This paper presents a fast way of implementing nonlinear model predictive control (NMPC) using the random shooting approach. Instead of calculating the optimal control sequence by solving the NMPC problem as a nonlinear programming (NLP) problem, which is time consuming, a sub-optimal, but feasible, sequence of control inputs is determined randomly. To minimize the induced sub-optimality, numerous random control sequences are selected and the one that yields the smallest cost is selected. By means of a motivating case study we demonstrate that the random shooting-based approach is superior, from a computational point of view, to state-of-the-art NLP solvers, and features a low level of sub-optimality. The case study involves a continuous stirred tank reactor where a fast multi-component chemical reaction takes place.
Allgöwer F, Zheng A (2012) Nonlinear model predictive control. Vol. 26. Birkhäuser.
Bakošová M, Oravec J, Matejičková K (2013) Model Predictive Control-Based Robust Stabilization of a Chemical Reactor. Chemical Papers, vol. 67, no. 9, pp. 1146–1156.
Bakošová M, Oravec J (2014) Robust MPC of an Unstable Chemical Reactor Using the Nominal System Optimization. Acta Chimica Slovaca, vol. 7, no. 2, pp. 87–93.
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge university press.
Čižniar M, Podmajerský M, Hirmajer T, Fikar M, Latifi MA (2009) Global optimization for parameter estimation of differential-algebraic systems. Chemical Papers, vol. 63, no. 3, pp. 274–283.
Dyer M, Kannan R, Stougie L (2014) A simple randomised algorithm for convex optimisation. Mathematical Programming, vol. 147, no. 1–2, pp. 207–229.
Fissore D (2008) Robust control in presence of parametric uncertainties: observer-based feedback controller design. Chemical Engineering Science, vol. 63, no. 7, pp. 1890–1900.
Kirkpatrick S, Gelatt C, Vecchi M (1983) Optimization by simulated annealing. Science, vol. 220, no. 4598, pp. 671–680.
Maciejowski J (2002) Predictive control: with constraints. Pearson education.
Martin P, Odloak D, Kassab F (2013) Robust model predictive control of a pilot plant distillation column. Control Engineering Practice, vol. 21, no. 3, pp. 231–241.
Oravec J, Bakošová M, Mészáros A, Míková N (2016) Experimental Investigation of Alternative Robust Model Predictive Control of a Heat Exchanger. Applied Thermal Engineering, vol. 105, pp. 774–782.
Oravec J, Bakošová M, Trafczynski M, Vasičkaninová A, Mészáros A, Markowski M (2018) Robust model predictive control and PID control of shell-and-tube heat exchangers. Energy, vol. 159, pp. 1–10.
Oravec J, Bakošová M (2012) Robust Constrained MPC Stabilization of a CSTR. Acta Chimica Slovaca, vol. 5, no. 2, pp. 153–158.
Oravec J, Bakošová M (2015) Robust Model-Based Predictive Control of Exothermic Chemical Reactor. Chemical Papers, vol. 69, no. 7.
Piovesan J, Tanner H (2009) Randomized model predictive control for robot navigation. In: IEEE International Conference on Robotics and Automation, pp. 94–99.
Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm intelligence, vol. 1, no. 1, pp. 33–57.
Qin S, Badgwell T (2003) A survey of industrial model predictive control technology. Control engineering practice, vol. 11, no. 7, pp. 733–764.
Sahoo S, Lampert C, Martius G (2018) Learning Equations for Extrapolation and Control. arXiv preprint arXiv:1806.07259.
Suard R, Lofberg J, Grieder P, Kvasnica M, Morari M (2004) Efficient computation of controller partitions in multi-parametric programming. In: Decision and Control, 2004. CDC. 43rd IEEE Conference on. Vol. 4, Citeseer, pp. 3643–3648.
Tempo R, Calafiore G, Dabbene F (2012) Randomized algorithms for analysis and control of uncertain systems: with applications. Springer Science &Business Media.
Vidyasagar M (2001) Randomized algorithms for robust controller synthesis using statistical learning theory. Automatica, vol. 37, no. 10, pp. 1515–1528.