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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.12882 |
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| _version_ | 1866914649484558336 |
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| author | Wang, Qi |
| author_facet | Wang, Qi |
| contents | This paper presents a δ-PI algorithm which is based on damped Newton method for the H{\infty} tracking control problem of unknown continuous-time nonlinear system. A discounted performance function and an augmented system are used to get the tracking Hamilton-Jacobi-Isaac (HJI) equation. Tracking HJI equation is a nonlinear partial differential equation, traditional reinforcement learning methods for solving the tracking HJI equation are mostly based on the Newton method, which usually only satisfies local convergence and needs a good initial guess. Based upon the damped Newton iteration operator equation, a generalized tracking Bellman equation is derived firstly. The δ-PI algorithm can seek the optimal solution of the tracking HJI equation by iteratively solving the generalized tracking Bellman equation. On-policy learning and off-policy learning δ-PI reinforcement learning methods are provided, respectively. Off-policy version δ-PI algorithm is a model-free algorithm which can be performed without making use of a priori knowledge of the system dynamics. NN-based implementation scheme for the off-policy δ-PI algorithms is shown. The suitability of the model-free δ-PI algorithm is illustrated with a nonlinear system simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Model-Free $δ$-Policy Iteration Based on Damped Newton Method for Nonlinear Continuous-Time H$\infty$ Tracking Control Wang, Qi Machine Learning This paper presents a δ-PI algorithm which is based on damped Newton method for the H{\infty} tracking control problem of unknown continuous-time nonlinear system. A discounted performance function and an augmented system are used to get the tracking Hamilton-Jacobi-Isaac (HJI) equation. Tracking HJI equation is a nonlinear partial differential equation, traditional reinforcement learning methods for solving the tracking HJI equation are mostly based on the Newton method, which usually only satisfies local convergence and needs a good initial guess. Based upon the damped Newton iteration operator equation, a generalized tracking Bellman equation is derived firstly. The δ-PI algorithm can seek the optimal solution of the tracking HJI equation by iteratively solving the generalized tracking Bellman equation. On-policy learning and off-policy learning δ-PI reinforcement learning methods are provided, respectively. Off-policy version δ-PI algorithm is a model-free algorithm which can be performed without making use of a priori knowledge of the system dynamics. NN-based implementation scheme for the off-policy δ-PI algorithms is shown. The suitability of the model-free δ-PI algorithm is illustrated with a nonlinear system simulation. |
| title | Model-Free $δ$-Policy Iteration Based on Damped Newton Method for Nonlinear Continuous-Time H$\infty$ Tracking Control |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2401.12882 |