TY - JOUR

T1 - A nonlinear tracking model predictive control scheme for dynamic target signals

AU - Köhler, Johannes

AU - Müller, Matthias A.

AU - Allgöwer, Frank

N1 - Funding information: The authors thank the German Research Foundation (DFG) for support of this work within the Research Training Group Soft Tissue Robotics ( GRK 2198/1 - 277536708 ). The material in this paper was presented at the 6th IFAC Conference on Nonlinear Model Predictive Control August 19–22, 2018, Madison, WI, USA. This paper was recommended for publication in revised form by Associate Editor Marcello Farina under the direction of Editor Ian R. Petersen.

PY - 2020/8

Y1 - 2020/8

N2 - We present a nonlinear model predictive control (MPC) scheme for tracking of dynamic target signals. The scheme combines stabilization and dynamic trajectory planning in one layer, thus ensuring constraint satisfaction irrespective of changes in the dynamic target signal. For periodic target signals we ensure exponential stability of the optimal reachable periodic trajectory using suitable terminal ingredients and a convexity condition for the underlying periodic optimal control problem. Furthermore, we introduce an online optimization of the terminal set size to automate the trade-off between fast convergence and operation close to the constraints. In addition, we show how stabilization and dynamic trajectory planning can be formulated as partially decoupled optimization problems, which reduces the computational demand while ensuring recursive feasibility and convergence. The main tool to enable the proposed design is a novel reference generic offline computation that provides suitable terminal ingredients for tracking of dynamic reference trajectories. The practicality of this approach is demonstrated on benchmark examples, which demonstrates superior performance compared to state of the art approaches.

AB - We present a nonlinear model predictive control (MPC) scheme for tracking of dynamic target signals. The scheme combines stabilization and dynamic trajectory planning in one layer, thus ensuring constraint satisfaction irrespective of changes in the dynamic target signal. For periodic target signals we ensure exponential stability of the optimal reachable periodic trajectory using suitable terminal ingredients and a convexity condition for the underlying periodic optimal control problem. Furthermore, we introduce an online optimization of the terminal set size to automate the trade-off between fast convergence and operation close to the constraints. In addition, we show how stabilization and dynamic trajectory planning can be formulated as partially decoupled optimization problems, which reduces the computational demand while ensuring recursive feasibility and convergence. The main tool to enable the proposed design is a novel reference generic offline computation that provides suitable terminal ingredients for tracking of dynamic reference trajectories. The practicality of this approach is demonstrated on benchmark examples, which demonstrates superior performance compared to state of the art approaches.

KW - Control of constrained systems

KW - Model predictive control

KW - Nonlinear systems

KW - Output regulation

KW - Periodic references

KW - Reference tracking

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=85084793687&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1911.03304

DO - 10.48550/arXiv.1911.03304

M3 - Article

VL - 118

JO - Automatica

JF - Automatica

SN - 0005-1098

M1 - 109030

ER -