameters a quadratically constrained quadratic program (QCQP) is developed subject to the constraints that are only required to be evaluated at sampled points. Simulations validate that the system model learned using the proposed method can reproduce the demonstrations inside a prescribed safe set while converging to the desired goal location starting from various different initial conditions inside the safe set. Furthermore, it is shown that the learned model can adapt to changes in goal location during reproductions without violating the stability and safety constraints.https://ieeexplore.ieee.org/document/9926168/Discrete-time control barrier functionextreme learning machinesafe model learning |
| spellingShingle | Iman Salehi Tyler Taplin Ashwin P. Dani Learning Discrete-Time Uncertain Nonlinear Systems With Probabilistic Safety and Stability Constraints IEEE Open Journal of Control Systems Discrete-time control barrier function extreme learning machine safe model learning |
| title | Learning Discrete-Time Uncertain Nonlinear Systems With Probabilistic Safety and Stability Constraints |
| title_full | Learning Discrete-Time Uncertain Nonlinear Systems With Probabilistic Safety and Stability Constraints |
| title_fullStr | Learning Discrete-Time Uncertain Nonlinear Systems With Probabilistic Safety and Stability Constraints |
| title_full_unstemmed | Learning Discrete-Time Uncertain Nonlinear Systems With Probabilistic Safety and Stability Constraints |
| title_short | Learning Discrete-Time Uncertain Nonlinear Systems With Probabilistic Safety and Stability Constraints |
| title_sort | learning discrete time uncertain nonlinear systems with probabilistic safety and stability constraints |
| topic | Discrete-time control barrier function extreme learning machine safe model learning |
| url | https://ieeexplore.ieee.org/document/9926168/ |
| work_keys_str_mv | AT imansalehi learningdiscretetimeuncertainnonlinearsystemswithprobabilisticsafetyandstabilityconstraints AT tylertaplin learningdiscretetimeuncertainnonlinearsystemswithprobabilisticsafetyandstabilityconstraints AT ashwinpdani learningdiscretetimeuncertainnonlinearsystemswithprobabilisticsafetyandstabilityconstraints |