RBF-ARX model-based predictive control approach to an inverted pendulum with self-triggered mechanism

This paper focuses on the issue of massive online computational burden generated by solving the optimization problem at each sampling instant during the predictive control process. Aiming at this objective, a self-triggered mechanism is designed to alleviate the online computational burden in a way of co-designing the feedback law and the triggered interval based on a locally linear model constructed by the RBF-ARX model (state-dependent auto-regressive model and its coefficients are evaluated by Radial Basis Function network). And the optimization problem can be established online in view of a modified state–space representation, then it can be clinched by applying the linear quadratic regulator (LQR) technology combined with the optimal control theory in finite time domain. In addition, the stability analysis is provided by certificating the boundedness of the RBF-ARX model with the behavior of converting the boundary problem of states between adjacent triggering instants into the boundary problem of the system’s outputs. Finally, the proposed self-triggered algorithm is successfully applied to the actual one-stage inverted pendulum system with fast-responding and nonlinear features, and the results of simulation and real time control experiment indicate that the significant amount of online computational burden can be reduced without sacrificing control performance approximately, which also demonstrate the effectiveness of the proposed self-triggered control algorithm based on the RBF-ARX model.