Order-independent optimal polynomial control of stochastic dynamical systems

As the traditional knowledge of optimal polynomial controls, the control effect of non-linear control strategy hinges on the order of the polynomial controllers either for linear systems or non-linear systems, In the present paper, a novel optimal polynomial control strategy against this knowledge, based on the framework of physical stochastic optimal control, for stochastic dynamical systems is proposed. The control criterion relies on the minimum of a performance function in an energy trade-off sense, as gauged by exceedance probability of system quantities of interest, involving an optimisation programme. For illustrative purposes, non-linear stochastic optimal controls of base-excited multi-degree-of-freedom linear and hysteretic structural systems are carried out, respectively. Numerical results reveal that the optimal polynomial control exhibits the order-independent behaviour that the linear control with the first-order controller suffices even for the hysteretic systems when the exceedance probability based control criterion is employed. This is practically meaningful since it bypasses the need to utilise non-linear controllers which might be associated with dynamical instabilities due to time delay and computational dynamics. It is noted, meanwhile, that the response performance of the controlled structural systems is improved significantly.