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D. A. Makarov The design of observer based tracking control for weakly nonlinear systems using differential matrix equations Riccati |
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Abstract. The paper deals with finite-horizon tracking control problem for a class of weakly nonlinear systems with statedependent coefficients. Synthesis of control and the state observer is carried out on the basis of an approximate solution of the corresponding differential matrix Riccati equations using the same numerical-analytical procedure. The advantage of this approach is the reduction in computational complexity. Numerical experiments showed the efficiency of the proposed control algorithm. Keywords: tracking problem, nonlinear control, state observer, matrix differential state-dependent Riccati equation. PP.63-71. DOI 10.14357/20718632180407 References 1. Mracek, C.P., and J. R. Cloutier, 1997. Full envelope missile longitudinal autopilot design using the state-dependent Riccati equation method. The AIAA “Guidance, Navigation and Control” Conference. New Orleans LA. 1697-1705. 2. Mracek, C.P., and J. R. Cloutier. 1998. Control designs for the nonlinear benchmark problem via the state-dependent Riccati equation method. International Journal of Robust and Nonlinear Control. 8: 401-433. 3. Çimen, T. 2012. Survey of state-dependent Riccati equation in nonlinear optimal feedback control synthesis. Journal of Guidance, Control, and Dynamics. 35(4): 1025-1047. 4. Cloutier, J.R. 1997. State-Dependent Riccati Equation Techniques: An Overview // American Control Conference. 2: 932-936. 5. Dmitriev, M.G., and D.A. Makarov. 2014. Gladkij nelinejnyj regulyator v slabo nelinejnoj sisteme upravleniya s koehfficientami, zavisyashchimi ot sostoyaniya [Smooth nonlinear controller in a weakly nonlinear control system with state-dependent coefficients]. Trudy Instituta sistemnogo analiza RAN [Proceedings of the Institute for System Analysis of RAS]. 64(4): 53-58. 6. Danik, Yu.E., M.G. Dmitriev, and D.A. Makarov. 2015. Odin algoritm postroeniya regulyatorov dlya nelinejnyh sistem s formal'nym malym parametrom [An algorithm for constructing regulators for nonlinear systems with the formal small parameter]. Informacionnye tekhnologii i vychislitel'nye sistemy [Information technology and computer systems]. 4: 35-44. 7. Dmitriev, M.G., and D.A. Makarov. 2016. The near optimality of the stabilizing control in a weakly nonlinear system with state-dependent coefficients. AIP Conference. 1759: 020016-1 – 020016-6. DOI: 10.1063/1.4959630 8. Makarov, D.A. 2017. Podhod k postroeniyu nelinejnogo upravleniya v zadache slezheniya s koehfficientami, zavisyashchimi ot sostoyaniya CHast' I. Algoritm [A nonlinear approach to a feedback control design for a tracking state-dependent problem. I. An algorithm]. Informacionnye tekhnologii i vychislitel'nye sistemy [Information technology and computer systems]. 3: 10-19. 9. Khamis A., and D. Naidu. 2013. Nonlinear optimal tracking using finite horizon state dependent Riccati equation (SDRE). The 4th International Conference on Circuits, Systems, Control, Signals (CSCS). Valencia. 37-42. 10. Khamis A., D.S. Naidu, and A.M. Kamel. 2014. Nonlinear Finite-Horizon Regulation and Tracking for Systems with Incomplete State Information Using Differential State Dependent Riccati Equation. International Journal of Aerospace Engineering. 2014(2014). http://dx.doi.org/10.1155/2014/178628. Available at: https://www.hindawi.com/journals/ijae/2014/178628/abs/(accessed September 26, 2018). 11. Makarov, D.A. 2017. Sintez upravleniya i nablyudatelya dlya slabo nelinejnyh sistem na osnove tekhniki psevdolinearizacii [Synthesis of Control and State Observer for Weakly Nonlinear Systems Based on the Pseudo-Linearization Technique]. Modelirovanie i analiz informacionnyh system [Modeling and Analysis of Information Systems]. 24(6): 802–810. DOI: 10.18255/1818-1015-2017-6-802-810. 12. Afanas'ev, V.N. 2007. Dinamicheskie sistemy upravleniya s nepolnoj informaciej: Algoritmicheskoe konstruirovanie [Dynamic control systems with incomplete information: Algorithmic design]. Мoscow: URSS. 216 p. ISBN 978-5-484-00787-5. 13. Haessig, D. A., and B. Friedland. 2002. State dependent differential Riccati equation for nonlinear estimation and control. IFAC Proceedings Volumes. 35(1): 405-410. 14. Pupkov, K.A., and N.D. Egupov. 2004. Metody klassicheskoj i sovremennoj teorii avtomaticheskogo upravleniya: Uchebnik v 5-i tt.; 2-e izd., pererab. i dop. T 4. Teoriya optimizacii sistem avtomaticheskogo upravleniya [Methods of classical and modern theory of automatic control: A textbook in 5 volumes; 2-nd ed., revised and enlarged. Volume 4. Theory of optimization of automatic control systems]. Мoscow: Publishing house MSTU. Bauman. 744 p. 15. Kvakernaak, H., and R. Sivan. 1977. Linejnye optimal'nye sistemy upravleniya [Linear optimal control systems]. Мoscow: “Mir”. 650 p. 16. Beikzadeh, H., and H. D. Taghirad. 2012. Exponential nonlinear observer based on the differential state-dependent Riccati equation. International Journal of Automation and Computing. 9(4): 358-368.
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