Neural approximations for optimal control of nonlinear stochastic systems

The problem of designing feedback feedforward control strategies to drive the state of a dynamic system (generally nonlinear) so as to track any desired trajectory stochastically specified while minimizing a certain cost function (generally nonquadratic) is considered. Random noises (generally non-Gaussian) act on both the dynamic system and the state observation channel. Conventional methods are difficult to apply because of the problem´s generality. An approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. A neural architecture based on the linear-structure-preserving principle is presented. The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations for computing the gradient components are presented, and simulation results related to non-LQG optimal control problems show the effectiveness of the proposed method