A convex approach for NMPC based on second order Volterra series models. (20th November 2014)

• Record Type: Journal Article
• Authors: Gruber, J. K.; Ramirez, D. R.; Limon, D.; Alamo, T.
• Is Part Of: International journal of robust and nonlinear control. Volume 25:Number 18(2015)
• Page Start: 3546
• Page End: 3571
• Publication Date: 2014-11-20
• Subjects: nonlinear model predictive control -- convex optimization -- convergence -- stability; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3279
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: In model predictive control (MPC), the input sequence is computed, minimizing a usually quadratic cost function based on the predicted evolution of the system output. In the case of nonlinear MPC (NMPC), the use of nonlinear prediction models frequently leads to non‐convex optimization problems with several minimums. This paper proposes a new NMPC strategy based on second order Volterra series models where the original performance index is approximated by quadratic functions, which represent a lower bound of the original performance index. Convexity of the approximating quadratic cost functions can be achieved easily by a suitable choice of the weighting of the control increments in the performance index. The approximating cost functions can be globally minimized by convex optimization techniques in order to compute the input sequence. The minimization of the performance index is carried out by an iterative optimization procedure, which guarantees convergence to the solution. Furthermore, for a nominal prediction model, asymptotic stability for the proposed NMPC strategy can be shown. In the case of considering an estimation error in the prediction model, input‐to‐state practical stability is assured. The control performance of the NMPC strategy is illustrated by experimental results. Copyright © 2014 John Wiley & Sons, Ltd.