Uncertainty quantification of model predictive control for nonlinear systems with parametric uncertainty using hybrid pseudo-spectral method

References

• Annunziato, M., & Borzì, A. (2013). A Fokker–Planck control framework for multidimensional stochastic processes. Journal of Computational and Applied Mathematics, 237, 487–18. doi:10.1016/j.cam.2012.06.019
   Web of Science ®Google Scholar
• Bavdekar, V. A., & Mesbah, A. (2016). Stochastic nonlinear model predictive control with joint chance constraints. IFAC-PapersOnLine, 49, 270–275. doi:10.1016/j.ifacol.2016.10.176
   Google Scholar
• Becerra, V. M. (2010). Solving complex optimal control problems at no cost with PSOPT. In Computer-Aided Control System Design (CACSD), Yokohama, Japan, 2010 IEEE International Symposium on (pp. 1391–1396.
   Google Scholar
• Cameron, R. H., & Martin, W. T. (1947). The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals. Annals of Mathematics, 385–392. doi:10.2307/1969178
   Web of Science ®Google Scholar
• Fornberg, B. (1998). A practical guide to pseudospectral methods (Vol. 1). Cambridge: Cambridge university press.
   Google Scholar
• Garcia, C. E., Prett, D. M., & Morari, M. (1989). Model predictive control: Theory and practice—A survey. Automatica, 25, 335–348. doi:10.1016/0005-1098(89)90002-2
   Web of Science ®Google Scholar
• Gong, Q., Kang, W., Bedrossian, N. S., Fahroo, F., Sekhavat, P., & Bollino, K. (2007). Pseudospectral optimal control for military and industrial applications. In Decision and Control, New Orleans, LA, USA, 2007 46th IEEE Conference on (pp. 4128–4142.
   Google Scholar
• Gong, Q., Ross, I. M., Kang, W., & Fahroo, F. (2008). Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control. Computational Optimization and Applications, 41, 307–335. doi:10.1007/s10589-007-9102-4
   Web of Science ®Google Scholar
• Grüne, L., & Pannek, J. (2011). Nonlinear model predictive control (pp. 43–66). London: Springer. ed.
   Google Scholar
• Harmon, F. G. (2017). Hybrid solution of nonlinear stochastic optimal control problems using Legendre Pseudospectral and generalized polynomial chaos algorithms. American Control Conference (ACC), 2017, 2642–2647.
   Google Scholar
• Mahmood, M., & Mhaskar, P. (2012). Lyapunov-based model predictive control of stochastic nonlinear systems. Automatica, 48, 2271–2276. doi:10.1016/j.automatica.2012.06.033
   Web of Science ®Google Scholar
• Matsuno, Y., Tsuchiya, T., & Matayoshi, N. (2015). Near-optimal control for aircraft conflict resolution in the presence of uncertainty. Journal of Guidance, Control, and Dynamics, 39, 326–338. doi:10.2514/1.G001227
   Web of Science ®Google Scholar
• Matsuno, Y., Tsuchiya, T., Wei, J., Hwang, I., & Matayoshi, N. (2015). Stochastic optimal control for aircraft conflict resolution under wind uncertainty. Aerospace Science and Technology, 43, 77–88. doi:10.1016/j.ast.2015.02.018
   Web of Science ®Google Scholar
• Mayne, D. Q., Kerrigan, E. C., Van Wyk, E., & Falugi, P. (2011). Tube‐based robust nonlinear model predictive control. International Journal of Robust and Nonlinear Control, 21, 1341–1353. doi:10.1002/rnc.v21.11
   Web of Science ®Google Scholar
• Mayne, D. Q., Rawlings, J. B., Rao, C. V., & Scokaert, P. O. (2000). Constrained model predictive control: Stability and optimality. Automatica, 36, 789–814. doi:10.1016/S0005-1098(99)00214-9
   Web of Science ®Google Scholar
• Muske, K. R., & Rawlings, J. B. (1993). Model predictive control with linear models. AIChE Journal, 39, 262–287. doi:10.1002/(ISSN)1547-5905
   Web of Science ®Google Scholar
• Namadchian, A., & Ramezani, M. (2017). Pseudo-spectral model predictive control of continuous stirred-tank reactor. Majlesi Journal of Mechatronic Systems, 6, 23–28.
   Google Scholar
• Patterson, M. A., & Rao, A. V. (2014). GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Transactions on Mathematical Software (TOMS), 41, 1. doi:10.1145/2684421
   Web of Science ®Google Scholar
• Rawlings, J., & Mayne, D. (2012). Postface to model predictive control: Theory and design. Nob Hill Pub, 5, 155–158.
   Google Scholar
• Ross, I. M. (2005). A historical introduction to the convector mapping principle. Proceedings of Astrodynamics Specialists Conference. Naval Postgraduate School (U.S.)
   Google Scholar
• Schwickart, T., Voos, H., Hadji‐Minaglou, J. R., & Darouach, M. (2016). A fast model‐predictive speed controller for minimised charge consumption of electric vehicles. Asian Journal of Control, 18, 133–149. doi:10.1002/asjc.1251
   Web of Science ®Google Scholar
• Visintini, A. L., Glover, W., Lygeros, J., & Maciejowski, J. (2006). Monte Carlo optimization for conflict resolution in air traffic control. IEEE Transactions on Intelligent Transportation Systems, 7, 470–482. doi:10.1109/TITS.2006.883108
   Web of Science ®Google Scholar
• Von Stryk, O., & Bulirsch, R. (1992). Direct and indirect methods for trajectory optimization. Annals of Operations Research, 37, 357–373. doi:10.1007/BF02071065
   Google Scholar
• Widd, A., Liao, H. H., Gerdes, J. C., Tunestål, P., & Johansson, R. (2014). Hybrid model predictive control of exhaust recompression HCCI. Asian Journal of Control, 16, 370–381.
   Web of Science ®Google Scholar
• Wiener, N. (1938). The homogeneous chaos. American Journal of Mathematics, 60, 897–936. doi:10.2307/2371268
   Web of Science ®Google Scholar
• Xiu, D., & Karniadakis, G. E. (2002). The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing, 24, 619–644. doi:10.1137/S1064827501387826
   Web of Science ®Google Scholar