Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems
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| Format: | Preprint |
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2025
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| _version_ | 1866910048273301504 |
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| author | Elamvazhuthi, Karthik Gadginmath, Darshan Pasqualetti, Fabio |
| author_facet | Elamvazhuthi, Karthik Gadginmath, Darshan Pasqualetti, Fabio |
| contents | In this paper, we propose a deterministic diffusion-based framework for controlling the probability density of nonlinear control-affine systems, with theoretical guarantees for drift-free and linear time-invariant (LTI) dynamics. The central idea is to first excite the system with white noise so that a forward diffusion process explores the reachable regions of state space, and then to design a deterministic feedback law that acts as a denoising mechanism driving the system back toward a desired target distribution supported on the target set. This denoising phase provides a feedback controller that steers the control system to the target set. In this framework, control synthesis reduces to constructing a deterministic reverse process that reproduces the desired evolution of state densities. We derive existence conditions ensuring such deterministic realizations of time-reversals for controllable drift-free and LTI systems, and show that the resulting feedback laws provide a tractable alternative to nonlinear control by viewing density control as a relaxation of controlling a system to target sets. Numerical studies on a unicycle model with obstacles, a five-dimensional driftless system, and a four-dimensional LTI system demonstrate reliable diffusion-inspired density control. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_09836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems Elamvazhuthi, Karthik Gadginmath, Darshan Pasqualetti, Fabio Optimization and Control Machine Learning Robotics Systems and Control In this paper, we propose a deterministic diffusion-based framework for controlling the probability density of nonlinear control-affine systems, with theoretical guarantees for drift-free and linear time-invariant (LTI) dynamics. The central idea is to first excite the system with white noise so that a forward diffusion process explores the reachable regions of state space, and then to design a deterministic feedback law that acts as a denoising mechanism driving the system back toward a desired target distribution supported on the target set. This denoising phase provides a feedback controller that steers the control system to the target set. In this framework, control synthesis reduces to constructing a deterministic reverse process that reproduces the desired evolution of state densities. We derive existence conditions ensuring such deterministic realizations of time-reversals for controllable drift-free and LTI systems, and show that the resulting feedback laws provide a tractable alternative to nonlinear control by viewing density control as a relaxation of controlling a system to target sets. Numerical studies on a unicycle model with obstacles, a five-dimensional driftless system, and a four-dimensional LTI system demonstrate reliable diffusion-inspired density control. |
| title | Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems |
| topic | Optimization and Control Machine Learning Robotics Systems and Control |
| url | https://arxiv.org/abs/2504.09836 |