Details
| Original language | English |
|---|---|
| Pages (from-to) | 4390-4405 |
| Number of pages | 16 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 67 |
| Issue number | 9 |
| Publication status | Published - 12 Apr 2022 |
Abstract
We develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small and hence, we can slide along the steady-state manifold towards the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Further, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper.
Keywords
- Manifolds, Nonlinear dynamical systems, Predictive models, Stability analysis, Steady-state, System dynamics, Target tracking, predictive control for linear systems, time varying systems, Nonlinear systems, tracking
ASJC Scopus subject areas
- Engineering(all)
- Electrical and Electronic Engineering
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Computer Science Applications
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In: IEEE Transactions on Automatic Control, Vol. 67, No. 9, 12.04.2022, p. 4390-4405.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Linear tracking MPC for nonlinear systems Part I
T2 - The model-based case
AU - Berberich, Julian
AU - Koehler, Johannes
AU - Muller, Matthias A.
AU - Allgower, Frank
N1 - Funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2075 - 390740016 and under grant 468094890. We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948679). The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Julian Berberich.
PY - 2022/4/12
Y1 - 2022/4/12
N2 - We develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small and hence, we can slide along the steady-state manifold towards the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Further, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper.
AB - We develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small and hence, we can slide along the steady-state manifold towards the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Further, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper.
KW - Manifolds
KW - Nonlinear dynamical systems
KW - Predictive models
KW - Stability analysis
KW - Steady-state
KW - System dynamics
KW - Target tracking
KW - predictive control for linear systems
KW - time varying systems
KW - Nonlinear systems
KW - tracking
UR - http://www.scopus.com/inward/record.url?scp=85128315958&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2105.08560
DO - 10.48550/arXiv.2105.08560
M3 - Article
AN - SCOPUS:85128315958
VL - 67
SP - 4390
EP - 4405
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 9
ER -