Robust adaptive minimum-time control of Piecewise Affine systems

This paper illustrates how an adaptive model predictive controller for the class of hybrid systems affected by parametric uncertainties can be synthesized. Specifically, we investigate the case where the hybrid system is modeled as a Piecewise Affine (PWA) system where certain elements of the PWA state-update matrices are expressed as symbolic parameters with unknown, but bounded values. For such parametric uncertain PWA systems we show that the control law can be constructed in a way such that all system states are pushed towards a pre-defined target set in the minimal possible number of time steps for all possible realizations of the uncertainty. The robust minimum-time control problem is solved using parametric programming techniques which leads the control law in a form of a look-up table. We illustrate that if the values of the parameters (unknown at the time of the synthesis of the control law) are measured on-line, the resulting feedback policy guarantees time-optimal convergence of the systems states towards a chosen terminal set.