Abstract.

The paper deals with investigation of nonlinear finite-horizon tracking control for weakly nonlinear control systems. That nonlinear tracking control is constructed using a differential matrix state-dependent Riccati equation. The obtained results of numerical simulations are compared with the results along the corresponding linear controls.

Keywords:

tracking problem, nonlinear control, state-dependent Riccati equation, numerical simulation.

PP. 20-23.

REFERENCES

1. 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.
2. Cloutier J.R. 1997. State-Dependent Riccati Equation Techniques: An Overview. Proc. American Control Conference. 2: 932-936.
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): 1210-1214.
4. 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. 25(15): 2687-2704.
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). 37-42.
6. Khamis A., Naidu D.S. and Kamel A.M. 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): 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 SD-DRE and SD-DVE 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 state-dependent coefficients. Proceedings of the Institute for System Analysis of RAS. 64(4): 53-58.
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: 35-44.
10. Dmitriev M.G. and Makarov D.A. 2016. The near optimality of the stabilizing control in a weakly nonlinear system with state-dependent coefficients. AIP Conference Proceedings. Kazakhstan, Almaty, Sep. 7-10. 1759. 020013 (2016).
11. Makarov D.A. 2017. A nonlinear approach to a feedback control design for a tracking state-dependent 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; 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.
13. Kvakernaak H. and Sivan R. 1977. Linear optimal control systems. Moscow: Mir. 650 p.
14. http://www.asctec.de/uav-applications/research/products/asctec-hummingbird/
15. Schoellig A.P., Mueller F.L. and D’Andrea R. 2012. Optimization-based iterative learning for precise quadrocopter trajectory tracking. Autonomous Robots. 33(1): 103-127.