Title :
A model predictive control approach to trajectory tracking problems via time-varying level sets of Lyapunov functions
Author :
Faulwasser, Timm ; Findeisen, Rolf
Author_Institution :
Inst. for Autom. Eng., Otto-von-Guericke Univ. Magdeburg, Magdeburg, Germany
Abstract :
We discuss a model predictive control approach to trajectory tracking problems of constrained nonlinear continuous time systems, where the reference trajectory is a priori known and asymptotically constant. The proposed NMPC scheme is able to explicitly consider input and state constraints while guaranteeing recursive feasibility. To handle the time-varying nature of the tracking problem we advocate the use of time-varying level sets of Lyapunov functions as terminal regions. We prove a necessary and sufficient condition for positive invariance of these sets and show how these sets can be efficiently computed, if a quadratic Lyapunov function is available. As an example we consider a nonlinear CSTR reactor.
Keywords :
Lyapunov methods; continuous time systems; nonlinear control systems; position control; predictive control; set theory; time-varying systems; NMPC scheme; asymptotically constant reference trajectory; constrained nonlinear continuous time systems; nonlinear CSTR reactor; nonlinear model predictive control approach; positive invariance; quadratic Lyapunov function; time-varying level set; trajectory tracking problem; Chemical reactors; Convergence; Level set; Lyapunov methods; Optimal control; Time varying systems; Trajectory; invariant sets; nonlinear model predictive control; time-varying level sets; trajectory tracking;
Conference_Titel :
Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
978-1-61284-800-6
Electronic_ISBN :
0743-1546
DOI :
10.1109/CDC.2011.6160492