Radial basis functions and multilayer feedforward neural networks for optimal control of nonlinear stochastic systems

The problem of designing a feedback feedforward controller to drive the state of a dynamic system so as to track any desired stochastically specified trajectory is addressed. In general, the dynamic system and the state observation channel are nonlinear, the cost function is non-quadratic, and process and observation noises are non-Gaussian. As the classical linear-quadratic-Gaussian (LQG) assumptions are not verified, an approximate solution is sought by constraining control strategies to take on a fixed structure in which a certain number of parameters have to be optimized. Two nonlinear control structures are considered, i.e., radial basis functions (RBFs) and multilayer feedforward neural networks. The control structures are also shaped on the basis of the linear structure preserving principle (the LISP principle). The original functional problem is then reduced to a nonlinear programming one, which is solved by means of a gradient method. Simulation results related to non-LQG optimal control problems show the effectiveness of the proposed technique