Details
| Original language | English |
|---|---|
| Title of host publication | 2020 59th IEEE Conference on Decision and Control, CDC 2020 |
| Pages | 4604-4609 |
| Number of pages | 6 |
| ISBN (electronic) | 9781728174471 |
| Publication status | Published - 2020 |
Publication series
| Name | Proceedings of the IEEE Conference on Decision and Control |
|---|---|
| Volume | 2020-December |
| ISSN (Print) | 0743-1546 |
| ISSN (electronic) | 2576-2370 |
Abstract
In this paper, we show that a simple model predictive control (MPC) scheme can solve the constrained nonlinear output regulation problem without explicitly solving the classical regulator (Francis-Byrnes-Isidori) equations. We first study the general problem of stabilizing a set with MPC using a positive semidefinite (input/output) cost function under suitable stabilizability and detectability assumptions, similar to Grimm et al. (2005) [1]. We show that in the output regulation setting, these conditions hold, if the nonlinear constrained regulation problem is (strictly) feasible, the plant is detectable (i-IOSS) and the control input can be uniquely reconstructed from the plant/reference output. Given these structural assumptions, by simply penalizing the predicted output error in the MPC stage cost, the closed loop implicitly stabilizes a state trajectory that solves the regulator equations, if a sufficiently large prediction horizon is used.
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Engineering(all)
- Control and Systems Engineering
- Mathematics(all)
- Modelling and Simulation
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2020 59th IEEE Conference on Decision and Control, CDC 2020. 2020. p. 4604-4609 9303983 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research
}
TY - GEN
T1 - Implicit solutions to constrained nonlinear output regulation using MPC
AU - Köhler, Johannes
AU - Müller, Matthias
AU - Allgöwer, Frank
N1 - Funding information: Johannes Köhler would like to thank the German Research Foundation (DFG) for financial support of the project within the International Research Training Group “Soft Tissue Robotics” (GRK 2198/1 - 277536708).
PY - 2020
Y1 - 2020
N2 - In this paper, we show that a simple model predictive control (MPC) scheme can solve the constrained nonlinear output regulation problem without explicitly solving the classical regulator (Francis-Byrnes-Isidori) equations. We first study the general problem of stabilizing a set with MPC using a positive semidefinite (input/output) cost function under suitable stabilizability and detectability assumptions, similar to Grimm et al. (2005) [1]. We show that in the output regulation setting, these conditions hold, if the nonlinear constrained regulation problem is (strictly) feasible, the plant is detectable (i-IOSS) and the control input can be uniquely reconstructed from the plant/reference output. Given these structural assumptions, by simply penalizing the predicted output error in the MPC stage cost, the closed loop implicitly stabilizes a state trajectory that solves the regulator equations, if a sufficiently large prediction horizon is used.
AB - In this paper, we show that a simple model predictive control (MPC) scheme can solve the constrained nonlinear output regulation problem without explicitly solving the classical regulator (Francis-Byrnes-Isidori) equations. We first study the general problem of stabilizing a set with MPC using a positive semidefinite (input/output) cost function under suitable stabilizability and detectability assumptions, similar to Grimm et al. (2005) [1]. We show that in the output regulation setting, these conditions hold, if the nonlinear constrained regulation problem is (strictly) feasible, the plant is detectable (i-IOSS) and the control input can be uniquely reconstructed from the plant/reference output. Given these structural assumptions, by simply penalizing the predicted output error in the MPC stage cost, the closed loop implicitly stabilizes a state trajectory that solves the regulator equations, if a sufficiently large prediction horizon is used.
UR - http://www.scopus.com/inward/record.url?scp=85094769583&partnerID=8YFLogxK
U2 - 10.1109/CDC42340.2020.9303983
DO - 10.1109/CDC42340.2020.9303983
M3 - Conference contribution
SN - 978-1-7281-7446-4
SN - 978-1-7281-7448-8
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4604
EP - 4609
BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020
ER -