INTEC   05402
INSTITUTO DE DESARROLLO TECNOLOGICO PARA LA INDUSTRIA QUIMICA
Unidad Ejecutora - UE
artículos
Título:
A Cost Reduction Procedure for Control-Restricted Nonlinear Systems
Autor/es:
PABLO S. RIVADENEIRA; VICENTE COSTANZA; JOHN A. GÓMEZ MÚNERA
Revista:
International Review of Automatic Control
Editorial:
Praise Worthy Prize
Referencias:
Año: 2017 vol. 10 p. 510 - 522
ISSN:
1974-6059
Resumen:
This paper describes a numerical scheme to approximate the solution of the optimal control problem for nonlinear systems with restrictions on the manipulated variable.  The method proposed here systematically reduces the cost associated with successively updated control strategies, after proposing an initial seed trajectory based on approximation arguments. The numerical scheme follows two main lines of reasoning: the first one relying on linearizations around a seed state/control trajectory, exploiting a theoretical expression for the increment of the cost, and mainly valid in regular situations, although after some adaptations can be used when saturations occur.  One of its advantages is that the decreasing of the cost can be assessed without integrating numerically the nonlinear dynamics. However, and because of the constraints, eventually this method fails, and an alternative approach must be activated to keep decreasing the cost. The second approach, based on specific control variations of the current control strategy, and it is activated depending on two theoretical criteria (failure alert) developed here.  The initial control variation is derived from the differential Riccati equation for the linearized system and appropriate quadratic cost functions.  Other variations, similar to those used in Pontryagin classical theorem for generating the final cone of states, are proposed by modifying the locations of `switching times´, and so producing oscillations in the interior of regular periods.  The performance of the numerical combined method and the related mathematical objects are illustrated by optimizing some two-dimensional nonlinear systems with scalar bounded controls.