Table of Contents
Journal of Nonlinear Dynamics
Volume 2013, Article ID 182034, 11 pages
Research Article

Suboptimal Control Strategies for Finite-Time Nonlinear Processes with Input Constraints

1L’UNAM, IRCCyN, UMR-CNRS 6597, 1 Rue de la Noë, 44321 Nantes Cedex 03, France
2Nonlinear System Group, INTEC, CONICET-UNL, Güemes 3450, 3000 Santa Fe, Argentina
3Universidad Nacional del Litoral, Facultad de Ingeniería Química, S3000AOM Santa Fe, Argentina

Received 6 June 2013; Revised 15 September 2013; Accepted 27 September 2013

Academic Editor: Huai-Ning Wu

Copyright © 2013 Pablo S. Rivadeneira and Eduardo J. Adam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Novel techniques for the optimization and control of finite-time processes in real-time are pursued. These are developed in the framework of the Hamiltonian optimal control. Two methods are designed. The first one constructs the reference control trajectory as an approximation of the optimal control via the Riccati equations in an adaptive fashion based on the solutions of a set of partial differential equations called the and matrices. These allow calculating the Riccati gain for a range of the duration of the process and the final penalization . The second method introduces input constraints to the general optimization formulation. The notions of linear matrix inequalities allow us to recuperate the Riccati gain as in the first method, but using an infinite horizon optimization method. Finally, the performance of the proposed strategies is illustrated through numerical simulations applied to a batch reactor and a penicillin fed-batch reactor.