Optimal Control Allocation for 2D Reaction-Diffusion Equations With Multiple Locally Distributed Inputs

In this article, the problem of stabilization of a 2D unstable parabolic equation with multiple distributed inputs is addressed using a spectral decomposition approach. Furthermore the underlying redundancy of the actuation arrangement is exploited and actively used by introducing a suitable control allocation architecture. In particular, two optimal allocation policies have been considered: gradient descent and linear quadratic allocation. A simulation study supports and illustrates the theoretical findings.