For instance: The List of VAK
About consortium subscription Contacts
(812) 923 41 97 Non-commercial partnership
St. Petersburg
Your order
To the amount of:


"Humanities and Science University Journal" №22 (Physical and mathematical, biological and technical science), 2016

Instrumental Analysis of Hybrid Systems with Non-trivial Event Functions

D. N. Dostovalov, A. E. Novikov, Yu.V. Shornikov
Price: 50 руб.
 The paper presents the architecture of instrumental environment for the simulation of hybrid systems. The description of main integration algorithms involved in numerical methods library is given. The way for designing a state chart of a hybrid system is shown by the example of the model defi ning motion of two objects in the limited space. The feature of this problem is complex existence conditions of modal behavior. The approach 
for choosing the integration stepsize is offered. This approach takes into account the event function dynamics.
Keywords: hybrid system, Runge-Kutta methods, state chart, modal behavior, event 
1. Kolesov, Yu.B., & Senichenkov, Yu.B. Modelling of systems. Dynamical and 
hybrid systems [Моделирование систем. Динамические и гибридные системы]. 
2012, St. Petersburg: BHV-Petersburg.
2. Novikov, E.A., & Shornikov, Yu.V. Computer simulation of stiff hybrid systems 
[Компьютерное моделирование жестких гибридных систем]. 2012, Novosibirsk: 
Publishing house of NSTU.
3. Novikov, E.A. Explicit methods for stiff systems [Явные методы для жестких 
систем]. 1997, Novosibirsk: Nauka.
4. Novikov, E.A., & Yumatova, L.A. Some methods for solving of ordinary differ-
ential equations unresolved with respect to derivative [Некоторые методы решения 
обыкновенных дифференциальных уравнений, неразрешенных относительно 
производной]. Reports of the USSR Academy of Sciences, 1987, 295(4), 809–812.
5. Esposito, J.M., & Kumar, V. A state event detection algorithm for numerically 
simulating hybrid systems with model singularities. ACM Transactions on Modeling 
and Computer Simulation, 2007, 17(1), 1–26. doi:10.1145/1189756.1189757
6. Shornikov, Yu.V., & Bessonov, A.V. A unifi ed approach to computer simulation 
of hybrid systems [Унифицированный подход к компьютерному моделированию 
гибридных систем]. Information Technology of Modeling and Control, 2015, 3 (93), 
7. Esposito, J., Kumar, V., & Pappas, G.J. Accurate event detection for simulat-
ing hybrid systems. Hybrid Systems: Computation and Control (HSCC), 1998, 2034, 
204–217. doi:10.1007/3-540-45351-2_19
8. Shornikov, Yu.V., & Dostovalov, D.N. Simulation of stiff hybrid systems with one-
sided events in the ISMA environment [Моделирование жестких гибридных систем 
с односторонними событиями в среде ИСМА]. Proceedings of the International 
Workshop “Computer simulation 2012”, 2012, St. Petersburg, pp. 34–41.
9. Hairer, E., & Wanner, G. Solving ordinary differential equations II. Stiff and 
differential-algebraic problems. Springer Series in Computational Mathematics, Vol. 14, 
1996, Berlin: Springer.
10. Shornikov, Yu.V., Novikov, A.E., & Novikov, E.A. Approximation of the Jacobi 
matrix in (2,2)-method for solving stiff systems [Аппроксимация матрицы Якоби в 
(2,2)–методе решения жестких задач]. Proceedings of the Russian Higher School of 
Academy of Sciences of Russian Federation, 2008, 1(10), 31–44.
11. Rosenbrock, H.H. Some general implicit processes for the numerical solution 
of differential equations. The Computer Journal, 1963, 5(4), 329–330. doi:10.1093/
12. Shornikov, Yu.V., & Bessonov, A.V. The component for specifi cation of hybrid 
systems models in the LISMA_PDE language. Certifi cate of computer program registra-
tion #2015617191. 2015, Moscow: Federal Service for Intellectual Property.
Price: 50 рублей
To order