Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 3100-3111 |
| Seitenumfang | 12 |
| Fachzeitschrift | AUTOMATICA |
| Jahrgang | 50 |
| Ausgabenummer | 12 |
| Publikationsstatus | Veröffentlicht - 1 Dez. 2014 |
| Extern publiziert | Ja |
Abstract
In this paper, we thoroughly investigate various aspects of economic model predictive control with average constraints, i.e., constraints on average values of state and input variables. In particular, we first show that a certain time-varying output constraint has to be included into the MPC problem formulation in order to ensure fulfillment of these average constraints. Optimizing a general (possibly economic) performance criterion may result in a non-converging behavior of the corresponding closed-loop system. While such a behavior might be acceptable in some cases, it may be undesirable for other types of applications. Hence as a second contribution, we provide a Lyapunov-like analysis to conclude that indeed asymptotic convergence to the optimal steady-state follows if the system satisfies a certain dissipativity condition. Finally, for the case that this dissipativity property is not satisfied but still a convergent behavior of the closed-loop is required, we examine two different methods how convergence can be enforced within an economic MPC setup by imposing additional average constraints on the system. In the first method, an additional average constraint is defined which results in the system being dissipative, while the second consists of imposing an additional even zero-moment average constraint. We illustrate our results with various examples.
ASJC Scopus Sachgebiete
- Ingenieurwesen (insg.)
- Steuerungs- und Systemtechnik
- Ingenieurwesen (insg.)
- Elektrotechnik und Elektronik
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in: AUTOMATICA, Jahrgang 50, Nr. 12, 01.12.2014, S. 3100-3111.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Convergence in economic model predictive control with average constraints
AU - Müller, Matthias A.
AU - Angeli, David
AU - Allgöwer, Frank
AU - Amrit, Rishi
AU - Rawlings, James B.
N1 - Publisher Copyright: © 2014 Elsevier Ltd. All rights reserved.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - In this paper, we thoroughly investigate various aspects of economic model predictive control with average constraints, i.e., constraints on average values of state and input variables. In particular, we first show that a certain time-varying output constraint has to be included into the MPC problem formulation in order to ensure fulfillment of these average constraints. Optimizing a general (possibly economic) performance criterion may result in a non-converging behavior of the corresponding closed-loop system. While such a behavior might be acceptable in some cases, it may be undesirable for other types of applications. Hence as a second contribution, we provide a Lyapunov-like analysis to conclude that indeed asymptotic convergence to the optimal steady-state follows if the system satisfies a certain dissipativity condition. Finally, for the case that this dissipativity property is not satisfied but still a convergent behavior of the closed-loop is required, we examine two different methods how convergence can be enforced within an economic MPC setup by imposing additional average constraints on the system. In the first method, an additional average constraint is defined which results in the system being dissipative, while the second consists of imposing an additional even zero-moment average constraint. We illustrate our results with various examples.
AB - In this paper, we thoroughly investigate various aspects of economic model predictive control with average constraints, i.e., constraints on average values of state and input variables. In particular, we first show that a certain time-varying output constraint has to be included into the MPC problem formulation in order to ensure fulfillment of these average constraints. Optimizing a general (possibly economic) performance criterion may result in a non-converging behavior of the corresponding closed-loop system. While such a behavior might be acceptable in some cases, it may be undesirable for other types of applications. Hence as a second contribution, we provide a Lyapunov-like analysis to conclude that indeed asymptotic convergence to the optimal steady-state follows if the system satisfies a certain dissipativity condition. Finally, for the case that this dissipativity property is not satisfied but still a convergent behavior of the closed-loop is required, we examine two different methods how convergence can be enforced within an economic MPC setup by imposing additional average constraints on the system. In the first method, an additional average constraint is defined which results in the system being dissipative, while the second consists of imposing an additional even zero-moment average constraint. We illustrate our results with various examples.
KW - Average constraints
KW - Economic model predictive control
KW - Nonlinear systems
UR - http://www.scopus.com/inward/record.url?scp=84901605872&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2014.10.059
DO - 10.1016/j.automatica.2014.10.059
M3 - Article
AN - SCOPUS:84901605872
VL - 50
SP - 3100
EP - 3111
JO - AUTOMATICA
JF - AUTOMATICA
SN - 0005-1098
IS - 12
ER -