A qLPV Nonlinear Model Predictive Control with Moving Horizon Estimation

Abstract

This paper presents a Model Predictive Control (MPC) algorithm for Nonlinear systems represented through quasi-Linear Parameter Varying (qLPV) embeddings. Input-to-state stability is ensured through parameter-dependent terminal ingredients, computed offline via Linear Matrix Inequalities. The online operation comprises three consecutive Quadratic Programs (QPs) and, thus, is computationally efficient and able to run in real-time for a variety of applications. These QPs stand for the control optimization (MPC) and a Moving-Horizon Estimation (MHE) scheme that predicts the behaviour of the scheduling parameters along the future horizon. The method is practical and simple to implement. Its effectiveness is assessed through a benchmark example (a CSTR system).

Keywords

Nonlinear Model Predictive Control / Quasi-Linear Parameter Varying Systems / Moving Horizon Estimation / Linear Matrix Inequalities / CSTR

References

[1] Camacho EF.Model predictive control.2013;Springer Science & Business Media

[2] Mayne DQ,Rao CV.Constrained model predictive control: Stability and optimality..Automatica,2000;36:789-814

[3] Allgöwer F.Nonlinear model predictive control, volume 26.2012;Birkhäuser

[4] Camacho EF.Nonlinear model predictive control: An introductory review. In Assessment and future directions of nonlinear model predictive control.2007;Springer1-16

[5] Gros S,Quirynen R,Diehl M.From linear to nonlinear MPC: bridging the gap via the real-time iteration..International Journal of Control2020;93:62-80

[6] Quirynen R,Zanon M.Autogenerating microsecond solvers for nonlinear MPC: a tutorial using ACADO integrators..Optimal Control Applications and Methods2015;36:685-704

[7] Englert T,Mesmer F,Graichen K.A software framework for embedded nonlinear model predictive control using a gradient-based augmented lagrangian approach (GRAMPC)..Optimization and Engineering2019;20:769-809

[8] Ohyama S.Parallelized nonlinear model predictive control on GPU. In 11th Asian Control Conference, pages 1620–1625.2017;IEEE

[9] Rathai KMM,Alamir M.GPU-based parameterized nmpc scheme for control of half car vehicle with semi-active suspension system..IEEE Control Systems Letters2019;3:631-6

[10] Hoffmann C.A survey of linear parameter-varying control applications validated by experiments or high- fidelity simulations..IEEE Transactions on Control Systems Technology2014;23:416-33

[11] Morato MM,Sename O.Model predictive control design for linear parameter varying systems: A survey..Annual Reviews in Control2020;49:64-80

[12] Boyd S,Feron E.Linear matrix inequalities in system and control theory, volume 15.1994;Siam

[13] Abbas HS,Petreczky M,Mohammadpour J.Embedding of nonlinear systems in a linear parameter-varying representation..IFAC Proceedings Volumes2014;47:6907-13

[14] Kunz K,Summers TH.Fast model predictive control of miniature helicopters. In 2013 European Control Conference (ECC), pages 1377–1382.2013;IEEE

[15] Cisneros Pablo SG.Wide range stabilization of a pendubot using quasi-LPV predictive control..IFAC-PapersOnLine2019;52:164-9

[16] Alcalá E,Quevedo J.LPV-MPC control for autonomous vehicles..IFAC-PapersOnLine2019;52:106-13

[17] Mate S,Bhartiya S.A stabilizing sub-optimal model predictive control for quasi-linear parameter varying systems..IEEE Control Systems Letters2019;

[18] Morato MM,Sename O.Novel qLPV MPC design with least-squares scheduling prediction..IFAC-PapersOnLine2019;52:158-63

[19] Morato MM,Sename O.Sub-optimal recursively feasible linear parameter-varying predictive algorithm for semi-active suspension control..2020;14:2764-75

[20] Cisneros PSG,Werner H.Efficient nonlinear model predictive control via quasi-LPV representation. In IEEE Conference on Decision and Control2016;IEEE3216-21

[21] Cisneros PG.Fast nonlinear MPC for reference tracking subject to nonlinear constraints via quasi-LPV representations..IFAC-PapersOnLine2017;50:11601-6

[22] Cisneros PS.Nonlinear model predictive control for models in quasi-linear parameter varying form..International Journal of Robust and Nonlinear Control2020;

[23] Jungers M,Oliveira RCLF.Model predictive control for linear parameter varying systems using path-dependent lyapunov functions..IFAC Proceedings Volumes2009;42:97-102

[24] Limon D,Alvarado I,Camacho EF.MPC for tracking of constrained nonlinear systems. In Nonlinear model predictive control2009;Springer315-23

[25] Limon D,Alvarado I.Nonlinear MPC for tracking piece-wise constant reference signals..IEEE Transactions on Automatic Control2018;63:3735-50

[26] Morari M.Nonlinear offset-free model predictive control..Automatica2012;48:2059-67

[27] Köhler J,Allgöwer F.A nonlinear tracking model predictive control scheme for dynamic target signals..Automatica2020;118:109030

[28] Qi L.Superlinearly convergent approximate newton methods for lc¹ optimization problems..Mathematical programming1994;64:277-94

[29] Wei Z,Yao S.The superlinear convergence of a new quasi-newton-sqp method for constrained optimization..Applied mathematics and computation2008;196:791-801

[30] Izmailov AF.On attraction of linearly constrained lagrangian methods and of stabilized and quasi-newton sqp methods to critical multipliers..Mathematical programming2011;126:231-57

[31] Boggs PT,Kearsley AJ.On the convergence of a trust region SQP algorithm for nonlinearly constrained optimization problems. In System Modelling and Optimization1996;Springer3-12

[32] Boggs PT.Sequential quadratic programming for large-scale nonlinear optimization..Journal of computational and applied mathematics2000;124:123-137

[33] Diehl M,Schlöder JP.A real-time iteration scheme for nonlinear optimization in optimal feedback control..SIAM Journal on control and optimization2005;43:1714-36

[34] Houska B,Diehl M.An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range..Automatica2011;47:2279-85

[35] Michalska H.Robust receding horizon control of constrained nonlinear systems..IEEE transactions on automatic control1993;38:1623-33

[36] Duan GR.LMIs in control systems: analysis, design and applications.2013;CRC press

[37] Morato MM,Sename O.Short-sighted robust lpv model predictive control: Application to semi-active suspension systems..In European Control Conference 2021 (ECC21), pages 1–72021;

[38] Wu F.A generalized LPV system analysis and control synthesis framework..International Journal of Control2001;74:745-59

[39] Chen H,Allgöwer F.Nonlinear predictive control of a benchmark CSTR..In Proceedings of 3rd European control conference, pages 3247–32521995;