A robust model predictive control algorithm for incrementally conic uncertain/nonlinear systems

• Published in: International journal of robust and nonlinear control Vol. 21; no. 5; pp. 563 - 590
• Main Authors: Açıkmeşe, Behçet, Carson III, John M., Bayard, David S.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 25.03.2011
• Subjects: Algorithms; Control systems; Feedback control; incrementally conic uncertainty; linear matrix inequalities; Lyapunov theory; Mathematical models; model predictive control; nonlinear systems; Nonlinearity; Policies; Predictive control; receding horizon control; robust control; Trajectories; uncertain systems
• ISSN: 1049-8923; 1099-1239; 1099-1239
• DOI: 10.1002/rnc.1613

This paper presents a robustly stabilizing model predictive control algorithm for systems with incrementally conic uncertain/nonlinear terms and bounded disturbances. The resulting control input consists of feedforward and feedback components. The feedforward control generates a nominal trajectory from online solution of a finite‐horizon constrained optimal control problem for a nominal system model. The feedback control policy is designed off‐line by utilizing a model of the uncertainty/nonlinearity and establishes invariant ‘state tubes’ around the nominal system trajectories. The entire controller is shown to be robustly stabilizing with a region of attraction composed of the initial states for which the finite‐horizon constrained optimal control problem is feasible for the nominal system. Synthesis of the feedback control policy involves solution of linear matrix inequalities. An illustrative numerical example is provided to demonstrate the control design and the resulting closed‐loop system performance. Copyright © 2010 John Wiley & Sons, Ltd.