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