×

zbMATH — the first resource for mathematics

The advanced-step NMPC controller: Optimality, stability and robustness. (English) Zbl 1154.93364
Summary: Widespread application of dynamic optimization with fast optimization solvers leads to increased consideration of first-principles models for Nonlinear Model Predictive Control (NMPC). However, significant barriers to this optimization-based control strategy are feedback delays and consequent loss of performance and stability due to on-line computation. To overcome these barriers, recently proposed NMPC controllers based on NonLinear Programming (NLP) sensitivity have reduced on-line computational costs and can lead to significantly improved performance. In this study, we extend this concept through a simple reformulation of the NMPC problem and propose the advanced-step NMPC controller. The main result of this extension is that the proposed controller enjoys the same nominal stability properties of the conventional NMPC controller without computational delay. In addition, we establish further robustness properties in a straightforward manner through input-to-state stability concepts. A case study example is presented to demonstrate the concepts.

MSC:
93B52 Feedback control
93B35 Sensitivity (robustness)
93B40 Computational methods in systems theory (MSC2010)
93A15 Large-scale systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Allgöwer, F.; Badgwell, T.A.; Qin, J.S.; Rawlings, J.B.; Wright, S.J., Nonlinear predictive control and moving horizon estimation: an introductory overview, (), 391-449
[2] Bartusiak, R.D., NLMPC: A platform for optimal control of feed- or product-flexible manufacturing, (), 282-367 · Zbl 1223.93036
[3] Bemporad, A.; Morari, M.; Dua, V.; Pistikopoulos, E.N., The explicit linear quadratic regulator for constrained systems, Automatica, 38, 1, 3-20, (2002) · Zbl 0999.93018
[4] Biegler, L.T., Efficient solution of dynamic optimization and NMPC problems, (), 219-244 · Zbl 0966.93048
[5] Bryson, A.E.; Ho, Y.C., Applied optimal control, (1975), Taylor & Francis
[6] Büskens, C.; Maurer, H., Sensitivity analysis and real-time optimization of parametric nonlinear programming problems, (), 3-16 · Zbl 0989.90122
[7] Büskens, C.; Maurer, H., Sensitivity analysis and real-time control of parametric control problems using nonlinear programming methods, (), 57-68 · Zbl 0992.49021
[8] Chen, W.; Balance, D.J.; O’Reilly, J., Model predictive control of nonlinear systems: computational burden and stability, IEEE Proceedings of control theory and applications, 147, 4, 387-394, (2000)
[9] De Oliveira, N.M.C.; Biegler, L.T., An extension of Newton-type algorithms for nonlinear process control, Automatica, 31, 2, 281-286, (1995) · Zbl 0825.93181
[10] Dennis, J.E.; Schnabel, R.B., Numerical methods for unconstrained optimization and nonlinear equations, (1996), SIAM Philadelphia · Zbl 0847.65038
[11] DeHaan, D.; Guay, M., A new real-time perspective on nonlinear model predictive control, Journal of process control, 16, 6, 615-624, (2006)
[12] de Nicolao, G.; Magni, L.; Scattolini, R., Stability and robustness of nonlinear receding horizon control, (), 3-22 · Zbl 0958.93512
[13] Diehl, M.; Bock, H.G.; Schlöder, J.P., A real-time iteration scheme for nonlinear optimization in optimal feedback control, SIAM journal on control and optimization, 43, 5, 1714-1736, (2005) · Zbl 1078.65060
[14] Diehl, M.; Findeisen, R.; Bock, H.G.; Schlöder, J.P.; Allgöwer, F., Nominal stability of the real-time iteration scheme for nonlinear model predictive control, IEEE control theory and applications, 152, 3, 296-308, (2005)
[15] Fiacco, A.V., Introduction to sensitivity and stability analysis in nonlinear programming, (1983), Academic Press New York · Zbl 0543.90075
[16] Fiacco, A.V., Sensitivity analysis for nonlinear programming using penalty methods, Mathematical programming, 10, 1, 287-311, (1976) · Zbl 0357.90064
[17] Findeisen, R., & Allgöwer, F. (2004). Computational delay in nonlinear model predictive control. In Proc. int. symp. adv. control of chemical processes
[18] Franke, R.; Doppelhamer, J., Integration of advanced model-based control with industrial IT, (), 399-406
[19] Grancharova, A.; Johansen, T.A.; Tondel, P., Computational aspects of approximate explicit nonlinear model predictive control, (), 181-192 · Zbl 1223.93030
[20] Hicks, G.A.; Ray, W.H., Approximation methods for optimal control synthesis, Canadian journal of chemical engineering, 49, 522-529, (1971)
[21] Jiang, Z.-P.; Wang, Y., Input-to-state stability for discrete-time nonlinear systems, Automatica, 37, 6, 857-869, (2001) · Zbl 0989.93082
[22] Keerthi, S.S.; Gilbert, E.G., Optimal infinite-horizon feedback laws for general class of constrained discrete-time systems: stability and moving-horizon approximations, IEEE transactions on automatic control, 57, 2, 265-293, (1988) · Zbl 0622.93044
[23] Kadam, J., & Marquardt, W. (2004). Sensitivity-based solution updates in closed-loop dynamic optimization. In Proceedings of 7th international symposium on dynamics and control of process systems
[24] Li, W.C.; Biegler, L.T., Process control strategies for constrained nonlinear systems, Industrial & engineering chemistry research, 27, 8, 1421-1433, (1988)
[25] Magni, L.; Scattolini, R., Robustness and robust design of MPC for nonlinear systems, (), 239-254 · Zbl 1223.93045
[26] Mayne, D.Q., Nonlinear model predictive control: challenges and opportunities, (), 23-44 · Zbl 0958.93511
[27] Nagy, Z.K.; Franke, R.; Mahn, B.; Allgöwer, F., Real-time implementation of nonlinear model predictive control of batch processes in an industrial framework, (), 465-472 · Zbl 1223.93046
[28] Nocedal, J.; Wright, S.J., Numerical optimization, (1999), Springer-Verlag New York · Zbl 0930.65067
[29] Ohtsuka, T., A continuation/GMRES method for fast computation of nonlinear receding horizon control, IEEE transactions on automatic control, 44, 3, 648-654, (1999)
[30] Pesch, H., Real-time computation of feedback controls for constrained optimal control problems. part 2: A correction method based on multiple shooting, Optimal control applications & methods, 10, 2, 147-171, (1989) · Zbl 0675.49024
[31] Santos, L.O.; Afonso, P.; Castro, J.; Oliveira, N.; Biegler, L.T., On-line implementation of nonlinear MPC: an experimental case study, Control engineering practice, 9, 8, 847-857, (2001)
[32] Santos, L.O.; Biegler, L.T., A tool to analyze robust stability for model predictive controllers, Journal of process control, 9, 1, 233-246, (1999)
[33] Santos, L.; Castro, J.A.; Biegler, L.T., A tool to analyze robust stability for constrained MPC, Journal of process control, 18, 383-390, (2008)
[34] Zavala, V.M.; Laird, C.D.; Biegler, L.T., Fast implementations and rigorous models: can both be accommodated in NMPC?, International journal of robust nonlinear control, 18, 8, 800-815, (2008) · Zbl 1284.93105
[35] Zavala, V.M.; Laird, C.D.; Biegler, L.T., A fast computational framework for large-scale moving horizon estimation, Journal of process control, 18, 9, 876-884, (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.