Trajectory-Oriented Control Using Gradient Descent: An Unconventional Approach
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914950582108160 |
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| author | Esmzad, Ramin Modares, Hamidreza |
| author_facet | Esmzad, Ramin Modares, Hamidreza |
| contents | In this work, we introduce a novel gradient descent-based approach for optimizing control systems, leveraging a new representation of stable closed-loop dynamics as a function of two matrices i.e. the step size or direction matrix and value matrix of the Lyapunov cost function. This formulation provides a new framework for analyzing and designing feedback control laws. We show that any stable closed-loop system can be expressed in this form with appropriate values for the step size and value matrices. Furthermore, we show that this parameterization of the closed-loop system is equivalent to a linear quadratic regulator for appropriately chosen weighting matrices. We also show that trajectories can be shaped using this approach to achieve a desired closed-loop behavior. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_10662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Trajectory-Oriented Control Using Gradient Descent: An Unconventional Approach Esmzad, Ramin Modares, Hamidreza Optimization and Control Systems and Control In this work, we introduce a novel gradient descent-based approach for optimizing control systems, leveraging a new representation of stable closed-loop dynamics as a function of two matrices i.e. the step size or direction matrix and value matrix of the Lyapunov cost function. This formulation provides a new framework for analyzing and designing feedback control laws. We show that any stable closed-loop system can be expressed in this form with appropriate values for the step size and value matrices. Furthermore, we show that this parameterization of the closed-loop system is equivalent to a linear quadratic regulator for appropriately chosen weighting matrices. We also show that trajectories can be shaped using this approach to achieve a desired closed-loop behavior. |
| title | Trajectory-Oriented Control Using Gradient Descent: An Unconventional Approach |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2409.10662 |