Data-driven control for discrete-time piecewise affine systems

This paper studies the problem of data-driven control for discrete-time piecewise affine (PWA) systems. Based on a sequel of sampled control inputs and states with satisfactory rank conditions, the closed loop dynamics of PWA systems can be represented and therefore the explicit information of system matrices is not needed in system stability analysis and controller synthesis processes. First, via S-procedure, system stability analysis results have been obtained, and then, two novel data-driven controller design methods in the form of linear matrix inequalities and equations have been proposed such that the resulting closed loop system is asymptotically stable. For PWA systems with unknown state space partition information, an online data-driven control method has been further proposed to guarantee the asymptotic stability of the resulting closed loop systems. Finally, simulation studies of two examples have been given to validate the effectiveness of the proposed data-driven controller design approaches.