Economic receding horizon control without terminal constraints

• Published in: Automatica (Oxford) Vol. 49; no. 3; pp. 725 - 734
• Main Author: Gruene, Lars
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2013; Elsevier
• Subjects: Applied sciences; Behavior. Attitude; Biological and medical sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Controllability; Convergence; Economic MPC; Economics; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; General aspects; Horizon; Mathematics; Optimal control; Optimization; Optimization and Control; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Social psychology; Stabilization; Steady state; Terminal constraints; Turnpike property; Turnpike property; Controllability; Economic MPC; Closed loop; Costs; Tracking; Stabilization; Economic sciences; Steady state; Terminal; Model predictive control; Consumer behavior; Optimal control; Tracking(movable target); Open ended horizon; Infinite horizon; Toll road; sadco
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2012.12.003

We consider a receding horizon control scheme without terminal constraints in which the stage cost is defined by economic criteria, i.e., not necessarily linked to a stabilization or tracking problem. We analyze the performance of the resulting receding horizon controller with a particular focus on the case of optimal steady states for the corresponding averaged infinite horizon problem. Using a turnpike property and suitable controllability properties we prove near optimal performance of the controller and convergence of the closed loop solution to a neighborhood of the optimal steady state. Two examples illustrate our findings numerically and show how to verify the imposed assumptions.