Optimal Control with Boltzmann Machines

This paper develops a LQ dynamic optimization control method for time-variant, discrete-time, multivariable system based on Boltzmann machines. By building the equivalent relation between the LQ performance index and the energy function of Boltzmann machines, the Boltzmann machine can be constructed and its parameters will be calculated. When the network operates from its initial state to the stable state, the desired optimal control sequence that corresponding to the state of the Boltzmann machine can be obtained. Theoretical analysis and an illustrated example are given, and the simulation results agree well with theoretical analysis.