
D.A. Makarov A nonlinear approach to a feedback control design for a tracking statedependent problem Part II. Numerical simulations 

Abstract. The paper deals with investigation of nonlinear finitehorizon tracking control for weakly nonlinear control systems. That nonlinear tracking control is constructed using a differential matrix statedependent Riccati equation. The obtained results of numerical simulations are compared with the results along the corresponding linear controls. Keywords: tracking problem, nonlinear control, statedependent Riccati equation, numerical simulation. PP. 2023. REFERENCES 1. Çimen T. 2012. Survey of statedependent Riccati equation in nonlinear optimal feedback control synthesis. Journal of Guidance, Control, and Dynamics. 35(4): 10251047. 2. Cloutier J.R. 1997. StateDependent Riccati Equation Techniques: An Overview. Proc. American Control Conference. 2: 932936. 3. Heydari A. and Balakrishnan S.N. Path Planning Using a Novel Finite Horizon Suboptimal Controller. 2013. Journal of guidance, control, and dynamics. 36(4): 12101214. 4. Heydari A. and Balakrishnan S.N. 2015. ClosedForm Solution to FiniteHorizon Suboptimal Control of Nonlinear Systems. International Journal of Robust and Nonlinear Control. 25(15): 26872704. 5. 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. 6. Khamis A., Naidu D.S. and Kamel A.M. Nonlinear FiniteHorizon Regulation and Tracking for Systems with Incomplete State Information Using Differential State Dependent Riccati Equation. International Journal of Aerospace Engineering. 2014 (2014): 12 pages. http://dx.doi.org/10.1155/2014/178628 7. Khamis A., Chen C. and Naidu D. S. 2016. Tracking of a robotic hand via SDDRE and SDDVE strategies. The 2016 UKACC International Conference on Control (UKACC Control 2016), Belfast, UK, August 2016. DOI: 10.1109/CONTROL.2016.7737638 8. 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. 9. 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. 10. Dmitriev M.G. and Makarov D.A. 2016. The near optimality of the stabilizing control in a weakly nonlinear system with statedependent coefficients. AIP Conference Proceedings. Kazakhstan, Almaty, Sep. 710. 1759. 020013 (2016). 11. Makarov D.A. 2017. A nonlinear approach to a feedback control design for a tracking statedependent problem. I. An algorithm. Information technology and computer systems. (accepted by the editors of “Information Technologies And Computer Systems”). 12. 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. 13. Kvakernaak H. and Sivan R. 1977. Linear optimal control systems. Moscow: Mir. 650 p. 14. http://www.asctec.de/uavapplications/research/products/asctechummingbird/ 15. Schoellig A.P., Mueller F.L. and D’Andrea R. 2012. Optimizationbased iterative learning for precise quadrocopter trajectory tracking. Autonomous Robots. 33(1): 103127.
