This paper introduces a tube-based model predictive control (MPC) for linear parameter-varying (LPV) systems which exploits knowledge about bounds on the parameters’ rate of change to extrapolate its admissible values over the prediction horizon. This information is used to construct state tubes to which the future trajectories of the state are confined. The tubes are consequently used for constraint tightening. Then, an MPC optimization problem subject to tightened sets for the state and control constraints is solved for only a nominal system corresponding to a nominal trajectory of the scheduling parameter starting from its current value. Recursive feasibility and asymptotic stability are proven and two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Experimental investigation on the damage and wave propagation characteristics in PVB laminated glass panels subjected to impact loading was conducted. By applying different impact energies, the effect of two projectile configurations, a wooden post and steel ball, was studied. The effect of impact location was also investigated. The dynamic response of the panels was measured at different locations on the test panels using strain gauges. Damage and transient response and wave propagation characteristics of test panels were reported and compared. The results showed that flexural wave was the predominant wave in the response. In addition, in-plane compressive wave was also observed. It was also shown that while the projectile contact area affected the maximum transient response and crack propagation characteristics, it had a limited effect on the perforation threshold. For panels impacted at the corners, coupled strain waves were created by wave reflection processes when the waves reached the panel boundaries. Moreover, the impact velocity had a pronounced effect on peak strain and strain rates of test panels.

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