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Journal Article

Numerical method for the solution of the regulator equation with application to nonlinear tracking

Rehák Branislav, Čelikovský Sergej

: Automatica vol.44, 5 (2008), p. 1358-1365

: CEZ:AV0Z10750506

: GP102/07/P413, GA ČR, GA102/08/0186, GA ČR

: nonlinear output regulation, finite-element method, optimization

(eng): A numerical method to solve the so-called regulator equation is presented here. This equation consists of partial differential equations combined with algebraic ones and arises when solving the output-regulation problem. Solving the regulator equation is becoming difficult especially for the nonminimum phase systems where reducing variables against algebraic part leads to a potentially unsolvable differential part. The proposed numerical method is based on the successive approximation of the differential part of the regulator equation by the finite-element method while trying to minimize a functional expressing the error of its algebraical part. The method is analyzed to obtain theoretical estimates of its convergence and it is tested on an example of the "two-carts with an inverted pendulum" system. Simulations are included to illustrate the suggested approach.

(cze): Je odvozena numerická metoda řešení regulační rovnice, což je parciální diferenciální rovnice s algebraickým omezením. Tato rovnice je použitelná pro návrh nelineární rgulace výstupu.Prezentovaná metoda je analyzována i z hlediska konvergence a je také využita k návrhu regulace některých praktických systémů, jako například soustavy dvou vozíků s obráceným kyvadlem.

: BC

07.01.2019 - 08:39