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Boundary optimal (LQ) control of coupled hyperbolic PDEs and ODEs. (English) Zbl 1259.49054
Summary: 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.

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
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