Optimal Port Allocation for Nonlinear Distributed Parameter Systems*

This paper proposes an optimal way of allocating collocated input-output pairs for stabilizing distributed parameter systems. We first introduce a finite-dimensional reduced model from sampled initial responses of the systems via the POD (Proper Orthogonal Decomposition)-Galerkin method. Next, optimal gains of the stabilizing controller for the reduced systems are designed by the stable manifold method that is an exact numerical solver of Hamilton-3Jacobi equations. Finally, we present three allocation methods derived from state shape matching, dissipation enhancement, and their mixed evaluation, and we show that the optimal allocations can be associated with energy controls in terms of port representations.