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A linear optimal regulator for uncertain system is designed through the application of the probability density evolution method to linear quadratic regulator controller. One important background of this work is bridge-vehicle/gun-projectile system. This type of optimal problem is currently transformed into a moving load problem. The developed optimal regulator can provide the law of probability densities of outputs varying with time. In order to make the advocated method reach an optimal performance, the beneficial weighting matrix pair (Q, R) is selected using a trade-off sense. The designed regulator is then applied to a coupled simply supported beam-moving mass system, choosing the mid-span deflection as an output response and considering stochastic system parameters. The numerical example shows that the robustness of the proposed optimal regulator cannot be overestimated in comparison with a deterministic linear quadratic regulator controller. Further, the proposed method can produce an efficient solution channel for modern optimal control theory, especially, when compared with different uncertain optimal control techniques.

Optimal vibration control of moving-mass beam systems with uncertainty