Suppressing constrained internal and external disturbances for impulse processes control in cognitive maps of complex systems
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2018.4.09Keywords:
cognitive map, linear matrix inequalities, invariant ellipsoid, state controller, closed-loop control systemAbstract
The possibility of suppressing constrained internal and external disturbances in complex systems of different nature is considered. Systems dynamics is described by mathematical models of impulse processes in cognitive maps (CM). Dynamic model of CM impulse process is split into two interrelated systems of difference equations with measurable and unmeasurable nodes coordinates, respectively. Changes in coordinates of unmeasurable CM nodes are considered as constrained external disturbances in the first equations system of the CM model for impulse processes with measurable coordinates. Oscillations of the measurable CM nodes coordinates, caused by changes in CM weights relative to their values, estimated based on previous identification, are considered as internal disturbances. To suppress these disturbances, a closed-loop robust control system is synthesized using the invariant ellipsoid method.References
Roberts F. Discrete Mathematical Models with Applications to Social, Biological, and Environmental Problems / F. Roberts // Englewood Cliffs, Prentice-Hall, 1976. — 559 p.
Poljak B.T. Robastnaja ustojchivost' i upravlenie / B.T. Poljak, P.S. Scherbakov. — M.: Nauka, 2002. — 303 s.
Nazin S.A. Podavlenie ogranichennyh vneshnih vozmuschenij s pomosch'ju metoda invariantnyh ellipsoidov / S.A. Nazin, B.T. Poljak, M.V. Topunov // Avtomatika i telemehanika. — 2007. — № 3. — S. 106–125.
Romanenko V.D. Avtomatizatsija upravlenija impul'snymi protsessami v kognitivnyh kartah s podavleniem ogranichennyh vozmuschenij na osnove metoda invariantnyh ellipsoidov / V.D. Romanenko, Ju.L. Miljavskij // Systemni doslidzhennja ta informatsijni tekhnolohiyi. — 2017. — № 2. — S. 29–39.
Gubarev V.F. Identifikatsija v kognitivnyh kartah v rezhime impul'snyh protsessov pri polnoj informatsii / V.F. Gubarev, V.D. Romanenko, Ju.L. Miljavskij // Problemy upravlenija i informatiki. — 2018. — № 4. — S. 30–43.
Polyak B.T. Convexity of quadratic transformations and its use in control and optimization / B.T. Polyak // J. Optim. Theory Appl. — 1998. — Vol. 99. — P. 553–583.
Hager W.W. Updating the inverse of a matrix / W.W. Hager // SIAM Review. — 1989. — 31 (2). — P. 221–239.
