Abstract. 

A mathematical problem of aggregation and Decomposition of Control Systems with Distributed Parameters is considered.

Keywords: 

differential equations, aggregation, decomposition

PP. 13-19.

DOI: 10.14357/20790279240102 

EDN: NRCTKA

 

References

1. Pavlovskii Yu.I. Group properties of dynamic control systems and phase organizational Structures. USSR Computational Mathematics and Mathematical Physics.1974;14(5):43-53.

2. Isidori A. Nonlinear Control Systems. New York, Springer Verlag, 1995. 549c.

3. Isidori A., Krener A.I., Gori-Giorgi C., and Monako S. Nonlinear Decoupling via Feedback: A Differential Geometric Approach, IEEE Trans. Automat. Control, 1981, V. 26 (2), 331-345.

4. Elkin V.I. “Affine control systems, affine distributions and t-codistributions”, Differ. Equ., 30:11 (1994), 1726–1734

5. Rashevsky P.K. Partial Differential Equations:A Geometric Theory. Moscow, Leningrad: Gostekhizdat; 1947. 354 p. (In Russ.)

6. Elkin V.I. “Controllable dynamic systems and underdetermined systems of differential equations”, Autom. Remote Control, 72:9 (2011), 1822–1832

7. Butkovsky A.G. Methods of Control of Systems with Distributed Parameters. Moscow: Nauka Publ 1975. 568 p. (In Russ.)

8. Elkin V.I. “Aggregation and decomposition of systems of partial differential equations and control systems with distributed parameters”, Comput. Math. Math. Phys., 63:9 (2023), 1741–1750

9. Olver P. Applications of Lie Groups to Differential Equations. Graduate Texts in Mathematics, Volume 107. New York, Berlin, Heidelberg, Tokyo: Springer-Verlag,1986. 497 p.

10. Eisenhart L.P. Continuous Groups of Transformations. Princeton : Princeton University Press, (1933). 319 p.

11. Elkin V.I. On a condition of controllability for control dynamical and distribution parameter systems. Proceedings of ISA RAS.2022 72(4): 11- 15 (In Russ).

12. Elkin V.I. On the conditions of aggregation of controlled dynamic systems. U.S.S.R. Comput. Math. Math. Phys.1978; 18(4) 107–114.

13. Elkin V.I. General solution of systems of partial differential equations with identical principal part. Differentsialʹnye Uravneniya .1985; 21(8) 1389–1398. (In Russ).