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DISCONTINUOUS TIME-REPARAMETERIZATION TECHNIQUE FOR OPTIMAL CONTROL OF HYBRID SYSTEMS WITH POLYNOMIAL IMPULSES

Annotation

We formulate a problem of optimal control for a dynamical system with trajectories of bounded variation subject to two types control inputs _ a usual bounded control, and a measure-type impulsive control, whose action results in polynomial impulsive effects. The model is described by a special measure differential equation and is subject to constraints on one-sided limits of a state trajectory, imposed over a set, where an impulsive control measure is concentrated (the so-called nonstandard mixed constraints [1]). We propose a technique for the problem transformation to an equivalent conventional variational problem with absolutely continuous trajectories. The technique can be further used for variational analysis of the original problem by means of regular analytical and numerical methods.

Keywords

optimal control; impulsive control; polynomial impulses; discontinuous time-reparameterization; measure differential equations; mixed constraints

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UDC

519.711

Pages

1099-1104

References

1. Goncharova E., Staritsyn M. Optimization of measure-driven hybrid systems // J. Optim. Theory Appl. 2012. V. 153. № 1. P. 139–156. 2. Branicky M., Borkar V., and Mitter S. A unified framework for hybrid control: Model and optimal control theory // IEEE Trans. Automat. Control. 1998. V. 43. № 1. P. 31–45. 3. Miller B.M., Rubinovich E.Ya. Optimizatsiya dinamicheskikh sistem s impul'snymi upravleniyami. M.: Nauka, 2005. 4. Goncharova E., Staritsyn M. Optimal control of dynamical systems with polynomial impulses // Discr. Cont. Dynam. Syst. 2015. V. 35. № 9. P. 139–156. 5. Arutyunov A., Karamzin D., Pereira F. On constrained impulsive control problems // J. Math. Sci. 2010. V. 165. № 6. P. 654–688. 6. Gurman V.I. Vyrozhdennye zadachi optimal'nogo upravleniya. M.: Nauka, 1977. 7. Zavalishchin S.T., Sesekin A.N. Impul'snye protsessy. Modeli i prilozheniya. M.: Nauka, 1991. 8. Dykhta V.A., Samsonyuk O.N. Optimal'noe impul'snoe upravlenie s prilozheniyami. M.: FIZMAT-LIT, 2000. 9. Bressan A., Rampazzo F. On systems with quadratic impulses and their application to Lagrangean mechanics // SIAM J. Control Optim. 1993. V. 31. P. 1205–1220.

Received

2015-05-26

Section of issue

Scientific articles

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