Nonlinear Reference Tracking: An Economic Model Predictive Control Perspective

• Published in: IEEE transactions on automatic control Vol. 64; no. 1; pp. 254 - 269
• Main Authors: Kohler, Johannes, Muller, Matthias A., Allgower, Frank
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic stability; Constrained control; Discrete time systems; Economic analysis; Economic models; Economics; incremental stability; Mathematical models; nonlinear model predictive control (MPC); Nonlinear systems; Optimization; Predictive control; reference tracking; Stability criteria; Terminal constraints; Tracking control; Trajectories; Trajectory
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2018.2800789

In this paper, we study the system theoretic properties of a reference tracking model predictive control (MPC) scheme for general reference trajectories and nonlinear discrete-time systems subject to input and state constraints. Contrary to other existing theoretical results for reference tracking MPC, we do not modify the optimization problem with artificial references or terminal ingredients. Instead, we consider a simple, intuitive implementation and derive theoretical guarantees under a stabilizability condition on the system and suitable conditions on the reference trajectory. We provide sufficient conditions for exponential reference tracking for reachable reference trajectories. In addition, we study unreachable reference trajectories and derive sufficient conditions to ensure practical stability of the unknown optimal reachable reference trajectory. For both cases, we characterize the region of attraction. The results build on the notion of incremental stabilizability, strict dissipativity, and results in (economic) MPC without terminal constraints.