Abstract
A significantly important part of model predictive control (MPC) with constraints are algorithms of numerical optimization. Reduction of the computational complexity of the optimization methods has been widely researched. The reason is that in certain cases of predictive control of fast dynamics processes an optimization algorithm may not be feasible within the sampling period time. This situation occurs particularly when requirements on control are more complex, e.g. in the multivariable control. Hildreth’s method based on the dual-problem-optimization-principles has been widely applied and implemented in model predictive control. However, modifications of this method are not widely described in context of model predictive control. This paper proposes a modification of Hildreth’s method, which reduces the computational complexity of the algorithm, and its application in the multivariable predictive control.
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
Kwon, W.H.: Receding Horizon Control: Model Predictive Control for State Models. Springer, Heidelberg (2005). ISBN 1-84628-024-9
Corriou, J.P.: Process Control: Theory and Applications. Springer, London (2004). ISBN 1-85233-776-1
Kubalcik, M., Bobal, V., Barot, T.: Predictive control of two-input two-output system with non-minimum phase. In: 31st European Conference on Modelling and Simulation, pp. 342–347. European Council for Modelling and Simulation (2017). ISBN 978-0-9932440-4-9
Lee, G.M., Tam, N.N., Yen, N.D.: Quadratic Programming and Affine Variational Inequalities: A Qualitative Study. Springer, Boston (2005). ISBN 0-387-24277-5
Dostal, Z.: Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities. Springer, Boston (2009). ISBN 978-0387848051
Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming. Springer, Boston (2008). ISBN 978-0-387-74502-2
Hunger, R.: Floating point operations in matrix-vector calculus (Version 1.3). Technical report. Technische Universität München, Associate Institute for Signal Processing (2007). https://mediatum.ub.tum.de/doc/625604/625604.pdf
Hertog, D.: Interior Point Approach to Linear, Quadratic, and Convex Programming: Algorithms and Complexity. Kluwer Academic Publishers, Dordrecht (1994)
Rao, S.S.: Engineering Optimization: Theory and Practice. Kluwer Academic Publishers, Hoboken (2009). ISBN 978-0-470-18352-6
Wang, L.: Model Predictive Control System Design and Implementation Using MATLAB. Springer, London (2009). ISBN 978-1-84882-330-3
Ingole, D., Holaza, J., Takacs, B., Kvasnica, M.: FPGA-based explicit model predictive control for closed loop control of intravenous anesthesia. In: 20th International Conference on Process Control (PC), pp. 42–47. IEEE (2015). ISBN 978-1-4673-6627-4
Krivy, I., Tvrdik, J., Krpec, R.: Stochastic algorithms in nonlinear regression. Comput. Stat. Data Anal. 33(12), 277–290 (2000)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Kubalcik, M., Bobal, V., Barot, T. (2019). Modified Hildreth’s Method Applied in Multivariable Model Predictive Control. In: Machado, J., Soares, F., Veiga, G. (eds) Innovation, Engineering and Entrepreneurship. HELIX 2018. Lecture Notes in Electrical Engineering, vol 505. Springer, Cham. https://doi.org/10.1007/978-3-319-91334-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-91334-6_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91333-9
Online ISBN: 978-3-319-91334-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)