
D.A. Makarov A nonlinear approach to a feedback control design for a tracking statedependent problem Part I. An algorithm 

Abstract. The paper deals with a nonlinear finitehorizon tracking control design for a plant with an additive linear part and statedependent coefficients. The tracking problem is reduced to an optimal control problem with terminal payoff where exact and approximate solutions are given. The last one is used in an algorithm for a design of a computationally efficient nonlinear control. Keywords: tracking problem, nonlinear control, small parameter, statedependent Riccati equation. PP. 1019. REFERENCES 1. Cloutier J.R. 1997. Statedependent Riccati equation techniques: an overview. Proceedings of American Control Conference. 2: 932936. 2. Çimen T. 2012. Survey of statedependent Riccati equation in nonlinear optimal feedback control synthesis. Journal of Guidance, Control, and Dynamics. 35(4): 10251047. 3. Afanas'ev V.N. 2011. Control of nonlinear plants with statedependent coefficients. Automation and Remote Control. 72: 713726. 4. Chang I. and Bentsman J. 2013. Constrained discretetime statedependent Riccati equation technique: A model predictive control approach. Proceedings of 52nd IEEE Conference on Decision and Control. Florence, Italy. 51255130. 5. Dmitriev M.G. and Makarov D.A. 2014. Smooth nonlinear controller in a weakly nonlinear control system with statedependent coefficients. Proceedings of the Institute for System Analysis of RAS. 64(4): 5358. 6. Dmitriev M.G. and Makarov D.A. 2016. The near optimality of the stabilizing control in a weakly nonlinear system with statedependent coefficients. Proceedings of AIP Conference. Kazakhstan, Almaty. 20016(2016): 0200161 – 0200166. DOI: 10.1063/1.4959630. 7. Heydari A. and Balakrishnan S.N. 2013. Path Planning Using a Novel Finite Horizon Suboptimal Controller. Journal of guidance, control, and dynamics. 36(4): 12101214. 8. Heydari A. and Balakrishnan S.N. 2015. ClosedForm Solution to FiniteHorizon Suboptimal Control of Nonlinear Systems // International Journal of Robust and Nonlinear Control. Vol. 25. №.15. Pp. 26872704. 9. Khamis A. and Naidu D. 2013. Nonlinear optimal tracking using finite horizon state dependent Riccati equation (SDRE). Proceedings of the 4th International Conference on Circuits, Systems, Control, Signals (WSEAS). 3742. 10. Khamis A., Naidu D.S. and Kamel A.M. 2014. Nonlinear FiniteHorizon Regulation and Tracking for Systems with Incomplete State Information Using Differential State Dependent Riccati Equation. International Journal of Aerospace Engineering. 2014 (2014). Available at: http://dx.doi.org/10.1155/2014/178628. 11. Khamis A., Naidu D.S. and Kamel A.M. 2014. Nonlinear Optimal Tracking For Missile Gimbaled Seeker Using FiniteHorizon State Dependent Riccati Equation. Int. Journal Of Electronics And Telecommunications. 60(2): 165–171. 12. Khamis A., Chen C. H. and Naidu D. S. 2016. Tracking of a robotic hand via SDDRE and SDDVE strategies. UKACC. Proceedings of 11th International Conference on. IEEE. 16. 13. Chernousko F.L. and Kolmanovskij V.B. 1977. Computational and approximate methods of optimal control. Journal of Soviet Mathematics. 14: 101166. 14. Dmitriev M.G. and Kurina G.A. 2006. Singular perturbations in control problems. Automation and Remote Control. 67(1): 1–43. 15. Methods of classical and modern theory of automatic control: A textbook in 5 volumes; 2nd ed., revised and enlarged. Volume 4. Theory of optimization of automatic control systems, edited by K.A. Pupkov and N.D. Egupov. 2004. Moscow: Publishing house MSTU. Bauman. 744p. 16. Kvakernaak H. and Sivan R. 1977. Linear optimal control systems. Moscow: Mir. 650 p. 17. The control handbook / edited by Levine W. S. 1996. CRC press. ISBN 9780849385704. 18. Danik Yu.E., Dmitriev M.G. and Makarov D.A. 2015. An algorithm for constructing regulators for nonlinear systems with the formal small parameter. Information technology and computer systems. 4:3544. 19. Danik Yu.E. 2016. LMIbased robustness analysis of the nonlinear regulator for discrete time nonlinear systems. Fullpapers EBook 6th. world Congress on Electrical Engineering, Computer Science and Information Technology (WCECIT 2016). Barcelona. 96101. 20. Danik Yu.E. 2016. Robustness of weakly nonlinear discrete system with respect to parametric perturbations. Proceedings of the IV AllRussian Scientific Conference of Young Scientists with international participation on Informatics, Control and Systems Analysis, Tver. I: 2738. 21. Makarov D.A. A nonlinear approach to a feedback control design for a tracking statedependent problem. II. The numerical simulations. Information technology and computer systems (accepted by the editors of “Information Technologies And Computer Systems”).
