Stability (learning theory)

Physics

Trajectory

Nonlinear system

Pedagogy

Mathematics

Algorithm

Mathematical optimization

Astronomy

Software engineering

Machine learning

Model predictive control

Reference model

Artificial intelligence

Psychology

Exponential stability

Control (management)

Tracking (education)

Terminal (telecommunication)

Computer science

Quantum mechanics

Control theory (sociology)

State (computer science)

Telecommunications

IEEE Transactions on Automatic Control

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.

Nonlinear Reference Tracking: An Economic Model Predictive Control Perspective