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

*(English)*Zbl 1259.49054Summary: 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.

##### MSC:

49N10 | Linear-quadratic optimal control problems |

49K15 | Optimality conditions for problems involving ordinary differential equations |

49K20 | Optimality conditions for problems involving partial differential equations |

49M30 | Other numerical methods in calculus of variations (MSC2010) |

35Q93 | PDEs in connection with control and optimization |

34H10 | Chaos control for problems involving ordinary differential equations |