MPC for Tracking Periodic References

Limón, Daniel; Pereira, M.; Peña, David Muñoz de la; Álamo, T.; Jones, Colin N.; Zeilinger, Melanie N.

doi:10.1109/tac.2015.2461811

Cited by 75 publications

(71 citation statements)

References 16 publications

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“…An online planner is included in the corresponding optimization problem in order to find the open-loop optimal periodic steady states that are subsequently set as the terminal states for economic MPC. This single-layer strategy for periodic operation is used in [25], where economic MPC without terminal constraints is designed for optimal periodic behavior under the dissipativity and controllability conditions. The closed-loop trajectory converges to the optimal periodic orbit.…”

Section: Introductionmentioning

confidence: 99%

Economic model predictive control based on a periodicity constraint

Wang

Salvador

Peña

et al. 2018

Journal of Process Control

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This paper addresses a novel economic model predictive control (MPC) formulation based on a periodicity constraint to achieve an optimal periodic operation for discrete-time linear systems. The proposed control strategy does not rely on forcing the terminal state by means of a terminal equality constraint and hence it does not require a priori knowledge of a periodic steady trajectory. Instead, at each sampling time step the economic cost function is optimized based on a periodicity constraint over all the periodic trajectories that include the current state. The recursive feasibility and the closed-loop convergence to a periodic steady trajectory are discussed. Moreover, an optimality certificate of this steady trajectory is provided based on the Karush-Kuhn-Tucker (KKT) optimality conditions. Finally, an application to a well-known water distribution network benchmark is presented to demonstrate the proposed economic MPC in which the closed-loop simulation results obtained with a linear model and a virtual-reality simulator are both provided.

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Section: Introductionmentioning

confidence: 99%

Economic model predictive control based on a periodicity constraint

Wang

Salvador

Peña

et al. 2018

Journal of Process Control

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“…One challenge includes tracking and output regulation with exogenous signals in order to accommodate online changing operation conditions. For this set of problems, the reference r might not satisfy Assumption 1 (due to sudden changes and unreachable signals), compare [3], [4], [5]. More generally, the minimization of a possibly online changing and non-convex economic cost is a (non-trivial) control problem which is often encountered, compare [6], [7], [8], [9].…”

Section: Conditionsmentioning

confidence: 99%

“…5], then the optimal reachable periodic trajectory is (uniformly) exponentially stable for the resulting closed-loop system. Thus, the terminal ingredients enable us to implement a nonlinear version of the tracking scheme in [3], [4], that ensures exponential stability of the optimal (periodic) operation. More details on the theoretical properties and numerical examples can be found in [18].…”

Section: A Nonlinear Periodic Tracking Mpc Subject To Changing Exogementioning

confidence: 99%

A Nonlinear Model Predictive Control Framework Using Reference Generic Terminal Ingredients

Köhler

Müller

Allgöwer

2020

IEEE Trans. Automat. Contr.

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In this paper, we present a quasi infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi infinite horizon terminal cost. As a result we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. As a corollary, the terminal cost can also be used to design nonlinear MPC schemes that reliably operate under online changing conditions, including unreachable reference signals. The practicality of this approach is demonstrated with a benchmark example.

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“…Considering the T -periodic operations for the management of WDNs, the optimal steady trajectory can be obtained by a finite-horizon open-loop optimization problem with a periodic terminal constraint as follows (Angeli et al, 2012;Limon et al, 2016):…”

Section: Pnempc Plannermentioning

confidence: 99%

Periodic Nonlinear Economic Model Predictive Control with Changing Horizon for Water Distribution Networks

et al. 2017

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A periodic nonlinear economic model predictive control (EMPC) with changing prediction horizon is proposed for the optimal management of water distribution networks (WDNs). The control model of the WDN is built by means of nonlinear differential-algebraic equations in which both the hydraulic pressure and flow variables are taken into account. The model allows the controller to consider minimum pressure constraints at the demands. A periodic terminal constraint is employed in order to guarantee closed-loop stability. The prediction horizon is modified on-line in order to guarantee convergence to the optimal periodic trajectory. The proposed control strategy is verified with the case study of the Richmond water network in a realistic hydraulic simulator. Although there are modeling errors between the control model and hydraulic model, the closed-loop system converges to a sub-optimal periodic trajectory satisfying all the constraints.

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MPC for Tracking Periodic References

Cited by 75 publications

References 16 publications

Economic model predictive control based on a periodicity constraint

Economic model predictive control based on a periodicity constraint

A Nonlinear Model Predictive Control Framework Using Reference Generic Terminal Ingredients

Periodic Nonlinear Economic Model Predictive Control with Changing Horizon for Water Distribution Networks

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