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


The paper deals with a nonlinear finite-horizon tracking control design for a plant with an additive linear part and state-dependent 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.


tracking problem, nonlinear control, small parameter, state-dependent Riccati equation.

PP. 10-19.


1. Cloutier J.R. 1997. State-dependent Riccati equation techniques: an overview. Proceedings of American Control Conference. 2: 932-936.
2. 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.
3. Afanas'ev V.N. 2011. Control of nonlinear plants with state-dependent coefficients. Automation and Remote Control. 72: 713-726.
4. Chang I. and Bentsman J. 2013. Constrained discrete-time state-dependent Riccati equation technique: A model predictive control approach. Proceedings of 52nd IEEE Conference on Decision and Control. Florence, Italy. 5125-5130.
5. Dmitriev M.G. and Makarov D.A. 2014. Smooth nonlinear controller in a weakly nonlinear control system with state-dependent coefficients. Proceedings of the Institute for System Analysis of RAS. 64(4): 53-58.
6. Dmitriev M.G. and Makarov D.A. 2016. The near optimality of the stabilizing control in a weakly nonlinear system with state-dependent coefficients. Proceedings of AIP Conference. Kazakhstan, Almaty. 20016(2016): 020016-1 – 020016-6. 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): 1210-1214.
8. Heydari A. and Balakrishnan S.N. 2015. Closed-Form Solution to Finite-Horizon Suboptimal Control of Nonlinear Systems // International Journal of Robust and Nonlinear Control. Vol. 25. №.15. Pp. 2687-2704.
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). 37-42.
10. Khamis A., Naidu D.S. and Kamel A.M. 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). Available at:
11. Khamis A., Naidu D.S. and Kamel A.M. 2014. Nonlinear Optimal Tracking For Missile Gimbaled Seeker Using Finite-Horizon 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 SD-DRE and SD-DVE strategies. UKACC. Proceedings of 11th International Conference on. IEEE. 1-6.
13. Chernousko F.L. and Kolmanovskij V.B. 1977. Computational and approximate methods of optimal control. Journal of Soviet Mathematics. 14: 101-166.
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; 2-nd 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. 4:35-44.
19. Danik Yu.E. 2016. LMI-based robustness analysis of the nonlinear regulator for discrete time nonlinear systems. Fullpapers E-Book 6th. world Congress on Electrical Engineering, Computer Science and Information Technology (WCECIT 2016). Barcelona. 96-101.
20. Danik Yu.E. 2016. Robustness of weakly nonlinear discrete system with respect to parametric perturbations. Proceedings of the IV All-Russian Scientific Conference of Young Scientists with international participation on Informatics, Control and Systems Analysis, Tver. I: 27-38.
21. Makarov D.A. A nonlinear approach to a feedback control design for a tracking state-dependent problem. II. The numerical simulations. Information technology and computer systems (accepted by the editors of “Information Technologies And Computer Systems”).

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