Abstract
The traditional “Receding Horizon Controller (RHC)” is a heuristic approach based on the concept of “Nonlinear Programming (NP)” that in the most general cases applies Lagrange’s “Reduced Gradient (RG)” method. Since its realization requires a huge amount of numerical calculations, in the practice it is often restricted to quadratic cost functions and “Linear Time Invariant (LTI)” approximation of the dynamic model of the controlled system as “Linear Quadratic Regulator (LQR)”. To release these restrictions a novel approach was recently invented that directly drives the gradient of the “auxiliary function” near zero by replacing the RG with a fixed point-based iteration. It was also shown that the same iteration technique allows the introduction of an “Adaptive Receding Horizon Controller (ARHC)”. Since the convergence of the ARHC strongly depends on the structure of the cost contributions in this paper the operation of the classic RG-based RHC is investigated in the control of the “TORA” system that is a popular paradigm for benchmarking purposes. Conclusions are drawn for the allowable or recommended parameter settings for the cost contributions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Richalet, J., Rault, A., Testud, J., Papon, J.: Model predictive heuristic control: applications to industrial processes. Automatica 14(5), 413–428 (1978)
Clarke, D., Mohtadi, C., Tuffs, P.: Generalized predictive control - I. The basic algorithm. Automatica 23, 137–148 (1987)
Clarke, D., Mohtadi, C., Tuffs, P.: Generalized predictive control - II. Extensions and interpretations. Automatica 23, 149–160 (1987)
Grancharova, A., Johansen, T.: Explicit Nonlinear Model Predictive Control. Springer, Heidelberg (2012)
Bellman, R.: Dynamic programming and a new formalism in the calculus of variations. Proc. Natl. Acad. Sci. 40(4), 231–235 (1954)
Kalman, R.: Contribution to the theory of optimal control. Boletin Sociedad Matematica Mexicana 5(1), 102–119 (1960)
Khan, H., Szeghegyi, A., Tar, J.: Fixed point transformation-based adaptive optimal control using NLP. In: Proceedings of the 2017 IEEE 30th Jubilee Neumann Colloquium, Budapest, Hungary, 24–25 November 2017, pp. 35–40 (2017)
Dineva, A., Tar, J., Várkonyi-Kóczy, A.: Novel generation of Fixed Point Transformation for the adaptive control of a nonlinear neuron model. In: Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, Hong Kong, 10–13 October 2015 (SMC 2015), pp. 987–992 (2015)
Csanádi, B., Tar, J., Bitó, J.: Matrix inversion-free quasi-differential approach in solving the inverse kinematic task. In: Proceedings of the 17th IEEE International Symposium on Computational Intelligence and Informatics (CINTI 2016), Budapest, Hungary, 17–19 November 2016, pp. 61–66 (2016)
Khan, H., Tar, J., Rudas, I., Eigner, G.: Adaptive model predictive control based on fixed point iteration. WSEAS Trans. Syst. Control 12, 347–354 (2017)
van der Pol, B.: Forced oscillations in a circuit with non-linear resistance (reception with reactive triode). Lond. Edinb. Dublin Philos. Mag. J. Sci. 7(3), 65–80 (1927)
Bupp, R., Bernstein, D., Coppola, V.: A benchmark problem for nonlinear control design: problem statement, experiment testbed and passive nonlinear compensation. In: Proceedings of the American Control Conference, Seattle, US, pp. 4363–4376 (1995)
Lagrange, J., Binet, J., Garnier, J.: Mécanique analytique (Binet, J.P.M., Garnier, J.G. (eds.)). Ve Courcier, Paris (1811)
Petres, Z., Varkonyi, P., Baranyi, P., Korondi, P.: Different affine decomposition of the model of the TORA system by TP model transformation. In: Proceedings of the 2005 IEEE International Conference on Intelligent Engineering Systems (INES 2005) (93–98), pp. 363–370 (2005)
Tar, J., Rudas, I., Preitl, S., Precup, R.E.: Adaptive control of the TORA system based on a simple causal filter. In: Proceedings of 16th International Workshop on Robotics in Alpe-Adria-Danube Region, Ljubljana, Slovenia, 07 June 2007, pp. 363–370 (2007)
Acknowledgments
Tamás Faitli has been supported by the “New National Excellence Program of the Ministry of Human Capacities”, application number ÚNKP-17-1-I for the period 01 September 2017–30 June 2018.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Faitli, T., Tar, J.K. (2019). Studying Various Cost Functions by Nonlinear Programming for the Control of an Underactuated Mechanical System. In: Aspragathos, N., Koustoumpardis, P., Moulianitis, V. (eds) Advances in Service and Industrial Robotics. RAAD 2018. Mechanisms and Machine Science, vol 67. Springer, Cham. https://doi.org/10.1007/978-3-030-00232-9_41
Download citation
DOI: https://doi.org/10.1007/978-3-030-00232-9_41
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00231-2
Online ISBN: 978-3-030-00232-9
eBook Packages: EngineeringEngineering (R0)