Boundary optimal (LQ) control of coupled hyperbolic PDEs and ODEs

This contribution addresses the development of a linear quadratic (LQ) regulator for a set of hyperbolic PDEs coupled with a set of ODEs through the boundary. The approach is based on an infinite-dimensional Hilbert state-space description of the system and the well-known operator Riccati equation (ORE). In order to solve the optimal control problem, the ORE is converted to a set of matrix Riccati equations. The feedback operator is found by solving the resulting matrix Riccati equations. The performance of the designed control policy is assessed by applying it to a system of interconnected continuous stirred tank reactor (CSTR) and a plug flow reactor (PFR) through a numerical simulation.