Abstract
The article investigates complex impulsive systems in which the so-called controlling systems jumps effect emerges. In particular, this research includes the correctness of the solution to the impulsive control system and approximation lemmas. A 3D model example is provided which illustrates the relevance of the considered approach to the study of complex impulsive systems.
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References
Lawden, D.F.: Optimal Trajectories for Space Navigation. Butterworth, London (1963)
Bressan, A., Rampazzo, F.: On differential systems with vector-valued impulsive controls. Boll. Un. Matematica Italiana 2-B, 641–656 (1988)
Miller, B., Rubinovich, E.: Impulsive Control in Continuous and Discrete-Continuous Systems. Springer (2002)
Dykhta, V.A., Samsonyuk, O.N.: Optimal Impulse Control with Applications, Moscow, Fizmatlit (2000) (in Russian)
Kurzhanski, A.B., Daryin, A.N.: Dynamic Programming for Impulse Controls. Annual Reviews in Control 32(2), 213–227 (2008)
Wolenski, P.R., Zabic, S.: A Sampling Method and Approximation Results for Impulsive Systems. SIAM J. Control Optim. 46(3), 983–998 (2007)
Code, W.J., Loewen, P.D.: Optimal Control of Non-convex Measure-driven Differential Inclusions. Set-Valued Anal. 19, 203–235 (2011)
Silva, G.N., Vinter, R.B.: Measure Driven Differential Inclusions. J. Math. Analysis and Applic. 202, 727–746 (1996)
Vinter, R.B., Pereira, F.L.: A Maximum Principle for Optimal Processes with Discontinuous Trajectories. SIAM J. Control Optim. 26, 205–229 (1988)
Arutyunov, A.V., Karamzin, D.Y., Pereira, F.L.: On constrained impulsive control problems: controlling system jumps. Journal of Mathematical Sciences 165(6), 654–687 (2010)
Arutyunov, A.V., Karamzin, D.Y., Pereira, F.L.: Pontryagin’s maximum principle for constrained impulsive control problems. Nonlinear Analysis, Theory, Methods and Applications 75(3), 1045–1057 (2012)
Arutyunov, A.V., Karamzin, D.Y., Pereira, F.L.: On the extension of classical calculus of variations and optimal control to problems with discontinuous trajectories. In: 51st IEEE Conf. on Decision and Control, Maui, Hawaii, December 10-13, pp. 6406–6411 (2012)
Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.: Mathematical Theory of Optimal Processes, Moscow, Nauka (1983)
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Karamzin, D., de Oliveira, V., Silva, G., Pereira, F.L. (2015). On the Study of Complex Impulsive Systems. In: Moreira, A., Matos, A., Veiga, G. (eds) CONTROLO’2014 – Proceedings of the 11th Portuguese Conference on Automatic Control. Lecture Notes in Electrical Engineering, vol 321. Springer, Cham. https://doi.org/10.1007/978-3-319-10380-8_5
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DOI: https://doi.org/10.1007/978-3-319-10380-8_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10379-2
Online ISBN: 978-3-319-10380-8
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