A B-spline-based pseudo-inversion approach for constrained optimal output transition. Issue 10 (3rd October 2018)

• Record Type: Journal Article
• Authors: Jetto, Leopoldo; Orsini, Valentina; Romagnoli, Raffaele
• Is Part Of: International journal of control. Volume 91:Issue 10(2018)
• Page Start: 2332
• Page End: 2344
• Publication Date: 2018-10-03
• Subjects: Continuous-time constrained control -- B-spline functions -- model pseudo-inversion -- feed-forward control; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2017.1344907
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: The contribution of this paper is to propose a new method for the continuous-time optimal output transition problem under constraints on the control effort. The new method situates in the recently proposed framework of pseudo-inversion, which proved to be very effective to achieve an almost perfect tracking. The presented method assumes a B-spline function as the external input reference r ( t ) forcing a given stable closed-loop system. The actual control input u ( t ) yielded by r ( t ) and forcing the plant is optimally approximated (in the least square sense) by a B-splineu ^ ( t ) . The control points of the B-splineu ^ ( t ) are chosen in such a way to satisfy the saturation constraints on u ( t ). The parameters of interest to define the solution of the considered problem are given by the control points of the B-splines r ( t ) andu ^ ( t ) . These parameters are simultaneously estimated as elements of the vector solving the constrained least-squares minimisation of a suitably defined multi-objective cost functional. Ifu ^ ( t ) is a sufficiently accurate approximation of u ( t ), the exact fulfilment of saturation constraints byu ^ ( t ) is transferred to u ( t ). The simulations on a practical case of a relevant interest show excellent results.