Diffusive Realization of a Lyapunov Equation Solution, and Its FPGA Implementation
World Congress, Volume # 18 | Part# 1
Yakoubi, Youssef; Lenczner, Michel; Goavec-Merou, Gwenael; Couturier, Raphaël; Friedt, Jean-Michel
Digital Object Identifier (DOI)
Digital implementation; Control of partial differential equations; Infinite-dimensional systems
In Yakoubi  and Lenczner et al.  we developed a theoretical framework of diffusive realization for state-realizations of some linear operators. Those are solutions to certain operator linear differential equations inone-dimensional bounded domains. We also illustrated the theory and developed a numerical method for a Lyapunov equation arising from optimal control theory of the heat equation. However, the principles of our numerical methods were only sketched, and now we provide more details. Then, we do not only provide validation results of the method, but we also report our experience in its implementation on a Field Programmable Gate Arrays (FPGA), for the purpose of promoting embedded real-time computation.
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