Details
| Original language | English |
|---|---|
| Pages (from-to) | 269-277 |
| Number of pages | 9 |
| Journal | Automatica |
| Volume | 82 |
| Early online date | 22 May 2017 |
| Publication status | Published - 1 Aug 2017 |
| Externally published | Yes |
Abstract
We consider model predictive control (MPC) without terminal costs and constraints. Firstly, we rigorously show that MPC based on quadratic stage costs may fail, i.e., there does not exist a prediction horizon length such that a (controlled) equilibrium is asymptotically stable for the MPC closed loop although the system is, e.g., finite time controllable. Hence, stability properties of the infinite horizon optimal control problem are, in general, not preserved in MPC as long as purely quadratic costs are employed. This shows the necessity of using the stage cost as a design parameter to achieve asymptotic stability. Furthermore, we relax the standard controllability assumption employed in MPC without terminal costs and constraints to alleviate its verification.
Keywords
- Asymptotic stabilization, Mobile robots, Model predictive control, Nonlinear systems, Quadratic costs
ASJC Scopus subject areas
- Engineering(all)
- Electrical and Electronic Engineering
- Engineering(all)
- Control and Systems Engineering
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In: Automatica, Vol. 82, 01.08.2017, p. 269-277.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quadratic costs do not always work in MPC
AU - Müller, Matthias A.
AU - Worthmann, Karl
N1 - Funding information: M.A. Müller and K. Worthmann are supported by the Deutsche Forschungsgemeinschaft, Grants WO 2056/1-1 and WO 2056/4-1. The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Giancarlo Ferrari-Trecate under the direction of Editor Ian R. Petersen.
PY - 2017/8/1
Y1 - 2017/8/1
N2 - We consider model predictive control (MPC) without terminal costs and constraints. Firstly, we rigorously show that MPC based on quadratic stage costs may fail, i.e., there does not exist a prediction horizon length such that a (controlled) equilibrium is asymptotically stable for the MPC closed loop although the system is, e.g., finite time controllable. Hence, stability properties of the infinite horizon optimal control problem are, in general, not preserved in MPC as long as purely quadratic costs are employed. This shows the necessity of using the stage cost as a design parameter to achieve asymptotic stability. Furthermore, we relax the standard controllability assumption employed in MPC without terminal costs and constraints to alleviate its verification.
AB - We consider model predictive control (MPC) without terminal costs and constraints. Firstly, we rigorously show that MPC based on quadratic stage costs may fail, i.e., there does not exist a prediction horizon length such that a (controlled) equilibrium is asymptotically stable for the MPC closed loop although the system is, e.g., finite time controllable. Hence, stability properties of the infinite horizon optimal control problem are, in general, not preserved in MPC as long as purely quadratic costs are employed. This shows the necessity of using the stage cost as a design parameter to achieve asymptotic stability. Furthermore, we relax the standard controllability assumption employed in MPC without terminal costs and constraints to alleviate its verification.
KW - Asymptotic stabilization
KW - Mobile robots
KW - Model predictive control
KW - Nonlinear systems
KW - Quadratic costs
UR - http://www.scopus.com/inward/record.url?scp=85019350974&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2017.04.058
DO - 10.1016/j.automatica.2017.04.058
M3 - Article
VL - 82
SP - 269
EP - 277
JO - Automatica
JF - Automatica
SN - 0005-1098
ER -