On the stability of constrained MPC without terminal constraint

Limón, Daniel; Álamo, T.; Salas, Francisco; Camacho, Eduardo F.

doi:10.1109/tac.2006.875014

Cited by 183 publications

(141 citation statements)

References 7 publications

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“…The discrete-time case was investigated in Limon et al (2006). The following two lemmas generalize these results to continuous-time systems as considered in this chapter.…”

Section: Appendix a -Reachability Of Clf Region (Theorem 1)mentioning

confidence: 78%

“…The sublevel set Γ α defines the domain of attraction for the MPC scheme without terminal constraints Limon et al, 2006). The proof of this statement is given in Appendix A.…”

Section: The Optimal Cost Satisfiesmentioning

confidence: 98%

“…An MPC formulation without terminal constraints has been subject of research by several authors, see for instance ; Ito & Kunisch (2002); Jadbabaie et al (2001); Limon et al (2006); Parisini & Zoppoli (1995). Instead of imposing a terminal constraint, it is often assumed that the terminal cost V represents a (local) Control Lyapunov Function (CLF) on an invariant set S β containing the origin.…”

Section: Domain Of Attraction and Stabilitymentioning

confidence: 99%

See 2 more Smart Citations

A Real-Time Gradient Method for Nonlinear Model Predictive Control

Graichen¹,

Käpernick²

2012

Frontiers of Model Predictive Control

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“…The discrete-time case was investigated in Limon et al (2006). The following two lemmas generalize these results to continuous-time systems as considered in this chapter.…”

Section: Appendix a -Reachability Of Clf Region (Theorem 1)mentioning

confidence: 78%

“…The sublevel set Γ α defines the domain of attraction for the MPC scheme without terminal constraints Limon et al, 2006). The proof of this statement is given in Appendix A.…”

Section: The Optimal Cost Satisfiesmentioning

confidence: 98%

Section: Domain Of Attraction and Stabilitymentioning

confidence: 99%

See 1 more Smart Citation

A Real-Time Gradient Method for Nonlinear Model Predictive Control

Graichen¹,

Käpernick²

2012

Frontiers of Model Predictive Control

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“…Moreover, the implementation of the terminal constraint can increase the computational burden of the optimization problem, possibly demanding longer computational times for a given tolerance than the sampling period (Allgöwer et al, 2004). Limon et al (2006) showed that weighting the terminal cost enlarges the domain of attraction of the MPC, proving also that, for any state of the system that can reach , there is a weight so that the state will go inside the attraction region of the controller.…”

Section: Formulation and Different Approaches For The Resolution Of Tmentioning

confidence: 95%

A Comparison of Performance and Implementation Characteristics of NMPC Formulations

Gonçalves¹,

Alvaristo²,

Silva³

et al. 2015

Anais Do XX Congresso Brasileiro De Engenharia Química

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-Three nonlinear model predictive control (NMPC) strategies are compared on the control of the isothermal CSTR (continuous stirred tank reactor) with van der Vusse kinetics, which is largely employed in control studies. This reactor exhibits sign change of the process static gain and nonminimum phase dynamic behavior. The first strategy considers a NMPC coupled with a state estimator. The second one uses neural networks as the internal NMPC multivariable model. In the last one, a proposed approach for the adaptation of the linear MPC (model predictive control) to nonlinear systems is employed in order to generate predictions through successive local linearizations around steady states. The results show that the NMPC with state estimation stabilized the system at the expense of higher computational cost. The strategy based on neural networks demanded a shorter time for the calculation of the control actions, allowing the use of a shorter sampling time. The adaptive MPC stabilizes the nonlinear system around points which are unstable under linear MPC control, demanding less computational effort than the NMPC with a state estimator.

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“…Receding horizon formulations in model predictive control often use terminal set or equality constraints to achieve stability. In the case of a free end point formulation as it is the case in (12), stability can be shown, e. g., if the terminal cost function ||Δθ(t i,f )|| 2 P represents a (local) control Lyapunov function [1,11,8] or if the horizon length t f is sufficiently large [5]. For the error dynamics (12b), which is time-dependent due to the feedforward trajectories, the rigorous proof of stability [3] as well as the consistency of this finite-dimensional control with the original infinite-dimensional system is subject of current research.…”

Section: δU Fb (T) = δū(T; δθmentioning

confidence: 99%

Combined Feedforward/Model Predictive Tracking Control Design for Nonlinear Diffusion-Convection-Reaction-Systems

Utz

Graichen

Kugi

2013

IFIP Advances in Information and Communication Technology

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Abstract. The tracking control design for setpoint transitions of a quasi-linear diffusion-convection-reaction system with boundary control is considered. For this a suitable model-based feedforward control is determined that relies on the flatness-based parametrization of the control input. A receding horizon feedback control is added within a two-degreesof-freedom control scheme to account for disturbances, model inaccuracies, and input constraints. The tracking performance of this control scheme is shown by means of simulation studies.A large class of chemical reactors with an interaction of diffusive, convective, and reactive effects leads to infinite-dimensional mathematical models in the form of nonlinear boundary-controlled parabolic partial differential equations (PDEs) [6]. The control design for setpoint transitions of chemical reactors, e. g., for ignition, extinction, or grade-transitions constitutes a challenging problem. In this contribution, the well-known two-degrees-of-freedom (2DOF) control scheme is applied in order to tackle this control task. The basic idea consists in first designing a feedforward control to steer the system along prescribed trajectories. The trajectory planning and feedforward control are complemented with a state feedback tracking control stabilizing the system about the desired trajectories.In the literature, there exists a variety of concepts for the design of both feedforward and feedback tracking controllers. For the feedforward control design, approaches using the flatness concept [2] have found widespread attention. The flatness property allows for a parametrization of the state and input in terms of a so-called flat output and its time derivatives and therefore provides a systematic approach for feedforward control design. Originally proposed for finitedimensional systems, generalizations of the flatness concept have been successfully carried over to certain classes of PDEs, see, e. g., [7,10,12]. In these so-called late lumping approaches the parametrization is directly solved for the underlying PDE. In contrast, the early lumping approach to control design is based on a

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On the stability of constrained MPC without terminal constraint

Cited by 183 publications

References 7 publications

A Real-Time Gradient Method for Nonlinear Model Predictive Control

A Real-Time Gradient Method for Nonlinear Model Predictive Control

A Comparison of Performance and Implementation Characteristics of NMPC Formulations

Combined Feedforward/Model Predictive Tracking Control Design for Nonlinear Diffusion-Convection-Reaction-Systems

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