Fast Adaptive Laws for Adaptive Control Under Stochastic Disturbances
In this work, we consider two classes of adaptive laws for the adaptive control of a class of discrete-time nonlinear systems with all states accessible perturbed by a stochastic disturbance. First, we consider high-order tuner algorithms based on accelerated gradient methods for the optimization of...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2023
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| Online Access: | https://hdl.handle.net/1721.1/151944 |
| _version_ | 1811094016514588672 |
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| author | Fisher, Peter |
| author2 | Annaswamy, Anuradha M. |
| author_facet | Annaswamy, Anuradha M. Fisher, Peter |
| author_sort | Fisher, Peter |
| collection | MIT |
| description | In this work, we consider two classes of adaptive laws for the adaptive control of a class of discrete-time nonlinear systems with all states accessible perturbed by a stochastic disturbance. First, we consider high-order tuner algorithms based on accelerated gradient methods for the optimization of convex loss functions, and derive a new adaptive law designed for stable adaptive control. Second, we review the state of the literature on recursive least-squares adaptive laws - especially those with variable-direction forgetting factor - and we derive an alternative to a recent method proposed in the literature.
Recently, a high-order tuner algorithm was recently developed for the minimization of convex loss functions with time-varying regressors in the context of an identification problem. Based on Nesterov's algorithm, the high-order tuner was shown to guarantee bounded parameter estimation when regressors vary with time, and to lead to accelerated convergence of the tracking error when regressors are constant. In this work, we derive a new high-order tuner algorithm that preserves the accelerated convergence of the original under constant regressors, but that is also provably stable with the addition of projection to a compact set. This latter property allows us to apply the new high-order tuner to the adaptive control of a particular class of discrete-time nonlinear dynamical systems under stochastic disturbances.
There has been a substantial body of literature on variable-direction forgetting methods for recursive least-squares-type adaptive laws. Recently, a new method has been developed that uses the SVD of the covariance matrix to apply directional forgetting. In this work, we place this method in the context of the broader RLS literature as well as other literature on variable-direction forgetting. We then use this context to argue that if the computation power is available for an SVD at every time step, it is better to simply use it to directly invert the covariance matrix at each time step rather than implementing variable-direction forgetting. We call this new adaptive law "Explicit Least-Squares" and show that ELS leads to provably stable adaptive control. |
| first_indexed | 2024-09-23T15:54:12Z |
| format | Thesis |
| id | mit-1721.1/151944 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T15:54:12Z |
| publishDate | 2023 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1519442023-08-24T03:05:36Z Fast Adaptive Laws for Adaptive Control Under Stochastic Disturbances Fisher, Peter Annaswamy, Anuradha M. Massachusetts Institute of Technology. Department of Mechanical Engineering In this work, we consider two classes of adaptive laws for the adaptive control of a class of discrete-time nonlinear systems with all states accessible perturbed by a stochastic disturbance. First, we consider high-order tuner algorithms based on accelerated gradient methods for the optimization of convex loss functions, and derive a new adaptive law designed for stable adaptive control. Second, we review the state of the literature on recursive least-squares adaptive laws - especially those with variable-direction forgetting factor - and we derive an alternative to a recent method proposed in the literature. Recently, a high-order tuner algorithm was recently developed for the minimization of convex loss functions with time-varying regressors in the context of an identification problem. Based on Nesterov's algorithm, the high-order tuner was shown to guarantee bounded parameter estimation when regressors vary with time, and to lead to accelerated convergence of the tracking error when regressors are constant. In this work, we derive a new high-order tuner algorithm that preserves the accelerated convergence of the original under constant regressors, but that is also provably stable with the addition of projection to a compact set. This latter property allows us to apply the new high-order tuner to the adaptive control of a particular class of discrete-time nonlinear dynamical systems under stochastic disturbances. There has been a substantial body of literature on variable-direction forgetting methods for recursive least-squares-type adaptive laws. Recently, a new method has been developed that uses the SVD of the covariance matrix to apply directional forgetting. In this work, we place this method in the context of the broader RLS literature as well as other literature on variable-direction forgetting. We then use this context to argue that if the computation power is available for an SVD at every time step, it is better to simply use it to directly invert the covariance matrix at each time step rather than implementing variable-direction forgetting. We call this new adaptive law "Explicit Least-Squares" and show that ELS leads to provably stable adaptive control. S.M. 2023-08-23T16:21:04Z 2023-08-23T16:21:04Z 2023-06 2023-07-19T18:45:11.156Z Thesis https://hdl.handle.net/1721.1/151944 0000-0001-7168-8381 In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Fisher, Peter Fast Adaptive Laws for Adaptive Control Under Stochastic Disturbances |
| title | Fast Adaptive Laws for Adaptive Control Under Stochastic Disturbances |
| title_full | Fast Adaptive Laws for Adaptive Control Under Stochastic Disturbances |
| title_fullStr | Fast Adaptive Laws for Adaptive Control Under Stochastic Disturbances |
| title_full_unstemmed | Fast Adaptive Laws for Adaptive Control Under Stochastic Disturbances |
| title_short | Fast Adaptive Laws for Adaptive Control Under Stochastic Disturbances |
| title_sort | fast adaptive laws for adaptive control under stochastic disturbances |
| url | https://hdl.handle.net/1721.1/151944 |
| work_keys_str_mv | AT fisherpeter fastadaptivelawsforadaptivecontrolunderstochasticdisturbances |