Abstract: In order to solve linear quadratic(LQ) optimal control problem of discrete-time system, the authors present a promising alternative based on random neural network-Boltzmann machines. By the method, the LQ performance index is transformed into the energy function of Boltzmann machine, and the control sequence is transformed into the neuron state vector of Boltzmann machines. Solving LQ dynamic optimization problem is equivalent to operating associated Boltzmann machines from its initial state to the terminal state that represents the optimal control sequence. The theoretical study indicates that we are able to find a relevant Boltzmann machines whose energy function is corresponding to the LQ performance index. Emulation experiment shows boltzmann machines can implement linear quadratic optimal control of any multivariable time-variant system.