Geodesic
Structurally stable design of output regulation for a class of nonlinear systems
Kybernetika, Tome 37 (2001) no. 5, pp. 547-564 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The problem of output regulation of the systems affected by unknown constant parameters is considered here. The main goal is to find a unique feedback compensator (independent on the actual values of unknown parameters) that drives a given error (control criterion) asymptotically to zero for all values of parameters from a certain neighbourhood of their nominal value. Such a task is usually referred to as the structurally stable output regulation problem. Under certain assumptions, such a problem is known to be solvable using dynamical error feedback. The corresponding necessary and sufficient conditions basically include the solvability of the so-called regulator equation and the existence of an immersion of a certain system with outputs into the one having favourable observability and controllability properties. Its model is then directly used for dynamic compensator construction. Usually, such an immersion may be selected as the one to an observable linear system with outputs. In a general case, the above mentioned conditions are highly nonconstructive and difficult to check. This paper studies a certain particular class of systems, the so-called strictly triangular polynomial systems, where that immersion to a linear system can be obtained in a constructive way. Moreover, it provides computer algorithm (based on MAPLE symbolic package) to design the corresponding solution to the structurally stable output regulation problem. Examples together with computer simulations are included to clarify the suggested approach.
The problem of output regulation of the systems affected by unknown constant parameters is considered here. The main goal is to find a unique feedback compensator (independent on the actual values of unknown parameters) that drives a given error (control criterion) asymptotically to zero for all values of parameters from a certain neighbourhood of their nominal value. Such a task is usually referred to as the structurally stable output regulation problem. Under certain assumptions, such a problem is known to be solvable using dynamical error feedback. The corresponding necessary and sufficient conditions basically include the solvability of the so-called regulator equation and the existence of an immersion of a certain system with outputs into the one having favourable observability and controllability properties. Its model is then directly used for dynamic compensator construction. Usually, such an immersion may be selected as the one to an observable linear system with outputs. In a general case, the above mentioned conditions are highly nonconstructive and difficult to check. This paper studies a certain particular class of systems, the so-called strictly triangular polynomial systems, where that immersion to a linear system can be obtained in a constructive way. Moreover, it provides computer algorithm (based on MAPLE symbolic package) to design the corresponding solution to the structurally stable output regulation problem. Examples together with computer simulations are included to clarify the suggested approach.
Classification : 93B07, 93B51, 93C10, 93D15, 93D20, 93D25
Keywords: nonlinear system; stable output regulation 
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     author = {Villanueva-Novelo, Celia and \v{C}elikovsk\'y, Sergej and Castillo-Toledo, Bernardino},
     title = {Structurally stable design of output regulation for a class of nonlinear systems},
     journal = {Kybernetika},
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Villanueva-Novelo, Celia; Čelikovský, Sergej; Castillo-Toledo, Bernardino. Structurally stable design of output regulation for a class of nonlinear systems. Kybernetika, Tome 37 (2001) no. 5, pp. 547-564. http://geodesic.mathdoc.fr/item/KYB_2001_37_5_a1/

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