Interpolated robust time-optimal controllers for linear systems

Interpolation techniques are well known in reducing the online computational effort of optimal control strategies, such as model predictive control. A general interpolation-based time-optimal control (TOC) for a constrained linear system with bounded disturbances is presented. The terminal controller is nonlinear, which interpolates among multiple predetermined linear feedback laws, and the corresponding terminal set is equal to or sometimes even larger than the convex hull of all constituent terminal sets. Starting from this relatively large terminal set, a large domain of attraction can be obtained by using a short horizon, consequently leading to a low online computational effort. By using multi-parametric programming, the proposed controller can be determined offline, thus further relaxing the online computational effort. Compared with the standard TOC implementations, the proposed approach provides an additional advantage combining ´a larger domain of attraction´, ´a better asymptotic behaviour´, and ´a lower online computational effort´. The performance of the proposed approach is assessed via two numerical examples.