A Lyapunov Function for Economic Optimizing Model Predictive Control

By Moritz Diehl, R. Amrit, James B. Rawlings. IEEE Transactions on Automatic Control, 2011

542 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/322c0a4857c2b858df2948358a2094ebf38f5c0b

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In Control and Systems Engineering

Citations in the corpus

Approximation Properties of Receding Horizon Optimal Control (2016, background): “In this context it should be noted that the majority of results in this paper apply to what in the MPC community is called Economic MPC [5,6,17,25,32].”
Economic optimization using model predictive control with a terminal cost (2011, background): “Previous work on stability of economic MPC (Diehl et al., 2011; Angeli et al., in press) define the economic objective function as VN;cðx;uÞ :¼ XN 1 k¼0 ‘ðxðkÞ;uðkÞÞ; xþ ¼ f ðx; uÞ; xð0Þ ¼ x ð2Þ in which N is the control horizon, u:={u(0), u(1), . . . ,u(N 1)} is the control sequence, and x is the…”
Safe Reinforcement Learning Using Robust MPC (2019, background): “While the literature on RL does not discuss the properties of the cost function (or rather reward function in RL), the distinction is relevant in relation to the stability properties of the closed-loop system and a thorough discussion on economic MPC can be found in [30], [31], [32].”
Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis (2019, background): “In the control community, studies on the above problem focus on economic model predictive control (EMPC), which is a variant of model predictive control (MPC) with a primary goal on optimizing economic costs [9, 10, 11, 12, 13, 14, 15, 16].”
Economic Model Predictive Control for building climate control in a Smart Grid (2012, background): “Recently Economic MPC has emerged as a general methodology with efficient numerical implementations and provable stability properties [13], [14].”
Using Nonlinear Model Predictive Control for Dynamic Decision Problems in Economics (2015, background): “…the problem (2.3) is numerically infeasible for the needed horizon lengths N , then one can improve the performance by using the infinite horizon optimal steady state x? as terminal constraint when solving (2.3), as proposed in Angeli et al. (2009); Angeli and Rawlings (2010); Diehl et al. (2011).”
On Average Performance and Stability of Economic Model Predictive Control (2012, background): “2 (ii)], usually referred to as strong duality (see for instance [8]).”
NMPC without terminal constraints (2012, methodology): “An example from this class, taken from Diehl et al. [2011], is a linearized model of a continuously stirred tank reactor with two dimensional affine linear dynamics”
Asymptotic stability and transient optimality of economic MPC without terminal conditions (2014, methodology): “4For linear control systems with strictly convex cost the storage function can always be chosen linear, see [6] or [5].”
Reinforcement learning for control: Performance, stability, and deep approximators (2018, methodology): “There exist of course exceptions – for instance, economic MPC methods (Diehl et al., 2011) rein-troduce “true” optimization objectives in MPC.”
Postface to “ Model Predictive Control : Theory and Design ” (2012, background): “A recent paper by Diehl, Amrit, and Rawlings (2011) has shown that a modified MPC cost function, termed rotated cost, is a Lyapunov function for the unreachable setpoint case and other more general cost functions required for optimizing process economics.”
Fundamentals of economic model predictive control (2012, methodology): “002I2 and checked numerically by solving the dual problem, presented in [25].”
A tutorial review of economic model predictive control methods (2014, methodology): “Along the same lines as [38], the infinite-horizon EMPC problem was divided into a finite-time horizon and an infinite-horizon tail in [112,113,130].”
Distributed model predictive control: A tutorial review and future research directions (2013, unknown): “There have been some recent advances in integrating economic optimization and process control in a single MPC using centralized approaches, for example the MPC for tracking schemes proposed in Ferramosca, Limon, Alvarado, Alamo, and Camacho (2009), Limon, Alvarado, Alamo, and Camacho (2008, 2010) an”