Receding-Horizon Policy Gradient for Polytopic Controller Synthesis
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917372645867520 |
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| author | Shakeri, Shiva Baranyi, Péter Mesbahi, Mehran |
| author_facet | Shakeri, Shiva Baranyi, Péter Mesbahi, Mehran |
| contents | We propose the Polytopic Receding-Horizon Policy Gradient (P-RHPG) algorithm for synthesizing Parallel Distributed Compensation (PDC) controllers via Tensor Product (TP) model transformation. Standard LMI-based PDC synthesis grows increasingly conservative as model fidelity improves; P-RHPG instead solves a finite-horizon integrated cost via backward-stage decomposition. The key result is that each stage subproblem is a strongly convex quadratic in the vertex gains, a consequence of the linear independence of the HOSVD weighting functions, guaranteeing a unique global minimizer and linear convergence of gradient descent from any initialization. With zero terminal cost, the optimal cost increases monotonically to a finite limit and the gain sequence remains bounded; terminal costs satisfying a mild Lyapunov condition yield non-increasing convergence. Experiments on an aeroelastic wing benchmark confirm convergence to a unique infinite-horizon optimum across all tested terminal cost choices and near-optimal performance relative to the pointwise Riccati lower bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29283 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Receding-Horizon Policy Gradient for Polytopic Controller Synthesis Shakeri, Shiva Baranyi, Péter Mesbahi, Mehran Systems and Control Optimization and Control We propose the Polytopic Receding-Horizon Policy Gradient (P-RHPG) algorithm for synthesizing Parallel Distributed Compensation (PDC) controllers via Tensor Product (TP) model transformation. Standard LMI-based PDC synthesis grows increasingly conservative as model fidelity improves; P-RHPG instead solves a finite-horizon integrated cost via backward-stage decomposition. The key result is that each stage subproblem is a strongly convex quadratic in the vertex gains, a consequence of the linear independence of the HOSVD weighting functions, guaranteeing a unique global minimizer and linear convergence of gradient descent from any initialization. With zero terminal cost, the optimal cost increases monotonically to a finite limit and the gain sequence remains bounded; terminal costs satisfying a mild Lyapunov condition yield non-increasing convergence. Experiments on an aeroelastic wing benchmark confirm convergence to a unique infinite-horizon optimum across all tested terminal cost choices and near-optimal performance relative to the pointwise Riccati lower bound. |
| title | Receding-Horizon Policy Gradient for Polytopic Controller Synthesis |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2603.29283 |