Velocity-form spline-based continuous-time MPC: explicit solution

This paper presents the design of a velocity form for spline-based continuous-time model predictive control to achieve offset-free tracking of piecewise constant reference signals in the presence of disturbances. To facilitate the closed-loop implementation, the resulting control problem is solved explicitly using parametric quadratic programming. The proposed approach offers some interesting advantages. First, it formulates the control signal as a polynomial spline function, the properties of which are determined by its control polygon that is subject to optimization. Second, all continuous constraints assumed along the prediction horizon are consistently transformed into constraints imposed on a finite number of elements of this control polygon. Moreover, a suitable choice of number and position of knots over the prediction horizon can substantially reduce complexity of the resulting explicit controllers while preserving control performance. Effectiveness of the proposed offset-free technique is demonstrated in a numerical simulation using model of a two-degrees-of-freedom laboratory-scale helicopter.