International Journal of Control, Vol.91, No.10, 2332-2344, 2018
A B-spline-based pseudo-inversion approach for constrained optimal output transition
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-spline <(u(t))over cap>. The control points of the B-spline <(u(t))over cap> 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) and <(u(t))over cap>. These parameters are simultaneously estimated as elements of the vector solving the constrained least-squares minimisation of a suitably defined multi-objective cost functional. If <(u(t))over cap> is a sufficiently accurate approximation of u(t), the exact fulfilment of saturation constraints by <(u(t))over cap> is transferred to u(t). The simulations on a practical case of a relevant interest show excellent results.