Receding-Horizon Policy Gradient for Polytopic Controller Synthesis
This addresses controller synthesis for polytopic systems, offering a less conservative alternative to LMI-based methods, but it appears incremental as it builds on existing receding-horizon and policy gradient techniques.
The paper tackled the problem of synthesizing Parallel Distributed Compensation controllers for polytopic systems, where standard methods become conservative with high model fidelity, by proposing the Polytopic Receding-Horizon Policy Gradient algorithm, which achieved convergence to a unique infinite-horizon optimum and near-optimal performance relative to a lower bound in experiments on an aeroelastic wing benchmark.
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.