Feedback Stabilization and Tracking for Heat Equations Using Thermo-Plasmonic Nanoparticles as Actuators
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arXiv
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| Format: | Preprint |
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2026
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| author | Mukherjee, Arpan Rodrigues, Sérgio S. Sini, Mourad |
| author_facet | Mukherjee, Arpan Rodrigues, Sérgio S. Sini, Mourad |
| contents | We propose a feedback strategy to track prescribed heat profiles using plasmonic nanoparticles as actuators. Starting from a thermo--plasmonic Maxwell--heat model, we use a time-domain discrete effective description in which the generated heat is approximated by a superposition of heat kernels centered at particle locations with amplitudes governed by a coupled Volterra system. We recast this dynamics as a heat equation on a bounded domain with finitely many point actuators and design a tracking feedback based on pointwise evaluations of $\mathcal A^{-1}y$, where $\mathcal A=I-A_0$ and $A_0$ is the Neumann diffusion operator. Working in the natural $V'$ setting with $V=D(\mathcal A)$, we prove exponential stabilization of the tracking error via distribution-actuator theory. For non-equilibrium reference profiles, we add a constant feedforward term and a low-mode fixed-point pre-compensation on $X_N$, ensuring exact steady matching on $X_N$ and an explicit bound on the residual tail mismatch. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14581 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Feedback Stabilization and Tracking for Heat Equations Using Thermo-Plasmonic Nanoparticles as Actuators Mukherjee, Arpan Rodrigues, Sérgio S. Sini, Mourad Analysis of PDEs We propose a feedback strategy to track prescribed heat profiles using plasmonic nanoparticles as actuators. Starting from a thermo--plasmonic Maxwell--heat model, we use a time-domain discrete effective description in which the generated heat is approximated by a superposition of heat kernels centered at particle locations with amplitudes governed by a coupled Volterra system. We recast this dynamics as a heat equation on a bounded domain with finitely many point actuators and design a tracking feedback based on pointwise evaluations of $\mathcal A^{-1}y$, where $\mathcal A=I-A_0$ and $A_0$ is the Neumann diffusion operator. Working in the natural $V'$ setting with $V=D(\mathcal A)$, we prove exponential stabilization of the tracking error via distribution-actuator theory. For non-equilibrium reference profiles, we add a constant feedforward term and a low-mode fixed-point pre-compensation on $X_N$, ensuring exact steady matching on $X_N$ and an explicit bound on the residual tail mismatch. |
| title | Feedback Stabilization and Tracking for Heat Equations Using Thermo-Plasmonic Nanoparticles as Actuators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.14581 |