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**A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem.**
*(English)*
Zbl 1165.93320

Summary: The regulator equation is the fundamental equation whose solution must be found in order to solve the output regulation problem. It is a system of first-order Partial Differential Equations (PDE) combined with an algebraic equation. The classical approach to its solution is to use the Taylor series with undetermined coefficients. In this contribution, another path is followed: the equation is solved using the finite-element method which is, nevertheless, suitable to solve PDE part only. This paper presents two methods to handle the algebraic condition: the first one is based on iterative minimization of a cost functional defined as the integral of the square of the algebraic expression to be equal to zero. The second method converts the algebraic-differential equation into a singularly perturbed system of partial differential equations only. Both methods are compared and the simulation results are presented including on-line control implementation to some practically motivated laboratory models.

### MSC:

93C10 | Nonlinear systems in control theory |

93C70 | Time-scale analysis and singular perturbations in control/observation systems |

93C20 | Control/observation systems governed by partial differential equations |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

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\textit{B. Rehák} et al., Kybernetika 45, No. 3, 427--444 (2009; Zbl 1165.93320)

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