Details
| Original language | English |
|---|---|
| Article number | 105396 |
| Journal | Systems and Control Letters |
| Volume | 170 |
| Publication status | Published - Dec 2022 |
Abstract
We consider nonlinear model predictive control (MPC) with multiple competing cost functions. This leads to the formulation of multiobjective optimal control problems (MO OCPs). Since the design of MPC algorithms for directly solving multiobjective problems is rather complicated, particularly if terminal conditions shall be avoided, we use an indirect approach via a weighted sum formulation for solving these MO OCPs. This way, for each set of weights we obtain an optimal control problem with a single objective. In economic MPC it is known that strict dissipativity is the key assumption for concluding performance and stability results. We thus investigate under which conditions a convex combination of strictly dissipative stage costs again yields a stage cost for which the system is strictly dissipative. We first give conditions for problems with linear dynamics and then move on to consider fully nonlinear optimal control problems. We derive both necessary and sufficient conditions on the individual cost functions and on the weights to conclude strict dissipativity and illustrate our findings with numerical examples.
Keywords
- Model predictive control, Multiobjective optimal control, Strict dissipativity, Weighted sum approach
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- General Computer Science
- Engineering(all)
- Mechanical Engineering
- Engineering(all)
- Electrical and Electronic Engineering
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In: Systems and Control Letters, Vol. 170, 105396, 12.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Multiobjective strict dissipativity via a weighted sum approach
AU - Grüne, Lars
AU - Krügel, Lisa
AU - Müller, Matthias A.
N1 - Funding Information: The authors are supported by DFG, Germany Grant Gr 1569/13-2 .
PY - 2022/12
Y1 - 2022/12
N2 - We consider nonlinear model predictive control (MPC) with multiple competing cost functions. This leads to the formulation of multiobjective optimal control problems (MO OCPs). Since the design of MPC algorithms for directly solving multiobjective problems is rather complicated, particularly if terminal conditions shall be avoided, we use an indirect approach via a weighted sum formulation for solving these MO OCPs. This way, for each set of weights we obtain an optimal control problem with a single objective. In economic MPC it is known that strict dissipativity is the key assumption for concluding performance and stability results. We thus investigate under which conditions a convex combination of strictly dissipative stage costs again yields a stage cost for which the system is strictly dissipative. We first give conditions for problems with linear dynamics and then move on to consider fully nonlinear optimal control problems. We derive both necessary and sufficient conditions on the individual cost functions and on the weights to conclude strict dissipativity and illustrate our findings with numerical examples.
AB - We consider nonlinear model predictive control (MPC) with multiple competing cost functions. This leads to the formulation of multiobjective optimal control problems (MO OCPs). Since the design of MPC algorithms for directly solving multiobjective problems is rather complicated, particularly if terminal conditions shall be avoided, we use an indirect approach via a weighted sum formulation for solving these MO OCPs. This way, for each set of weights we obtain an optimal control problem with a single objective. In economic MPC it is known that strict dissipativity is the key assumption for concluding performance and stability results. We thus investigate under which conditions a convex combination of strictly dissipative stage costs again yields a stage cost for which the system is strictly dissipative. We first give conditions for problems with linear dynamics and then move on to consider fully nonlinear optimal control problems. We derive both necessary and sufficient conditions on the individual cost functions and on the weights to conclude strict dissipativity and illustrate our findings with numerical examples.
KW - Model predictive control
KW - Multiobjective optimal control
KW - Strict dissipativity
KW - Weighted sum approach
UR - http://www.scopus.com/inward/record.url?scp=85140803905&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2207.00373
DO - 10.48550/arXiv.2207.00373
M3 - Article
AN - SCOPUS:85140803905
VL - 170
JO - Systems and Control Letters
JF - Systems and Control Letters
SN - 0167-6911
M1 - 105396
ER -