Dual and Adaptive Control of Nonlinear Stochastic Systems Using Neural Networks

A suboptimal dual adaptive system is developed for control of stochastic, nonlinear, discrete-time plants that are affine in the control input. The nonlinear functions are assumed to be unknown and neural networks are used to approximate them. Both Gaussian radial basis function and sigmodial multilayer perceptron neural networks are considered and parameter adjustment is based on Kalman filtering techniques. The result is a control law that takes into consideration the uncertainty of the parameter estimates, thereby, eliminating the need of performing prior open-loop plant identification. The performance of the system is analysed by simulation and Monte Carlo analysis and the advantages of the scheme are clearly outlined.