Dual Adaptive Control of Nonlinear Systems

Abstract

In this chapter, two suboptimal dual adaptive control schemes for a stochastic class of functional uncertain nonlinear systems are developed. The two schemes are based on GaRBF and sigmoidal MLP neural networks respectively. The idea of applying dual control principles within a functional adaptive context first appeared in [72]. Most other approaches typically adopt an HCE procedure that often leads to an inadequate transient response because the initial uncertainty of the unknown network parameters is large. Some of the neural network control schemes that have been put forward avoid this by performing intensive off-line training to identify the plant in open-loop and reduce the prior uncertainty of the unknown parameters [53, 193, 215]. Only later is an adaptive control phase started, with the initial network parameters set to the pre-trained values that are already substantially close to the optimal. In a certain sense this procedure defeats the main objective of adaptive control because the off-line training phase reduces most of the uncertainty existing prior to application of the control.